XGitUrl: http://git.xiph.org/?p=opus.git;a=blobdiff_plain;f=doc%2Fdraftietfcodecopus.xml;h=bc7d3746ce26bc5ff5fd4f164b9f4d248ededce8;hp=abb2ce05e0bed92e215ab93c44b467d846a3b47f;hb=45b27da44c042e93ca154439ef5fc3b30d05ddaa;hpb=154486bb830ae2905ca92135f027ff7911aa567f
diff git a/doc/draftietfcodecopus.xml b/doc/draftietfcodecopus.xml
index abb2ce05..bc7d3746 100644
 a/doc/draftietfcodecopus.xml
+++ b/doc/draftietfcodecopus.xml
@@ 1,8 +1,8 @@

+

+Definition of the Opus Audio Codec
@@ 19,7 +19,7 @@
Canada+1 514 2828858
jeanmarc.valin@octasic.com
+jmvalin@jmvalin.ca
@@ 38,8 +38,22 @@
+
+Mozilla Corporation
+
+
+650 Castro Street
+Mountain View
+CA
+94041
+USA
+
++1 650 9030800
+tterriberry@mozilla.com
+
+

+
General
@@ 47,8 +61,8 @@
This document describes the Opus codec, designed for interactive speech and audio
transmission over the Internet.
+This document defines the Opus codec, designed for interactive speech and audio
+ transmission over the Internet.
@@ 57,296 +71,4540 @@ transmission over the Internet.
We propose the Opus codec based on a linear prediction layer (LP) and an
MDCTbased enhancement layer. The main idea behind the proposal is that
the speech low frequencies are usually more efficiently coded using
linear prediction codecs (such as CELP variants), while the higher frequencies
are more efficiently coded in the transform domain (e.g. MDCT). For low
sampling rates, the MDCT layer is not useful and only the LPbased layer is
used. On the other hand, nonspeech signals are not always adequately coded
using linear prediction, so for music only the MDCTbased layer is used.
+The Opus codec is a realtime interactive audio codec composed of a linear
+ prediction (LP)based layer and a Modified Discrete Cosine Transform
+ (MDCT)based layer.
+The main idea behind using two layers is that in speech, linear prediction
+ techniques (such as CELP) code low frequencies more efficiently than transform
+ (e.g., MDCT) domain techniques, while the situation is reversed for music and
+ higher speech frequencies.
+Thus a codec with both layers available can operate over a wider range than
+ either one alone and, by combining them, achieve better quality than either
+ one individually.
In this proposed prototype, the LP layer is based on the
SILK codec
 and the MDCT layer is based on the
CELT codec
 .
+The primary normative part of this specification is provided by the source code
+ in .
+In general, only the decoder portion of this software is normative, though a
+ significant amount of code is shared by both the encoder and decoder.
+
+The decoder contains significant amounts of integer and fixedpoint arithmetic
+ which must be performed exactly, including all rounding considerations, so any
+ useful specification must make extensive use of domainspecific symbolic
+ language to adequately define these operations.
+Additionally, any
+conflict between the symbolic representation and the included reference
+implementation must be resolved. For the practical reasons of compatibility and
+testability it would be advantageous to give the reference implementation
+priority in any disagreement. The C language is also one of the most
+widely understood humanreadable symbolic representations for machine
+behavior.
+For these reasons this RFC uses the reference implementation as the sole
+ symbolic representation of the codec.
This is a work in progress.

+
+While the symbolic representation is unambiguous and complete it is not
+always the easiest way to understand the codec's operation. For this reason
+this document also describes significant parts of the codec in English and
+takes the opportunity to explain the rationale behind many of the more
+surprising elements of the design. These descriptions are intended to be
+accurate and informative, but the limitations of common English sometimes
+result in ambiguity, so it is expected that the reader will always read
+them alongside the symbolic representation. Numerous references to the
+implementation are provided for this purpose. The descriptions sometimes
+differ from the reference in ordering or through mathematical simplification
+wherever such deviation makes an explanation easier to understand.
+For example, the right shift and left shift operations in the reference
+implementation are often described using division and multiplication in the text.
+In general, the text is focused on the "what" and "why" while the symbolic
+representation most clearly provides the "how".
+

+
+
+The key words "MUST", "MUST NOT", "REQUIRED", "SHALL", "SHALL NOT", "SHOULD",
+ "SHOULD NOT", "RECOMMENDED", "MAY", and "OPTIONAL" in this document are to be
+ interpreted as described in RFC 2119.
+
+
+Even when using floatingpoint, various operations in the codec require
+ bitexact fixedpoint behavior.
+The notation "Q<n>", where n is an integer, denotes the number of binary
+ digits to the right of the decimal point in a fixedpoint number.
+For example, a signed Q14 value in a 16bit word can represent values from
+ 2.0 to 1.99993896484375, inclusive.
+This notation is for informational purposes only.
+Arithmetic, when described, always operates on the underlying integer.
+E.g., the text will explicitly indicate any shifts required after a
+ multiplication.
+
+
+Expressions, where included in the text, follow C operator rules and
+ precedence, with the exception that syntax like "2**n" is used to indicate 2
+ raised to the power n.
+The text also makes use of the following functions:
+
+
+
+
+The smallest of two values x and y.
+
+
+
In hybrid mode, each frame is coded first by the LP layer and then by the MDCT
layer. In the current prototype, the cutoff frequency is 8 kHz. In the MDCT
layer, all bands below 8 kHz are discarded, such that there is no coding
redundancy between the two layers. Also both layers use the same instance of
the range coder to encode the signal, which ensures that no "padding bits" are
wasted. The hybrid approach makes it easy to support both constant bitrate
(CBR) and varaible bitrate (VBR) coding. Although the SILK layer used is VBR,
it is easy to make the bit allocation of the CELT layer produce a final stream
that is CBR by using all the bits left unused by the SILK layer.
+The largest of two values x and y.
+
The implementation of SILKbased LP layer is similar to the description in
the SILK InternetDraft with the main exception that
SILK was modified to
use the same range coder as CELT. The implementation of the CELTbased MDCT
layer is available from the CELT website and is a more recent version (0.8.1)
of the CELT InternetDraft.
The main changes
include better support for 20 ms frames as well as the ability to encode
only the higher bands using a range coder partially filled by the SILK layer.
+
+
+
+With this definition, if lo>hi, the lower bound is the one that is enforced.
+
+
+
In addition to their frame size, the SILK and CELT codecs require
a lookahead of 5.2 ms and 2.5 ms, respectively. SILK's lookahead is due to
noise shaping estimation (5 ms) and the internal resampling (0.2 ms), while
CELT's lookahead is due to the overlapping MDCT windows. To compensate for the
difference, the CELT encoder input is delayed by 2.7 ms. This ensures that low
frequencies and high frequencies arrive at the same time.
+The sign of x, i.e.,
+
+
+
+
+The basetwo logarithm of f.
+
+

+
The source code is currently available in a
Git repository
which references two other
repositories (for SILK and CELT). Some snapshots are provided for
convenience at along
with sample files.
Although the build system is very primitive, some instructions are provided
in the toplevel README file.
This is very early development so both the quality and feature set should
greatly improve over time. In the current version, only 48 kHz audio is
supported, but support for all configurations listed in
 is planned.
+The minimum number of bits required to store a positive integer n in two's
+ complement notation, or 0 for a nonpositive integer n.
+
+Examples:
+
+ilog(1) = 0
+ilog(0) = 0
+ilog(1) = 1
+ilog(2) = 2
+ilog(3) = 2
+ilog(4) = 3
+ilog(7) = 3
+
+
+
+
+
+
+The Opus codec scales from 6 kb/s narrowband mono speech to 510 kb/s
+ fullband stereo music, with algorithmic delays ranging from 5 ms to
+ 65.2 ms.
+At any given time, either the LP layer, the MDCT layer, or both, may be active.
+It can seamlessly switch between all of its various operating modes, giving it
+ a great deal of flexibility to adapt to varying content and network
+ conditions without renegotiating the current session.
+Internally, the codec always operates at a 48 kHz sampling rate, though it
+ allows input and output of various bandwidths, defined as follows:
+
+
+Abbreviation
+Audio Bandwidth
+Sampling Rate (Effective)
+NB (narrowband)4 kHz8 kHz
+MB (mediumband)6 kHz12 kHz
+WB (wideband)8 kHz16 kHz
+SWB (superwideband)12 kHz24 kHz
+FB (fullband)20 kHz48 kHz
+
+
+These can be chosen independently on the encoder and decoder side, e.g., a
+ fullband signal can be decoded as wideband, or vice versa.
+This approach ensures a sender and receiver can always interoperate, regardless
+ of the capabilities of their actual audio hardware.
+
+
+
+Opus defines superwideband (SWB) mode to have an effective sampling rate of
+ 24 kHz, unlike some other audio coding standards that use 32 kHz.
+This was chosen for a number of reasons.
+The band layout in the MDCT layer naturally allows skipping coefficients for
+ frequencies over 12 kHz, but does not allow cleanly dropping frequencies
+ over 16 kHz.
+The choice of 24 kHz also makes resampling in the MDCT layer easier, as 24
+ evenly divides 48, and when 24 kHz is sufficient, it can save computation
+ in other processing, such as Acoustic Echo Cancellation (AEC).
+Experimental changes to the band layout to allow a 16 kHz cutoff showed
+ potential quality degredations, and at typical bitrates the number of bits
+ saved by using such a cutoff instead of coding in fullband (FB) mode is very
+ small.
+Therefore, if an application wishes to process a signal sampled at 32 kHz,
+ it should just use FB mode.
+
+
+
+The LP layer is based on the
+ SILK codec
+ .
+It supports NB, MB, or WB audio and frame sizes from 10 ms to 60 ms,
+ and requires an additional 5.2 ms lookahead for noise shaping estimation
+ (5 ms) and internal resampling (0.2 ms).
+Like Vorbis and many other modern codecs, SILK is inherently designed for
+ variablebitrate (VBR) coding, though an encoder can with sufficient effort
+ produce constantbitrate (CBR) or nearCBR streams.
+
+
+
+The MDCT layer is based on the
+ CELT codec
+ .
+It supports sampling NB, WB, SWB, or FB audio and frame sizes from 2.5 ms
+ to 20 ms, and requires an additional 2.5 ms lookahead due to the
+ overlapping MDCT windows.
+The CELT codec is inherently designed for CBR coding, but unlike many CBR
+ codecs it is not limited to a set of predetermined rates.
+It internally allocates bits to exactly fill any given target budget, and an
+ encoder can produce a VBR stream by varying the target on a perframe basis.
+The MDCT layer is not used for speech when the audio bandwidth is WB or less,
+ as it is not useful there.
+On the other hand, nonspeech signals are not always adequately coded using
+ linear prediction, so for music only the MDCT layer should be used.
+
+
+
+A hybrid mode allows the use of both layers simultaneously with a frame size of
+ 10 or 20 ms and a SWB or FB audio bandwidth.
+Each frame is split into a low frequency signal and a high frequency signal,
+ with a cutoff of 8 kHz.
+The LP layer then codes the low frequency signal, followed by the MDCT layer
+ coding the high frequency signal.
+In the MDCT layer, all bands below 8 kHz are discarded, so there is no
+ coding redundancy between the two layers.
+
+
+
+At the decoder, the two decoder outputs are simply added together.
+To compensate for the different lookaheads required by each layer, the CELT
+ encoder input is delayed by an additional 2.7 ms.
+This ensures that low frequencies and high frequencies arrive at the same time.
+This extra delay MAY be reduced by an encoder by using less lookahead for noise
+ shaping or using a simpler resampler in the LP layer, but this will reduce
+ quality.
+However, the base 2.5 ms lookahead in the CELT layer cannot be reduced in
+ the encoder because it is needed for the MDCT overlap, whose size is fixed by
+ the decoder.
+
+
+
+Both layers use the same entropy coder, avoiding any waste from "padding bits"
+ between them.
+The hybrid approach makes it easy to support both CBR and VBR coding.
+Although the LP layer is VBR, the bit allocation of the MDCT layer can produce
+ a final stream that is CBR by using all the bits left unused by the LP layer.
+
+
+
+
There are three possible operating modes for the proposed prototype:
+As described, the two layers can be combined in three possible operating modes:
A linear prediction (LP) mode for use in low bitrate connections with up to 8 kHz audio bandwidth (16 kHz sampling rate)
A hybrid (LP+MDCT) mode for fullbandwidth speech at medium bitrates
An MDCTonly mode for very low delay speech transmission as well as music transmission.
+A LPonly mode for use in low bitrate connections with an audio bandwidth of
+ WB or less,
+A hybrid (LP+MDCT) mode for SWB or FB speech at medium bitrates, and
+An MDCTonly mode for very low delay speech transmission as well as music
+ transmission.
Each of these modes supports a number of difference frame sizes and sampling
rates. In order to distinguish between the various modes and configurations,
we need to define a simple header that can used in the transport layer
(e.g RTP) to signal this information. The following describes the proposed
header.
+
+
+A single packet may contain multiple audio frames.
+However, they must share a common set of parameters, including the operating
+ mode, audio bandwidth, frame size, and channel count.
+This section describes the possible combinations of these parameters and the
+ internal framing used to pack multiple frames into a single packet.
+This framing is not selfdelimiting.
+Instead, it assumes that a higher layer (such as UDP or RTP or Ogg or Matroska)
+ will communicate the length, in bytes, of the packet, and it uses this
+ information to reduce the framing overhead in the packet itself.
+A decoder implementation MUST support the framing described in this section.
+An alternative, selfdelimiting variant of the framing is described in
+ .
+Support for that variant is OPTIONAL.
+
The LP mode supports the following configurations (numbered from 00000...01011 in binary):

8 kHz: 10, 20, 40, 60 ms (00000...00011)
12 kHz: 10, 20, 40, 60 ms (00100...00111)
16 kHz: 10, 20, 40, 60 ms (01000...01011)

for a total of 12 configurations.
+An Opus packet begins with a singlebyte tableofcontents (TOC) header that
+ signals which of the various modes and configurations a given packet uses.
+It is composed of a frame count code, "c", a stereo flag, "s", and a
+ configuration number, "config", arranged as illustrated in
+ .
+A description of each of these fields follows.
+
+
The hybrid mode supports the following configurations (numbered from 01100...01111):

32 kHz: 10, 20 ms (01100...01101)
48 kHz: 10, 20 ms (01110...01111)

for a total of 4 configurations.
+The top five bits of the TOC byte, labeled "config", encode one of 32 possible
+ configurations of operating mode, audio bandwidth, and frame size.
+ lists the parameters for each configuration.
+
+Configuration Number(s)
+Mode
+Bandwidth
+Frame Size(s)
+0...3LPonlyNB10, 20, 40, 60 ms
+4...7LPonlyMB10, 20, 40, 60 ms
+8...11LPonlyWB10, 20, 40, 60 ms
+12...13HybridSWB10, 20 ms
+14...15HybridFB10, 20 ms
+16...19MDCTonlyNB2.5, 5, 10, 20 ms
+20...23MDCTonlyWB2.5, 5, 10, 20 ms
+24...27MDCTonlySWB2.5, 5, 10, 20 ms
+28...31MDCTonlyFB2.5, 5, 10, 20 ms
+
The MDCTonly mode supports the following configurations (numbered from 10000...11101):

8 kHz: 2.5, 5, 10, 20 ms (10000...10011)
16 kHz: 2.5, 5, 10, 20 ms (10100...10111)
32 kHz: 2.5, 5, 10, 20 ms (11000...11011)
48 kHz: 2.5, 5, 10, 20 ms (11100...11111)

for a total of 16 configurations.
+One additional bit, labeled "s", is used to signal mono vs. stereo, with 0
+ indicating mono and 1 indicating stereo.
There is thus a total of 32 configurations, so 5 bits are necessary to
indicate the mode, frame size and sampling rate (MFS). This leaves 3 bits for the number of frames per packets (codes 0 to 7):
+The remaining two bits of the TOC byte, labeled "c", code the number of frames
+ per packet (codes 0 to 3) as follows:
02: 13 frames in the packet, each with equal compressed size
3: arbitrary number of frames in the packet, each with equal compressed size (one size needs to be encoded)
45: 23 frames in the packet, with different compressed sizes, which need to be encoded (except the last one)
6: arbitrary number of frames in the packet, with different compressed sizes, each of which needs to be encoded
7: The first frame has this MFS, but others have different MFS. Each compressed size needs to be encoded.
+0: 1 frame in the packet
+1: 2 frames in the packet, each with equal compressed size
+2: 2 frames in the packet, with different compressed sizes
+3: an arbitrary number of frames in the packet
When code 7 is used and the last frames of a packet have the same MFS, it is
allowed to switch to another code for them.
+This draft refers to a packet as a code 0 packet, code 1 packet, etc., based on
+ the value of "c".
+
+
+
+A wellformed Opus packet MUST contain at least one byte with the TOC
+ information, though the frame(s) within a packet MAY be zero bytes long.
+
+
+
+
+
+
+This section describes how frames are packed according to each possible value
+ of "c" in the TOC byte.
+
The compressed size of the frames (if needed) is indicated  usually  with one byte, with the following meaning:
+When a packet contains multiple VBR frames, the compressed length of one or
+ more of these frames is indicated with a one or two byte sequence, with the
+ meaning of the first byte as follows:
0: No frame (DTX or lost packet)
1251: Size of the frame in bytes
252255: A second byte is needed. The total size is (size[1]*4)+(size[0]%4)+252
+0: No frame (discontinuous transmission (DTX) or lost packet)
+
+1...251: Size of the frame in bytes
+252...255: A second byte is needed. The total size is (size[1]*4)+size[0]
The maximum size representable is 255*4+3+252=1275 bytes. For 20 ms frames, that
represents a bitrate of 510 kb/s, which is really the highest rate anyone would want
to use in stereo mode (beyond that point, lossless codecs would be more appropriate).
+The maximum representable size is 255*4+255=1275 bytes. This limit MUST NOT
+be exceeded, even when no length field is used.
+For 20 ms frames, this represents a bitrate of 510 kb/s, which is
+ approximately the highest useful rate for lossily compressed fullband stereo
+ music.
+Beyond this point, lossless codecs are more appropriate.
+It is also roughly the maximum useful rate of the MDCT layer, as shortly
+ thereafter quality no longer improves with additional bits due to limitations
+ on the codebook sizes.

Simplest case: one packet
+No length is transmitted for the last frame in a VBR packet, or for any of the
+ frames in a CBR packet, as it can be inferred from the total size of the
+ packet and the size of all other data in the packet.
+However, the length of any individual frame MUST NOT exceed 1275 bytes, to
+ allow for repacketization by gateways, conference bridges, or other software.
+
+
+
+
+
+
+For code 0 packets, the TOC byte is immediately followed by N1 bytes
+ of compressed data for a single frame (where N is the size of the packet),
+ as illustrated in .
+
+
+
+
+
+
+For code 1 packets, the TOC byte is immediately followed by the
+ (N1)/2 bytes of compressed data for the first frame, followed by
+ (N1)/2 bytes of compressed data for the second frame, as illustrated in
+ .
+The number of payload bytes available for compressed data, N1, MUST be even
+ for all code 1 packets.
+
+
+
+
+
+
+For code 2 packets, the TOC byte is followed by a one or two byte sequence
+ indicating the length of the first frame (marked N1 in the figure below),
+ followed by N1 bytes of compressed data for the first frame.
+The remaining NN12 or NN13 bytes are the compressed data for the
+ second frame.
+This is illustrated in .
+The length of the first frame, N1, MUST be no larger than the size of the
+ payload remaining after decoding that length for all code 2 packets.
+
+
+
+
+
+
+Code 3 packets may encode an arbitrary number of frames, as well as additional
+ padding, called "Opus padding" to indicate that this padding is added at the
+ Opus layer, rather than at the transport layer.
+For code 3 packets, the TOC byte is followed by a byte encoding the number of
+ frames in the packet in bits 0 to 5 (marked "M" in the figure below), with bit
+ 6 indicating whether or not Opus padding is inserted (marked "p" in the figure
+ below), and bit 7 indicating VBR (marked "v" in the figure below).
+M MUST NOT be zero, and the audio duration contained within a packet MUST NOT
+ exceed 120 ms.
+This limits the maximum frame count for any frame size to 48 (for 2.5 ms
+ frames), with lower limits for longer frame sizes.
+ illustrates the layout of the frame count
+ byte.
+
+
+
+When Opus padding is used, the number of bytes of padding is encoded in the
+ bytes following the frame count byte.
+Values from 0...254 indicate that 0...254 bytes of padding are included,
+ in addition to the byte(s) used to indicate the size of the padding.
+If the value is 255, then the size of the additional padding is 254 bytes,
+ plus the padding value encoded in the next byte.
+The additional padding bytes appear at the end of the packet, and SHOULD be set
+ to zero by the encoder.
+The decoder MUST accept any value for the padding bytes, however.
+By using code 255 multiple times, it is possible to create a packet of any
+ specific, desired size.
+Let P be the total amount of padding, including both the trailing padding bytes
+ themselves and the header bytes used to indicate how many there are.
+Then P MUST be no more than N2 for CBR packets, or NM1 for VBR packets.
+
+
+In the CBR case, the compressed length of each frame in bytes is equal to the
+ number of remaining bytes in the packet after subtracting the (optional)
+ padding, (N2P), divided by M.
+This number MUST be an integer multiple of M.
+The compressed data for all M frames then follows, each of size
+ (N2P)/M bytes, as illustrated in .
+
+
+
+
+
+In the VBR case, the (optional) padding length is followed by M1 frame
+ lengths (indicated by "N1" to "N[M1]" in the figure below), each encoded in a
+ one or two byte sequence as described above.
+The packet MUST contain enough data for the M1 lengths after the (optional)
+ padding, and the sum of these lengths MUST be no larger than the number of
+ bytes remaining in the packet after decoding them.
+The compressed data for all M frames follows, each frame consisting of the
+ indicated number of bytes, with the final frame consuming any remaining bytes
+ before the final padding, as illustrated in .
+The number of header bytes (TOC byte, frame count byte, padding length bytes,
+ and frame length bytes), plus the length of the first M1 frames themselves,
+ plus the length of the padding MUST be no larger than N, the total size of the
+ packet.
+
+
+
+
+
+Simplest case, one NB mono 20 ms SILK frame:
+
+
+
+
+Two FB mono 5 ms CELT frames of the same compressed size:
+
+
Four frames of the same compressed size:
+Two FB mono 20 ms hybrid frames of different compressed size:
+
+
+Four FB stereo 20 ms CELT frames of the same compressed size:
+
+
+
+
+
+
+A receiver MUST NOT process packets which violate the rules above as normal
+ Opus packets.
+They are reserved for future applications, such as inband headers (containing
+ metadata, etc.) or multichannel support.
+
+
+
+
+
+
+
+The Opus decoder consists of two main blocks: the SILK decoder and the CELT decoder.
+The output of the Opus decode is the sum of the outputs from the SILK and CELT decoders
+with proper sample rate conversion and delay compensation as illustrated in the
+block diagram below. At any given time, one or both of the SILK and CELT decoders
+may be active.
+
+
+
+
+
+Opus uses an entropy coder based on ,
+which is itself a rediscovery of the FIFO arithmetic code introduced by .
+It is very similar to arithmetic encoding, except that encoding is done with
+digits in any base instead of with bits,
+so it is faster when using larger bases (i.e., an octet). All of the
+calculations in the range coder must use bitexact integer arithmetic.
+
+
+Symbols may also be coded as "raw bits" packed directly into the bitstream,
+ bypassing the range coder.
+These are packed backwards starting at the end of the frame, as illustrated in
+ .
+This reduces complexity and makes the stream more resilient to bit errors, as
+ corruption in the raw bits will not desynchronize the decoding process, unlike
+ corruption in the input to the range decoder.
+Raw bits are only used in the CELT layer.
+
+
+
+
+
+Each symbol coded by the range coder is drawn from a finite alphabet and coded
+ in a separate "context", which describes the size of the alphabet and the
+ relative frequency of each symbol in that alphabet.
+Opus only uses static contexts.
+They are not adapted to the statistics of the data as it is coded.
+
+
+Suppose there is a context with n symbols, identified with an index that ranges
+ from 0 to n1.
+The parameters needed to encode or decode a symbol in this context are
+ represented by a threetuple (fl[k], fh[k], ft), with
+ 0 <= fl[k] < fh[k] <= ft <= 65535.
+The values of this tuple are derived from the probability model for the
+ symbol, represented by traditional "frequency counts" (although, since Opus
+ uses static contexts, these are not updated as symbols are decoded).
+Let f[i] be the frequency of symbol i.
+Then the threetuple corresponding to symbol k is given by
+
+
+
+The range decoder extracts the symbols and integers encoded using the range
+ encoder in .
+The range decoder maintains an internal state vector composed of the twotuple
+ (val,rng), representing the difference between the high end of the current
+ range and the actual coded value, minus one, and the size of the current
+ range, respectively.
+Both val and rng are 32bit unsigned integer values.
+The decoder initializes rng to 128 and initializes val to 127 minus the top 7
+ bits of the first input octet.
+The remaining bit is saved for use in the renormalization procedure described
+ in , which the decoder invokes
+ immediately after initialization to read additional bits and establish the
+ invariant that rng > 2**23.
+
+
+
+
+Decoding a symbol is a twostep process.
+The first step determines a 16bit unsigned value fs, which lies within the
+ range of some symbol in the current context.
+The second step updates the range decoder state with the threetuple
+ (fl[k], fh[k], ft) corresponding to that symbol.
+
+
+The first step is implemented by ec_decode() (entdec.c), which computes
+
+The divisions here are exact integer division.
+
+
+The decoder then identifies the symbol in the current context corresponding to
+ fs; i.e., the value of k whose threetuple (fl[k], fh[k], ft)
+ satisfies fl[k] <= fs < fh[k].
+It uses this tuple to update val according to
+
+If fl[k] is greater than zero, then the decoder updates rng using
+
+Otherwise, it updates rng using
+
+
+
+Using a special case for the first symbol (rather than the last symbol, as is
+ commonly done in other arithmetic coders) ensures that all the truncation
+ error from the finite precision arithmetic accumulates in symbol 0.
+This makes the cost of coding a 0 slightly smaller, on average, than its
+ estimated probability indicates and makes the cost of coding any other symbol
+ slightly larger.
+When contexts are designed so that 0 is the most probable symbol, which is
+ often the case, this strategy minimizes the inefficiency introduced by the
+ finite precision.
+It also makes some of the specialcase decoding routines in
+ particularly simple.
+
+
+After the updates, implemented by ec_dec_update() (entdec.c), the decoder
+ normalizes the range using the procedure in the next section, and returns the
+ index k.
+
+
+
+
+To normalize the range, the decoder repeats the following process, implemented
+ by ec_dec_normalize() (entdec.c), until rng > 2**23.
+If rng is already greater than 2**23, the entire process is skipped.
+First, it sets rng to (rng<<8).
+Then it reads the next octet of the payload and combines it with the leftover
+ bit buffered from the previous octet to form the 8bit value sym.
+It takes the leftover bit as the high bit (bit 7) of sym, and the top 7 bits
+ of the octet it just read as the other 7 bits of sym.
+The remaining bit in the octet just read is buffered for use in the next
+ iteration.
+If no more input octets remain, it uses zero bits instead.
+Then, it sets
+
+
+
+It is normal and expected that the range decoder will read several bytes
+ into the raw bits data (if any) at the end of the packet by the time the frame
+ is completely decoded, as illustrated in .
+This same data MUST also be returned as raw bits when requested.
+The encoder is expected to terminate the stream in such a way that the decoder
+ will decode the intended values regardless of the data contained in the raw
+ bits.
+ describes a procedure for doing this.
+If the range decoder consumes all of the bytes belonging to the current frame,
+ it MUST continue to use zero when any further input bytes are required, even
+ if there is additional data in the current packet from padding or other
+ frames.
+
+
+
+
+
+
+
+
+The reference implementation uses three additional decoding methods that are
+ exactly equivalent to the above, but make assumptions and simplifications that
+ allow for a more efficient implementation.
+
+
+
+The first is ec_decode_bin() (entdec.c), defined using the parameter ftb
+ instead of ft.
+It is mathematically equivalent to calling ec_decode() with
+ ft = (1<<ftb), but avoids one of the divisions.
+
+
+
+
+The next is ec_dec_bit_logp() (entdec.c), which decodes a single binary symbol,
+ replacing both the ec_decode() and ec_dec_update() steps.
+The context is described by a single parameter, logp, which is the absolute
+ value of the base2 logarithm of the probability of a "1".
+It is mathematically equivalent to calling ec_decode() with
+ ft = (1<<logp), followed by ec_dec_update() with
+ the 3tuple (fl[k] = 0, fh[k] = (1<<logp)1,
+ ft = (1<<logp)) if the returned value
+ of fs is less than (1<<logp)1 (a "0" was decoded), and with
+ (fl[k] = (1<<logp)1,
+ fh[k] = ft = (1<<logp)) otherwise (a "1" was
+ decoded).
+The implementation requires no multiplications or divisions.
+
+
+
+
+The last is ec_dec_icdf() (entdec.c), which decodes a single symbol with a
+ tablebased context of up to 8 bits, also replacing both the ec_decode() and
+ ec_dec_update() steps, as well as the search for the decoded symbol in between.
+The context is described by two parameters, an icdf
+ ("inverse" cumulative distribution function) table and ftb.
+As with ec_decode_bin(), (1<<ftb) is equivalent to ft.
+idcf[k], on the other hand, stores (1<<ftb)fh[k], which is equal to
+ (1<<ftb)fl[k+1].
+fl[0] is assumed to be 0, and the table is terminated by a value of 0 (where
+ fh[k] == ft).
+
+
+The function is mathematically equivalent to calling ec_decode() with
+ ft = (1<<ftb), using the returned value fs to search the table
+ for the first entry where fs < (1<<ftb)icdf[k], and
+ calling ec_dec_update() with fl[k] = (1<<ftb)icdf[k1] (or 0
+ if k == 0), fh[k] = (1<<ftb)idcf[k], and
+ ft = (1<<ftb).
+Combining the search with the update allows the division to be replaced by a
+ series of multiplications (which are usually much cheaper), and using an
+ inverse CDF allows the use of an ftb as large as 8 in an 8bit table without
+ any special cases.
+This is the primary interface with the range decoder in the SILK layer, though
+ it is used in a few places in the CELT layer as well.
+
+
+Although icdf[k] is more convenient for the code, the frequency counts, f[k],
+ are a more natural representation of the probability distribution function
+ (PDF) for a given symbol.
+Therefore this draft lists the latter, not the former, when describing the
+ context in which a symbol is coded as a list, e.g., {4, 4, 4, 4}/16 for a
+ uniform context with four possible values and ft=16.
+The value of ft after the slash is always the sum of the entries in the PDF,
+ but is included for convenience.
+Contexts with identical probabilities, f[k]/ft, but different values of ft
+ (or equivalently, ftb) are not the same, and cannot, in general, be used in
+ place of one another.
+An icdf table is also not capable of representing a PDF where the first symbol
+ has 0 probability.
+In such contexts, ec_dec_icdf() can decode the symbol by using a table that
+ drops the entries for any initial zeroprobability values and adding the
+ constant offset of the first value with a nonzero probability to its return
+ value.
+
+
+
+
+
+
+The raw bits used by the CELT layer are packed at the end of the packet, with
+ the least significant bit of the first value packed in the least significant
+ bit of the last byte, filling up to the most significant bit in the last byte,
+ continuing on to the least significant bit of the penultimate byte, and so on.
+The reference implementation reads them using ec_dec_bits() (entdec.c).
+Because the range decoder must read several bytes ahead in the stream, as
+ described in , the input consumed by the
+ raw bits MAY overlap with the input consumed by the range coder, and a decoder
+ MUST allow this.
+The format should render it impossible to attempt to read more raw bits than
+ there are actual bits in the frame, though a decoder MAY wish to check for
+ this and report an error.
+
+
+
+
+
+The ec_dec_uint() (entdec.c) function decodes one of ft equiprobable values in
+ the range 0 to ft1, inclusive, each with a frequency of 1, where ft may be as
+ large as 2**321.
+Because ec_decode() is limited to a total frequency of 2**161, this is split
+ up into a range coded symbol representing up to 8 of the high bits of the
+ value, and, if necessary, raw bits representing the remaining bits.
+The limit of 8 bits in the range coded symbol is a tradeoff between
+ implementation complexity, modeling error (since the symbols no longer truly
+ have equal coding cost), and rounding error introduced by the range coder
+ itself (which gets larger as more bits are included).
+Using raw bits reduces the maximum number of divisions required in the worst
+ case, but means that it may be possible to decode a value outside the range
+ 0 to ft1, inclusive.
+
+
+
+ec_dec_uint() takes a single, positive parameter, ft, which is not necessarily
+ a power of two, and returns an integer, t, whose value lies between 0 and
+ ft1, inclusive.
+Let ftb = ilog(ft1), i.e., the number of bits required to store ft1 in two's
+ complement notation.
+If ftb is 8 or less, then t is decoded with t = ec_decode(ft), and the range
+ coder state is updated using the threetuple (t,t+1,ft).
+
+
+If ftb is greater than 8, then the top 8 bits of t are decoded using
+ t = ec_decode((ft1>>ftb8)+1),
+ the decoder state is updated using the threetuple
+ (t,t+1,(ft1>>ftb8)+1), and the remaining bits are decoded as raw bits,
+ setting t = t<<ftb8ec_dec_bits(ftb8).
+If, at this point, t >= ft, then the current frame is corrupt.
+In that case, the decoder should assume there has been an error in the coding,
+ decoding, or transmission and SHOULD take measures to conceal the
+ error and/or report to the application that a problem has occurred.
+
+
+
+
+
+
+The bit allocation routines in the CELT decoder need a conservative upper bound
+ on the number of bits that have been used from the current frame thus far,
+ including both range coder bits and raw bits.
+This drives allocation decisions that must match those made in the encoder.
+The upper bound is computed in the reference implementation to wholebit
+ precision by the function ec_tell() (entcode.h) and to fractional 1/8th bit
+ precision by the function ec_tell_frac() (entcode.c).
+Like all operations in the range coder, it must be implemented in a bitexact
+ manner, and must produce exactly the same value returned by the same functions
+ in the encoder after encoding the same symbols.
+
+
+ec_tell() is guaranteed to return ceil(ec_tell_frac()/8.0).
+In various places the codec will check to ensure there is enough room to
+ contain a symbol before attempting to decode it.
+In practice, although the number of bits used so far is an upper bound,
+ decoding a symbol whose probability model suggests it has a worstcase cost of
+ p 1/8th bits may actually advance the return value of ec_tell_frac() by
+ p1, p, or p+1 1/8th bits, due to approximation error in that upper bound,
+ truncation error in the range coder, and for large values of ft, modeling
+ error in ec_dec_uint().
+
+
+However, this error is bounded, and periodic calls to ec_tell() or
+ ec_tell_frac() at precisely defined points in the decoding process prevent it
+ from accumulating.
+For a range coder symbol that requires a whole number of bits (i.e.,
+ ft/(fh[k]fl[k]) is a power of two), where there are at least p 1/8th bits
+ available, decoding the symbol will never advance the decoder past the end of
+ the frame ("bust the budget").
+In this case the return value of ec_tell_frac() will only advance by more than
+ p 1/8th bits if there was an additional, fractional number of bits remaining,
+ and it will never advance beyond the next wholebit boundary, which is safe,
+ since frames always contain a whole number of bits.
+However, when p is not a whole number of bits, an extra 1/8th bit is required
+ to ensure that decoding the symbol will not bust the budget.
+
+
+The reference implementation keeps track of the total number of whole bits that
+ have been processed by the decoder so far in the variable nbits_total,
+ including the (possibly fractional) number of bits that are currently
+ buffered, but not consumed, inside the range coder.
+nbits_total is initialized to 33 just after the initial range renormalization
+ process completes (or equivalently, it can be initialized to 9 before the
+ first renormalization).
+The extra two bits over the actual amount buffered by the range coder
+ guarantees that it is an upper bound and that there is enough room for the
+ encoder to terminate the stream.
+Each iteration through the range coder's renormalization loop increases
+ nbits_total by 8.
+Reading raw bits increases nbits_total by the number of raw bits read.
+
+
+
+
+The whole number of bits buffered in rng may be estimated via l = ilog(rng).
+ec_tell() then becomes a simple matter of removing these bits from the total.
+It returns (nbits_total  l).
+
+
+In a newly initialized decoder, before any symbols have been read, this reports
+ that 1 bit has been used.
+This is the bit reserved for termination of the encoder.
+
+
+
+
+
+ec_tell_frac() estimates the number of bits buffered in rng to fractional
+ precision.
+Since rng must be greater than 2**23 after renormalization, l must be at least
+ 24.
+Let r = rng>>(l16), so that 32768 <= r < 65536, an unsigned Q15
+ value representing the fractional part of rng.
+Then the following procedure can be used to add one bit of precision to l.
+First, update r = r*r>>15.
+Then add the 16th bit of r to l via l = 2*l + (r>>16).
+Finally, if this bit was a 1, reduce r by a factor of two via r = r>>1,
+ so that it once again lies in the range 32768 <= r < 65536.
+
+
+This procedure is repeated three times to extend l to 1/8th bit precision.
+ec_tell_frac() then returns (nbits_total*8  l).
+
+
+
+
+
+
+
+
+
+The decoder's LP layer uses a modified version of the SILK codec (herein simply
+ called "SILK"), which runs a decoded excitation signal through adaptive
+ longterm and shortterm prediction synthesis filters.
+It runs in NB, MB, and WB modes internally.
+When used in a hybrid frame in SWB or FB mode, the LP layer itself still only
+ runs in WB mode.
+
+
+Internally, the LP layer of a single Opus frame is composed of either a single
+ 10 ms regular SILK frame or between one and three 20 ms regular SILK
+ frames.
+A stereo Opus frame may double the number of regular SILK frames (up to a total
+ of six), since it includes separate frames for a mid channel and, optionally,
+ a side channel.
+Optional Low BitRate Redundancy (LBRR) frames, which are reducedbitrate
+ encodings of previous SILK frames, may be included to aid in recovery from
+ packet loss.
+If present, these appear before the regular SILK frames.
+They are in most respects identical to regular, active SILK frames, except that
+ they are usually encoded with a lower bitrate.
+This draft uses "SILK frame" to refer to either one and "regular SILK frame" if
+ it needs to draw a distinction between the two.
+
+
+Each SILK frame is in turn composed of either two or four 5 ms subframes.
+Various parameters, such as the quantization gain of the excitation and the
+ pitch lag and filter coefficients can vary on a subframebysubframe basis.
+
+
+All of these frames and subframes are decoded from the same range coder, with
+ no padding between them.
+Thus packing multiple SILK frames in a single Opus frame saves, on average,
+ half a byte per SILK frame.
+It also allows some parameters to be predicted from prior SILK frames in the
+ same Opus frame, since this does not degrade packet loss robustness (beyond
+ any penalty for merely using fewer, larger packets to store multiple frames).
+
+
+
+Stereo support in SILK uses a variant of midside coding, allowing a mono
+ decoder to simply decode the mid channel.
+However, the data for the two channels is interleaved, so a mono decoder must
+ still unpack the data for the side channel.
+It would be required to do so anyway for hybrid Opus frames, or to support
+ decoding individual 20 ms frames.
+
+
+
+Symbol(s)
+PDF(s)
+Condition
+
+VAD flags
+{1, 1}/2
+
+
+LBRR flag
+{1, 1}/2
+
+
+Perframe LBRR flags
+
+
+
+LBRR Frame(s)
+
+
+
+Regular SILK Frame(s)
+
+
+
+
+Organization of the SILK layer of an Opus frame.
+
+
+
+
+
+An overview of the decoder is given in .
+
+
+
+
+
+ The range decoder decodes the encoded parameters from the received bitstream. Output from this function includes the pulses and gains for generating the excitation signal, as well as LTP and LSF codebook indices, which are needed for decoding LTP and LPC coefficients needed for LTP and LPC synthesis filtering the excitation signal, respectively.
+
+
+
+
+
+ Pulses and gains are decoded from the parameters that were decoded by the range decoder.
+
+
+
+ When a voiced frame is decoded and LTP codebook selection and indices are received, LTP coefficients are decoded using the selected codebook by choosing the vector that corresponds to the given codebook index in that codebook. This is done for each of the four subframes.
+ The LPC coefficients are decoded from the LSF codebook by first adding the chosen LSF vector and the decoded LSF residual signal. The resulting LSF vector is stabilized using the same method that was used in the encoder; see
+ . The LSF coefficients are then converted to LPC coefficients, and passed on to the LPC synthesis filter.
+
+
+
+
+
+ The pulses signal is multiplied with the quantization gain to create the excitation signal.
+
+
+
+
+
+ For voiced speech, the excitation signal e(n) is input to an LTP synthesis filter that recreates the longterm correlation removed in the LTP analysis filter and generates an LPC excitation signal e_LPC(n), according to
+
+ using the pitch lag L, and the decoded LTP coefficients b_i.
+ The number of LTP coefficients is 5, and thus d = 2.
+
+ For unvoiced speech, the output signal is simply a copy of the excitation signal, i.e., e_LPC(n) = e(n).
+
+
+
+
+
+ In a similar manner, the shortterm correlation that was removed in the LPC analysis filter is recreated in the LPC synthesis filter. The LPC excitation signal e_LPC(n) is filtered using the LTP coefficients a_i, according to
+
+ where d_LPC is the LPC synthesis filter order, and y(n) is the decoded output signal.
+
+
+
+
+
+
+
+
+The LP layer begins with two to eight header bits, decoded in silk_Decode()
+ (silk_dec_API.c).
+These consist of one Voice Activity Detection (VAD) bit per frame (up to 3),
+ followed by a single flag indicating the presence of LBRR frames.
+For a stereo packet, these flags correspond to the mid channel, and a second
+ set of flags is included for the side channel.
+
+
+Because these are the first symbols decoded by the range coder, they can be
+ extracted directly from the upper bits of the first byte of compressed data.
+Thus, a receiver can determine if an Opus frame contains any active SILK frames
+ without the overhead of using the range decoder.
+
+
+
+
+
+For Opus frames longer than 20 ms, a set of perframe LBRR flags is
+ decoded for each channel that has its LBRR flag set.
+For 40 ms Opus frames the 2frame LBRR flag PDF from
+ is used, and for 60 ms Opus frames
+ the 3frame LBRR flag PDF is used.
+For each channel, the resulting 2 or 3bit integer contains the corresponding
+ LBRR flag for each frame, packed in order from the LSb to the MSb.
+
+
+
+Frame Size
+PDF
+40 ms{0, 53, 53, 150}/256
+60 ms{0, 41, 20, 29, 41, 15, 28, 82}/256
+
+
+
+
+
+
+The LBRR frames, if present, immediately follow, one per set LBRR flag, and
+ prior to any regular SILK frames.
+ describes their exact contents.
+LBRR frames do not include their own separate VAD flags.
+LBRR frames are only meant to be transmitted for active speech, thus all LBRR
+ frames are treated as active.
+
+
+
+In a stereo Opus frame longer than 20 ms, although all the perframe LBRR
+ flags for the mid channel are coded before the perframe LBRR flags for the
+ side channel, the LBRR frames themselves are interleaved.
+The LBRR frame for the mid channel of a given 20 ms interval (if present)
+ is immediately followed by the corresponding LBRR frame for the side channel
+ (if present).
+
+
+
+
+
+The regular SILK frame(s) follow the LBRR frames (if any).
+ describes their contents, as well.
+Unlike the LBRR frames, a regular SILK frame is always coded for each time
+ interval in an Opus frame, even if the corresponding VAD flag is unset.
+Like the LBRR frames, in stereo Opus frames longer than 20 ms, the mid and
+ side frames are interleaved for each 20 ms interval.
+The side frame may be skipped by coding an appropriate flag, as detailed in
+ .
+
+
+
+
+
+Each SILK frame includes a set of side information that encodes the frame type,
+ quantization type and gains, shortterm prediction filter coefficients, an LSF
+ interpolation weight, longterm prediction filter lags and gains, and a
+ linear congruential generator (LCG) seed.
+The quantized excitation signal follows these at the end of the frame.
+ details the overall organization of a
+ SILK frame.
+
+
+
+Symbol(s)
+PDF(s)
+Condition
+
+Stereo Prediction Weights
+
+
+
+MidOnly Flag
+
+
+
+Frame Type
+
+
+
+Subframe Gains
+
+
+
+Normalized LSF Stage 1 Index
+
+
+
+Normalized LSF Stage 2 Residual
+
+
+
+Normalized LSF Interpolation Weight
+
+
+
+Primary Pitch Lag
+
+Voiced frame
+
+Subframe Pitch Contour
+
+Voiced frame
+
+Periodicity Index
+
+Voiced frame
+
+LTP Filter
+
+Voiced frame
+
+LTP Scaling
+
+
+
+LCG Seed
+
+
+
+Excitation Rate Level
+
+
+
+Excitation Pulse Counts
+
+
+
+Excitation Pulse Locations
+
+Nonzero pulse count
+
+Excitation LSb's
+
+
+
+Excitation Signs
+
+
+
+
+Order of the symbols in an individual SILK frame.
+
+
+
+
+
+A SILK frame corresponding to the mid channel of a stereo Opus frame begins
+ with a pair of side channel prediction weights, designed such that zeros
+ indicate normal midside coupling.
+Since these weights can change on every frame, the first portion of each frame
+ linearly interpolates between the previous weights and the current ones, using
+ zeros for the previous weights if none are available.
+These prediction weights are never included in a mono Opus frame, and the
+ previous weights are reset to zeros on any transition from a mono to stereo.
+They are also not included in an LBRR frame for the side channel, even if the
+ LBRR flags indicate the corresponding mid channel was not coded.
+In that case, the previous weights are used, again substituting in zeros if no
+ previous weights are available since the last decoder reset.
+
+
+
+The prediction weights are coded in three separate pieces, which are decoded
+ by silk_stereo_decode_pred() (silk_decode_stereo_pred.c).
+The first piece jointly codes the highorder part of a table index for both
+ weights.
+The second piece codes the loworder part of each table index.
+The third piece codes an offset used to linearly interpolate between table
+ indices.
+The details are as follows.
+
+
+
+Let n be an index decoded with the 25element stage1 PDF in
+ .
+Then let i0 and i1 be indices decoded with the stage2 and stage3 PDFs in
+ , respectively, and let i2 and i3
+ be two more indices decoded with the stage2 and stage3 PDFs, all in that
+ order.
+
+
+
+Stage
+PDF
+Stage 1
+{7, 2, 1, 1, 1,
+ 10, 24, 8, 1, 1,
+ 3, 23, 92, 23, 3,
+ 1, 1, 8, 24, 10,
+ 1, 1, 1, 2, 7}/256
+
+Stage 2
+{85, 86, 85}/256
+
+Stage 3
+{51, 51, 52, 51, 51}/256
+
+
+
+Then use n, i0, and i2 to form two table indices, wi0 and wi1, according to
+
+ where the division is exact integer division.
+The range of these indices is 0 to 14, inclusive.
+Let w[i] be the i'th weight from .
+Then the two prediction weights, w0_Q13 and w1_Q13, are
+
+
+
+
+Index
+Weight (Q13)
+ 013732
+ 110050
+ 28266
+ 37526
+ 46500
+ 55000
+ 62950
+ 7820
+ 8820
+ 92950
+105000
+116500
+127526
+138266
+1410050
+1513732
+
+
+
+
+
+
+A flag appears after the stereo prediction weights that indicates if only the
+ mid channel is coded for this time interval.
+It is omitted when there are no stereo weights, i.e., unless the SILK frame
+ corresponds to the mid channel of a stereo Opus frame, and it is also omitted
+ for an LBRR frame when the corresponding LBRR flags indicate the side channel
+ is present.
+When present, the decoder reads a single value using the PDF in
+ , as implemented in
+ silk_stereo_decode_mid_only() (silk_decode_stereo_pred.c).
+If the flag is set, then there is no corresponding SILK frame for the side
+ channel, the entire decoding process for the side channel is skipped, and
+ zeros are used during the stereo unmixing process.
+As stated above, LBRR frames still include this flag when the LBRR flag
+ indicates that the side channel is not coded.
+In that case, if this flag is zero (indicating that there should be a side
+ channel), then Packet Loss Concealment (PLC, see
+ ) SHOULD be invoked to recover a
+ side channel signal.
+
+
+
+PDF
+{192, 64}/256
+
+
+
+
+
+
+Each SILK frame contains a single "frame type" symbol that jointly codes the
+ signal type and quantization offset type of the corresponding frame.
+If the current frame is a regular SILK frame whose VAD bit was not set (an
+ "inactive" frame), then the frame type symbol takes on a value of either 0 or
+ 1 and is decoded using the first PDF in .
+If the frame is an LBRR frame or a regular SILK frame whose VAD flag was set
+ (an "active" frame), then the value of the symbol may range from 2 to 5,
+ inclusive, and is decoded using the second PDF in
+ .
+ translates between the value of the
+ frame type symbol and the corresponding signal type and quantization offset
+ type.
+
+
+
+VAD Flag
+PDF
+Inactive{26, 230, 0, 0, 0, 0}/256
+Active{0, 0, 24, 74, 148, 10}/256
+
+
+
+Frame Type
+Signal Type
+Quantization Offset Type
+0InactiveLow
+1InactiveHigh
+2UnvoicedLow
+3UnvoicedHigh
+4VoicedLow
+5VoicedHigh
+
+
+
+
+
+
+A separate quantization gain is coded for each 5 ms subframe.
+These gains control the step size between quantization levels of the excitation
+ signal and, therefore, the quality of the reconstruction.
+They are independent of the pitch gains coded for voiced frames.
+The quantization gains are themselves uniformly quantized to 6 bits on a
+ log scale, giving them a resolution of approximately 1.369 dB and a range
+ of approximately 1.94 dB to 88.21 dB.
+
+
+For the first LBRR frame, an LBRR frame where the previous LBRR frame in the
+ same channel is not coded, or the first regular SILK frame in the current
+ channel of an Opus frame, the first subframe uses an independent coding
+ method.
+In a stereo Opus frame, the midonly flag (from
+ ) may cause the first regular SILK frame in
+ the side channel to occur in a later time interval than the first regular SILK
+ frame in the mid channel.
+The 3 most significant bits of the quantization gain are decoded using a PDF
+ selected from based on the
+ decoded signal type.
+
+
+
+Signal Type
+PDF
+Inactive{32, 112, 68, 29, 12, 1, 1, 1}/256
+Unvoiced{2, 17, 45, 60, 62, 47, 19, 4}/256
+Voiced{1, 3, 26, 71, 94, 50, 9, 2}/256
+
+
+
+The 3 least significant bits are decoded using a uniform PDF:
+
+
+PDF
+{32, 32, 32, 32, 32, 32, 32, 32}/256
+
+
+
+For all other subframes (including the first subframe of frames not listed as
+ using independent coding above), the quantization gain is coded relative to
+ the gain from the previous subframe (in the same channel).
+In particular, unlike an LBRR frame where the previous frame is not coded, in a
+ 60 ms stereo Opus frame, if the first and third regular SILK frames
+ in the side channel are coded, but the second is not, the first subframe of
+ the third frame is still coded relative to the last subframe in the first
+ frame.
+The PDF in yields a delta gain index
+ between 0 and 40, inclusive.
+
+
+PDF
+{6, 5, 11, 31, 132, 21, 8, 4,
+ 3, 2, 2, 2, 1, 1, 1, 1,
+ 1, 1, 1, 1, 1, 1, 1, 1,
+ 1, 1, 1, 1, 1, 1, 1, 1,
+ 1, 1, 1, 1, 1, 1, 1, 1, 1}/256
+
+
+The following formula translates this index into a quantization gain for the
+ current subframe using the gain from the previous subframe:
+
+
+
+silk_gains_dequant() (silk_gain_quant.c) dequantizes the gain for the
+ k'th subframe and converts it into a linear Q16 scale factor via
+
+
+
+The function silk_log2lin() (silk_log2lin.c) computes an approximation of
+ of 2**(inLog_Q7/128.0), where inLog_Q7 is its Q7 input.
+Let i = inLog_Q7>>7 be the integer part of inLogQ7 and
+ f = inLog_Q7&127 be the fractional part.
+Then, if i < 16, then
+
+ yields the approximate exponential.
+Otherwise, silk_log2lin uses
+
+
+
+
+
+
+Normalized Line Spectral Frequency (LSF) coefficients follow the quantization
+ gains in the bitstream, and represent the Linear Predictive Coding (LPC)
+ coefficients for the current SILK frame.
+Once decoded, the normalized LSFs form an increasing list of Q15 values between
+ 0 and 1.
+These represent the interleaved zeros on the unit circle between 0 and pi
+ (hence "normalized") in the standard decomposition of the LPC filter into a
+ symmetric part and an antisymmetric part (P and Q in
+ ).
+Because of nonlinear effects in the decoding process, an implementation SHOULD
+ match the fixedpoint arithmetic described in this section exactly.
+An encoder SHOULD also use the same process.
+
+
+The normalized LSFs are coded using a twostage vector quantizer (VQ)
+ ( and ).
+NB and MB frames use an order10 predictor, while WB frames use an order16
+ predictor, and thus have different sets of tables.
+After reconstructing the normalized LSFs
+ (), the decoder runs them through a
+ stabilization process (), interpolates
+ them between frames (), converts them
+ back into LPC coefficients (), and then runs
+ them through further processes to limit the range of the coefficients
+ () and the gain of the filter
+ ().
+All of this is necessary to ensure the reconstruction process is stable.
+
+
+
+
+The first VQ stage uses a 32element codebook, coded with one of the PDFs in
+ , depending on the audio bandwidth and
+ the signal type of the current SILK frame.
+This yields a single index, I1, for the entire frame.
+This indexes an element in a coarse codebook, selects the PDFs for the
+ second stage of the VQ, and selects the prediction weights used to remove
+ intraframe redundancy from the second stage.
+The actual codebook elements are listed in
+ and
+ , but they are not needed until the last
+ stages of reconstructing the LSF coefficients.
+
+
+
+Audio Bandwidth
+Signal Type
+PDF
+NB or MBInactive or unvoiced
+
+{44, 34, 30, 19, 21, 12, 11, 3,
+ 3, 2, 16, 2, 2, 1, 5, 2,
+ 1, 3, 3, 1, 1, 2, 2, 2,
+ 3, 1, 9, 9, 2, 7, 2, 1}/256
+
+NB or MBVoiced
+
+{1, 10, 1, 8, 3, 8, 8, 14,
+13, 14, 1, 14, 12, 13, 11, 11,
+12, 11, 10, 10, 11, 8, 9, 8,
+ 7, 8, 1, 1, 6, 1, 6, 5}/256
+
+WBInactive or unvoiced
+
+{31, 21, 3, 17, 1, 8, 17, 4,
+ 1, 18, 16, 4, 2, 3, 1, 10,
+ 1, 3, 16, 11, 16, 2, 2, 3,
+ 2, 11, 1, 4, 9, 8, 7, 3}/256
+
+WBVoiced
+
+{1, 4, 16, 5, 18, 11, 5, 14,
+15, 1, 3, 12, 13, 14, 14, 6,
+14, 12, 2, 6, 1, 12, 12, 11,
+10, 3, 10, 5, 1, 1, 1, 3}/256
+
+
+
+
+
+
+
+A total of 16 PDFs are available for the LSF residual in the second stage: the
+ 8 (a...h) for NB and MB frames given in
+ , and the 8 (i...p) for WB frames
+ given in .
+Which PDF is used for which coefficient is driven by the index, I1,
+ decoded in the first stage.
+ lists the letter of the
+ corresponding PDF for each normalized LSF coefficient for NB and MB, and
+ lists the same information for WB.
+
+
+
+Codebook
+PDF
+a{1, 1, 1, 15, 224, 11, 1, 1, 1}/256
+b{1, 1, 2, 34, 183, 32, 1, 1, 1}/256
+c{1, 1, 4, 42, 149, 55, 2, 1, 1}/256
+d{1, 1, 8, 52, 123, 61, 8, 1, 1}/256
+e{1, 3, 16, 53, 101, 74, 6, 1, 1}/256
+f{1, 3, 17, 55, 90, 73, 15, 1, 1}/256
+g{1, 7, 24, 53, 74, 67, 26, 3, 1}/256
+h{1, 1, 18, 63, 78, 58, 30, 6, 1}/256
+
+
+
+Codebook
+PDF
+i{1, 1, 1, 9, 232, 9, 1, 1, 1}/256
+j{1, 1, 2, 28, 186, 35, 1, 1, 1}/256
+k{1, 1, 3, 42, 152, 53, 2, 1, 1}/256
+l{1, 1, 10, 49, 126, 65, 2, 1, 1}/256
+m{1, 4, 19, 48, 100, 77, 5, 1, 1}/256
+n{1, 1, 14, 54, 100, 72, 12, 1, 1}/256
+o{1, 1, 15, 61, 87, 61, 25, 4, 1}/256
+p{1, 7, 21, 50, 77, 81, 17, 1, 1}/256
+
+
+
+I1
+Coefficient
+
+0 1 2 3 4 5 6 7 8 9
+ 0
+a a a a a a a a a a
+ 1
+b d b c c b c b b b
+ 2
+c b b b b b b b b b
+ 3
+b c c c c b c b b b
+ 4
+c d d d d c c c c c
+ 5
+a f d d c c c c b b
+ g
+a c c c c c c c c b
+ 7
+c d g e e e f e f f
+ 8
+c e f f e f e g e e
+ 9
+c e e h e f e f f e
+10
+e d d d c d c c c c
+11
+b f f g e f e f f f
+12
+c h e g f f f f f f
+13
+c h f f f f f g f e
+14
+d d f e e f e f e e
+15
+c d d f f e e e e e
+16
+c e e g e f e f f f
+17
+c f e g f f f e f e
+18
+c h e f e f e f f f
+19
+c f e g h g f g f e
+20
+d g h e g f f g e f
+21
+c h g e e e f e f f
+22
+e f f e g g f g f e
+23
+c f f g f g e g e e
+24
+e f f f d h e f f e
+25
+c d e f f g e f f e
+26
+c d c d d e c d d d
+27
+b b c c c c c d c c
+28
+e f f g g g f g e f
+29
+d f f e e e e d d c
+30
+c f d h f f e e f e
+31
+e e f e f g f g f e
+
+
+
+I1
+Coefficient
+
+0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
+ 0
+i i i i i i i i i i i i i i i i
+ 1
+k l l l l l k k k k k j j j i l
+ 2
+k n n l p m m n k n m n n m l l
+ 3
+i k j k k j j j j j i i i i i j
+ 4
+i o n m o m p n m m m n n m m l
+ 5
+i l n n m l l n l l l l l l k m
+ 6
+i i i i i i i i i i i i i i i i
+ 7
+i k o l p k n l m n n m l l k l
+ 8
+i o k o o m n m o n m m n l l l
+ 9
+k j i i i i i i i i i i i i i i
+j0
+i j i i i i i i i i i i i i i j
+11
+k k l m n l l l l l l l k k j l
+12
+k k l l m l l l l l l l l k j l
+13
+l m m m o m m n l n m m n m l m
+14
+i o m n m p n k o n p m m l n l
+15
+i j i j j j j j j j i i i i j i
+16
+j o n p n m n l m n m m m l l m
+17
+j l l m m l l n k l l n n n l m
+18
+k l l k k k l k j k j k j j j m
+19
+i k l n l l k k k j j i i i i i
+20
+l m l n l l k k j j j j j k k m
+21
+k o l p p m n m n l n l l k l l
+22
+k l n o o l n l m m l l l l k m
+23
+j l l m m m m l n n n l j j j j
+24
+k n l o o m p m m n l m m l l l
+25
+i o j j i i i i i i i i i i i i
+26
+i o o l n k n n l m m p p m m m
+27
+l l p l n m l l l k k l l l k l
+28
+i i j i i i k j k j j k k k j j
+29
+i l k n l l k l k j i i j i i j
+30
+l n n m p n l l k l k k j i j i
+31
+k l n l m l l l k j k o m i i i
+
+
+
+Decoding the second stage residual proceeds as follows.
+For each coefficient, the decoder reads a symbol using the PDF corresponding to
+ I1 from either or
+ , and subtracts 4 from the result
+ to give an index in the range 4 to 4, inclusive.
+If the index is either 4 or 4, it reads a second symbol using the PDF in
+ , and adds the value of this second symbol
+ to the index, using the same sign.
+This gives the index, I2[k], a total range of 10 to 10, inclusive.
+
+
+
+PDF
+{156, 60, 24, 9, 4, 2, 1}/256
+
+
+
+The decoded indices from both stages are translated back into normalized LSF
+ coefficients in silk_NLSF_decode() (silk_NLSF_decode.c).
+The stage2 indices represent residuals after both the first stage of the VQ
+ and a separate backwardsprediction step.
+The backwards prediction process in the encoder subtracts a prediction from
+ each residual formed by a multiple of the coefficient that follows it.
+The decoder must undo this process.
+ contains lists of prediction weights
+ for each coefficient.
+There are two lists for NB and MB, and another two lists for WB, giving two
+ possible prediction weights for each coefficient.
+
+
+
+Coefficient
+A
+B
+C
+D
+ 017911617568
+ 11386714862
+ 21408216066
+ 31485917660
+ 41519217872
+ 514972173117
+ 615310017485
+ 71518916490
+ 816392177118
+ 9174136
+10196151
+11182142
+12198160
+13192142
+14182155
+
+
+
+The prediction is undone using the procedure implemented in
+ silk_NLSF_residual_dequant() (silk_NLSF_decode.c), which is as follows.
+Each coefficient selects its prediction weight from one of the two lists based
+ on the stage1 index, I1.
+ gives the selections for each
+ coefficient for NB and MB, and gives
+ the selections for WB.
+Let d_LPC be the order of the codebook, i.e., 10 for NB and MB, and 16 for WB,
+ and let pred_Q8[k] be the weight for the k'th coefficient selected by this
+ process for 0 <= k < d_LPC1.
+Then, the stage2 residual for each coefficient is computed via
+
+ where qstep is the Q16 quantization step size, which is 11796 for NB and MB
+ and 9830 for WB (representing step sizes of approximately 0.18 and 0.15,
+ respectively).
+
+
+
+I1
+Coefficient
+
+0 1 2 3 4 5 6 7 8
+ 0
+A B A A A A A A A
+ 1
+B A A A A A A A A
+ 2
+A A A A A A A A A
+ 3
+B B B A A A A B A
+ 4
+A B A A A A A A A
+ 5
+A B A A A A A A A
+ 6
+B A B B A A A B A
+ 7
+A B B A A B B A A
+ 8
+A A B B A B A B B
+ 9
+A A B B A A B B B
+10
+A A A A A A A A A
+11
+A B A B B B B B A
+12
+A B A B B B B B A
+13
+A B B B B B B B A
+14
+B A B B A B B B B
+15
+A B B B B B A B A
+16
+A A B B A B A B A
+17
+A A B B B A B B B
+18
+A B B A A B B B A
+19
+A A A B B B A B A
+20
+A B B A A B A B A
+21
+A B B A A A B B A
+22
+A A A A A B B B B
+23
+A A B B A A A B B
+24
+A A A B A B B B B
+25
+A B B B B B B B A
+26
+A A A A A A A A A
+27
+A A A A A A A A A
+28
+A A B A B B A B A
+29
+A A A B A A A A A
+30
+A A A B B A B A B
+31
+B A B B A B B B B
+
+
+
+I1
+Coefficient
+
+0 1 2 3 4 5 6 7 8 9 10 11 12 13 14
+ 0
+C C C C C C C C C C C C C C D
+ 1
+C C C C C C C C C C C C C C C
+ 2
+C C D C C D D D C D D D D C C
+ 3
+C C C C C C C C C C C C D C C
+ 4
+C D D C D C D D C D D D D D C
+ 5
+C D C C C C C C C C C C C C C
+ 6
+D C C C C C C C C C C D C D C
+ 7
+C D D C C C D C D D D C D C D
+ 8
+C D C D D C D C D C D D D D D
+ 9
+C C C C C C C C C C C C C C D
+10
+C D C C C C C C C C C C C C C
+11
+C C D C D D D D D D D C D C C
+12
+C C D C C D C D C D C C D C C
+13
+C C C C D D C D C D D D D C C
+14
+C D C C C D D C D D D C D D D
+15
+C C D D C C C C C C C C D D C
+16
+C D D C D C D D D D D C D C C
+17
+C C D C C C C D C C D D D C C
+18
+C C C C C C C C C C C C C C D
+19
+C C C C C C C C C C C C D C C
+20
+C C C C C C C C C C C C C C C
+21
+C D C D C D D C D C D C D D C
+22
+C C D D D D C D D C C D D C C
+23
+C D D C D C D C D C C C C D C
+24
+C C C D D C D C D D D D D D D
+25
+C C C C C C C C C C C C C C D
+26
+C D D C C C D D C C D D D D D
+27
+C C C C C D C D D D D C D D D
+28
+C C C C C C C C C C C C C C D
+29
+C C C C C C C C C C C C C C D
+30
+D C C C C C C C C C C D C C C
+31
+C C D C C D D D C C D C C D C
+
+
+
+
+
+
+Once the stage1 index I1 and the stage2 residual res_Q10[] have been decoded,
+ the final normalized LSF coefficients can be reconstructed.
+
+
+The spectral distortion introduced by the quantization of each LSF coefficient
+ varies, so the stage2 residual is weighted accordingly, using the
+ lowcomplexity Inverse Harmonic Mean Weighting (IHMW) function proposed in
+ .
+The weights are derived directly from the stage1 codebook vector.
+Let cb1_Q8[k] be the k'th entry of the stage1 codebook vector from
+ or
+ .
+Then for 0 <= k < d_LPC the following expression
+ computes the square of the weight as a Q18 value:
+
+ where cb1_Q8[1] = 0 and cb1_Q8[d_LPC] = 256, and the
+ division is exact integer division.
+This is reduced to an unsquared, Q9 value using the following squareroot
+ approximation:
+
+The cb1_Q8[] vector completely determines these weights, and they may be
+ tabulated and stored as 13bit unsigned values (with a range of 1819 to 5227,
+ inclusive) to avoid computing them when decoding.
+The reference implementation already requires code to compute these weights on
+ unquantized coefficients in the encoder, in silk_NLSF_VQ_weights_laroia()
+ (silk_NLSF_VQ_weights_laroia.c) and its callers, so it reuses that code in the
+ decoder instead of using a precomputed table to reduce the amount of ROM
+ required.
+
+
+
+I1
+Codebook (Q8)
+
+ 0 1 2 3 4 5 6 7 8 9
+0
+12 35 60 83 108 132 157 180 206 228
+1
+15 32 55 77 101 125 151 175 201 225
+2
+19 42 66 89 114 137 162 184 209 230
+3
+12 25 50 72 97 120 147 172 200 223
+4
+26 44 69 90 114 135 159 180 205 225
+5
+13 22 53 80 106 130 156 180 205 228
+6
+15 25 44 64 90 115 142 168 196 222
+7
+19 24 62 82 100 120 145 168 190 214
+8
+22 31 50 79 103 120 151 170 203 227
+9
+21 29 45 65 106 124 150 171 196 224
+10
+30 49 75 97 121 142 165 186 209 229
+11
+19 25 52 70 93 116 143 166 192 219
+12
+26 34 62 75 97 118 145 167 194 217
+13
+25 33 56 70 91 113 143 165 196 223
+14
+21 34 51 72 97 117 145 171 196 222
+15
+20 29 50 67 90 117 144 168 197 221
+16
+22 31 48 66 95 117 146 168 196 222
+17
+24 33 51 77 116 134 158 180 200 224
+18
+21 28 70 87 106 124 149 170 194 217
+19
+26 33 53 64 83 117 152 173 204 225
+20
+27 34 65 95 108 129 155 174 210 225
+21
+20 26 72 99 113 131 154 176 200 219
+22
+34 43 61 78 93 114 155 177 205 229
+23
+23 29 54 97 124 138 163 179 209 229
+24
+30 38 56 89 118 129 158 178 200 231
+25
+21 29 49 63 85 111 142 163 193 222
+26
+27 48 77 103 133 158 179 196 215 232
+27
+29 47 74 99 124 151 176 198 220 237
+28
+33 42 61 76 93 121 155 174 207 225
+29
+29 53 87 112 136 154 170 188 208 227
+30
+24 30 52 84 131 150 166 186 203 229
+31
+37 48 64 84 104 118 156 177 201 230
+
+
+
+I1
+Codebook (Q8)
+
+ 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
+0
+ 7 23 38 54 69 85 100 116 131 147 162 178 193 208 223 239
+1
+13 25 41 55 69 83 98 112 127 142 157 171 187 203 220 236
+2
+15 21 34 51 61 78 92 106 126 136 152 167 185 205 225 240
+3
+10 21 36 50 63 79 95 110 126 141 157 173 189 205 221 237
+4
+17 20 37 51 59 78 89 107 123 134 150 164 184 205 224 240
+5
+10 15 32 51 67 81 96 112 129 142 158 173 189 204 220 236
+6
+ 8 21 37 51 65 79 98 113 126 138 155 168 179 192 209 218
+7
+12 15 34 55 63 78 87 108 118 131 148 167 185 203 219 236
+8
+16 19 32 36 56 79 91 108 118 136 154 171 186 204 220 237
+9
+11 28 43 58 74 89 105 120 135 150 165 180 196 211 226 241
+10
+ 6 16 33 46 60 75 92 107 123 137 156 169 185 199 214 225
+11
+11 19 30 44 57 74 89 105 121 135 152 169 186 202 218 234
+12
+12 19 29 46 57 71 88 100 120 132 148 165 182 199 216 233
+13
+17 23 35 46 56 77 92 106 123 134 152 167 185 204 222 237
+14
+14 17 45 53 63 75 89 107 115 132 151 171 188 206 221 240
+15
+ 9 16 29 40 56 71 88 103 119 137 154 171 189 205 222 237
+16
+16 19 36 48 57 76 87 105 118 132 150 167 185 202 218 236
+17
+12 17 29 54 71 81 94 104 126 136 149 164 182 201 221 237
+18
+15 28 47 62 79 97 115 129 142 155 168 180 194 208 223 238
+19
+ 8 14 30 45 62 78 94 111 127 143 159 175 192 207 223 239
+20
+17 30 49 62 79 92 107 119 132 145 160 174 190 204 220 235
+21
+14 19 36 45 61 76 91 108 121 138 154 172 189 205 222 238
+22
+12 18 31 45 60 76 91 107 123 138 154 171 187 204 221 236
+23
+13 17 31 43 53 70 83 103 114 131 149 167 185 203 220 237
+24
+17 22 35 42 58 78 93 110 125 139 155 170 188 206 224 240
+25
+ 8 15 34 50 67 83 99 115 131 146 162 178 193 209 224 239
+26
+13 16 41 66 73 86 95 111 128 137 150 163 183 206 225 241
+27
+17 25 37 52 63 75 92 102 119 132 144 160 175 191 212 231
+28
+19 31 49 65 83 100 117 133 147 161 174 187 200 213 227 242
+29
+18 31 52 68 88 103 117 126 138 149 163 177 192 207 223 239
+30
+16 29 47 61 76 90 106 119 133 147 161 176 193 209 224 240
+31
+15 21 35 50 61 73 86 97 110 119 129 141 175 198 218 237
+
+
+
+Given the stage1 codebook entry cb1_Q8[], the stage2 residual res_Q10[], and
+ their corresponding weights, w_Q9[], the reconstructed normalized LSF
+ coefficients are
+
+ where the division is exact integer division.
+However, nothing in either the reconstruction process or the
+ quantization process in the encoder thus far guarantees that the coefficients
+ are monotonically increasing and separated well enough to ensure a stable
+ filter.
+When using the reference encoder, roughly 2% of frames violate this constraint.
+The next section describes a stabilization procedure used to make these
+ guarantees.
+
+
+
+
+
+
+The normalized LSF stabilization procedure is implemented in
+ silk_NLSF_stabilize() (silk_NLSF_stabilize.c).
+This process ensures that consecutive values of the normalized LSF
+ coefficients, NLSF_Q15[], are spaced some minimum distance apart
+ (predetermined to be the 0.01 percentile of a large training set).
+ gives the minimum spacings for NB and MB
+ and those for WB, where row k is the minimum allowed value of
+ NLSF_Q[k]NLSF_Q[k1].
+For the purposes of computing this spacing for the first and last coefficient,
+ NLSF_Q15[1] is taken to be 0, and NLSF_Q15[d_LPC] is taken to be 32768.
+
+
+
+Coefficient
+NB and MB
+WB
+ 0250100
+ 133
+ 2640
+ 333
+ 433
+ 533
+ 645
+ 7314
+ 8314
+ 9310
+1046111
+113
+128
+139
+147
+153
+16347
+
+
+
+The procedure starts off by trying to make small adjustments which attempt to
+ minimize the amount of distortion introduced.
+After 20 such adjustments, it falls back to a more direct method which
+ guarantees the constraints are enforced but may require large adjustments.
+
+
+Let NDeltaMin_Q15[k] be the minimum required spacing for the current audio
+ bandwidth from .
+First, the procedure finds the index i where
+ NLSF_Q15[i]  NLSF_Q15[i1]  NDeltaMin_Q15[i] is the
+ smallest, breaking ties by using the lower value of i.
+If this value is nonnegative, then the stabilization stops; the coefficients
+ satisfy all the constraints.
+Otherwise, if i == 0, it sets NLSF_Q15[0] to NDeltaMin_Q15[0], and if
+ i == d_LPC, it sets NLSF_Q15[d_LPC1] to
+ (32768  NDeltaMin_Q15[d_LPC]).
+For all other values of i, both NLSF_Q15[i1] and NLSF_Q15[i] are updated as
+ follows:
+
+Then the procedure repeats again, until it has either executed 20 times or
+ has stopped because the coefficients satisfy all the constraints.
+
+
+After the 20th repetition of the above procedure, the following fallback
+ procedure executes once.
+First, the values of NLSF_Q15[k] for 0 <= k < d_LPC
+ are sorted in ascending order.
+Then for each value of k from 0 to d_LPC1, NLSF_Q15[k] is set to
+
+Next, for each value of k from d_LPC1 down to 0, NLSF_Q15[k] is set to
+
+
+
+
+
+
+
+For 20 ms SILK frames, the first half of the frame (i.e., the first two
+ subframes) may use normalized LSF coefficients that are interpolated between
+ the decoded LSFs for the most recent coded frame (in the same channel) and the
+ current frame.
+A Q2 interpolation factor follows the LSF coefficient indices in the bitstream,
+ which is decoded using the PDF in .
+This happens in silk_decode_indices() (silk_decode_indices.c).
+For the first frame after a decoder reset, when no prior LSF coefficients are
+ available, the decoder still decodes this factor, but ignores its value and
+ always uses 4 instead.
+For 10 ms SILK frames, this factor is not stored at all.
+
+
+
+PDF
+{13, 22, 29, 11, 181}/256
+
+
+
+Let n2_Q15[k] be the normalized LSF coefficients decoded by the procedure in
+ , n0_Q15[k] be the LSF coefficients
+ decoded for the prior frame, and w_Q2 be the interpolation factor.
+Then the normalized LSF coefficients used for the first half of a 20 ms
+ frame, n1_Q15[k], are
+
+This interpolation is performed in silk_decode_parameters()
+ (silk_decode_parameters.c).
+
+
+
+
+
+Any LPC filter A(z) can be split into a symmetric part P(z) and an
+ antisymmetric part Q(z) such that
+
+with
+
+The even normalized LSF coefficients correspond to a pair of conjugate roots of
+ P(z), while the odd coefficients correspond to a pair of conjugate roots of
+ Q(z), all of which lie on the unit circle.
+In addition, P(z) has a root at pi and Q(z) has a root at 0.
+Thus, they may be reconstructed mathematically from a set of normalized LSF
+ coefficients, n[k], as
+
+
+
+However, SILK performs this reconstruction using a fixedpoint approximation so
+ that all decoders can reproduce it in a bitexact manner to avoid prediction
+ drift.
+The function silk_NLSF2A() (silk_NLSF2A.c) implements this procedure.
+
+
+To start, it approximates cos(pi*n[k]) using a table lookup with linear
+ interpolation.
+The encoder SHOULD use the inverse of this piecewise linear approximation,
+ rather than the true inverse of the cosine function, when deriving the
+ normalized LSF coefficients.
+
+
+The top 7 bits of each normalized LSF coefficient index a value in the table,
+ and the next 8 bits interpolate between it and the next value.
+Let i = n[k]>>8 be the integer index and
+ f = n[k]&255 be the fractional part of a given coefficient.
+Then the approximated cosine, c_Q17[k], is
+
+ where cos_Q13[i] is the corresponding entry of
+ .
+
+
+
+
+0
+1
+2
+3
+0
+ 8192819081828170
+4
+ 8152813081048072
+8
+ 8034799479467896
+12
+ 7840777877147644
+16
+ 7568749074067318
+20
+ 7226712870266922
+24
+ 6812669865806458
+28
+ 6332620460705934
+32
+ 5792564855025352
+36
+ 5198504048804718
+40
+ 4552438242124038
+44
+ 3862368435023320
+48
+ 3136294827602570
+52
+ 2378218619901794
+56
+ 1598140012021002
+60
+ 802602402202
+64
+ 0202402602
+68
+ 802100212021400
+72
+1598179419902186
+76
+2378257027602948
+80
+3136332035023684
+84
+3862403842124382
+88
+4552471848805040
+92
+5198535255025648
+96
+5792593460706204
+100
+6332645865806698
+104
+6812692270267128
+108
+7226731874067490
+112
+7568764477147778
+116
+7840789679467994
+120
+8034807281048130
+124
+8152817081828190
+128
+8192
+
+
+
+Given the list of cosine values, silk_NLSF2A_find_poly() (silk_NLSF2A.c)
+ computes the coefficients of P and Q, described here via a simple recurrence.
+Let p_Q16[k][j] and q_Q16[k][j] be the coefficients of the products of the
+ first (k+1) root pairs for P and Q, with j indexing the coefficient number.
+Only the first (k+2) coefficients are needed, as the products are symmetric.
+Let p_Q16[0][0] = q_Q16[0][0] = 1<<16,
+ p_Q16[0][1] = c_Q17[0], q_Q16[0][1] = c_Q17[1], and
+ d2 = d_LPC/2.
+As boundary conditions, assume
+ p_Q16[k][j] = q_Q16[k][j] = 0 for all
+ j < 0.
+Also, assume p_Q16[k][k+2] = p_Q16[k][k] and
+ q_Q16[k][k+2] = q_Q16[k][k] (because of the symmetry).
+Then, for 0 <k < d2 and 0 <= j <= k+1,
+
+The use of Q17 values for the cosine terms in an otherwise Q16 expression
+ implicitly scales them by a factor of 2.
+The multiplications in this recurrence may require up to 48 bits of precision
+ in the result to avoid overflow.
+In practice, each row of the recurrence only depends on the previous row, so an
+ implementation does not need to store all of them.
+
+
+silk_NLSF2A() uses the values from the last row of this recurrence to
+ reconstruct a 32bit version of the LPC filter (without the leading 1.0
+ coefficient), a32_Q17[k], 0 <= k < d2:
+
+The sum and difference of two terms from each of the p_Q16 and q_Q16
+ coefficient lists reflect the (1 + z**1) and
+ (1  z**1) factors of P and Q, respectively.
+The promotion of the expression from Q16 to Q17 implicitly scales the result
+ by 1/2.
+
+
+
+
+
+The a32_Q17[] coefficients are too large to fit in a 16bit value, which
+ significantly increases the cost of applying this filter in fixedpoint
+ decoders.
+Reducing them to Q12 precision doesn't incur any significant quality loss,
+ but still does not guarantee they will fit.
+silk_NLSF2A() applies up to 10 rounds of bandwidth expansion to limit
+ the dynamic range of these coefficients.
+Even floatingpoint decoders SHOULD perform these steps, to avoid mismatch.
+
+
+For each round, the process first finds the index k such that abs(a32_Q17[k])
+ is largest, breaking ties by choosing the lowest value of k.
+Then, it computes the corresponding Q12 precision value, maxabs_Q12, subject to
+ an upper bound to avoid overflow in subsequent computations:
+
+If this is larger than 32767, the procedure derives the chirp factor,
+ sc_Q16[0], to use in the bandwidth expansion as
+
+ where the division here is exact integer division.
+This is an approximation of the chirp factor needed to reduce the target
+ coefficient to 32767, though it is both less than 0.999 and, for
+ k > 0 when maxabs_Q12 is much greater than 32767, still slightly
+ too large.
+
+
+silk_bwexpander_32() (silk_bwexpander_32.c) performs the bandwidth expansion
+ (again, only when maxabs_Q12 is greater than 32767) using the following
+ recurrence:
+
+The first multiply may require up to 48 bits of precision in the result to
+ avoid overflow.
+The second multiply must be unsigned to avoid overflow with only 32 bits of
+ precision.
+The reference implementation uses a slightly more complex formulation that
+ avoids the 32bit overflow using signed multiplication, but is otherwise
+ equivalent.
+
+
+After 10 rounds of bandwidth expansion are performed, they are simply saturated
+ to 16 bits:
+
+Because this performs the actual saturation in the Q12 domain, but converts the
+ coefficients back to the Q17 domain for the purposes of prediction gain
+ limiting, this step must be performed after the 10th round of bandwidth
+ expansion, regardless of whether or not the Q12 version of any coefficient
+ still overflows a 16bit integer.
+This saturation is not performed if maxabs_Q12 drops to 32767 or less prior to
+ the 10th round.
+
+
+
+
+
+Even if the Q12 coefficients would fit, the resulting filter may still have a
+ significant gain (especially for voiced sounds), making the filter unstable.
+silk_NLSF2A() applies up to 18 additional rounds of bandwidth expansion to
+ limit the prediction gain.
+Instead of controlling the amount of bandwidth expansion using the prediction
+ gain itself (which may diverge to infinity for an unstable filter),
+ silk_NLSF2A() uses LPC_inverse_pred_gain_QA() (silk_LPC_inv_pred_gain.c)
+ to compute the reflection coefficients associated with the filter.
+The filter is stable if and only if the magnitude of these coefficients is
+ sufficiently less than one.
+The reflection coefficients, rc[k], can be computed using a simple Levinson
+ recurrence, initialized with the LPC coefficients
+ a[d_LPC1][n] = a[n], and then updated via
+
+
+
+However, LPC_inverse_pred_gain_QA() approximates this using fixedpoint
+ arithmetic to guarantee reproducible results across platforms and
+ implementations.
+It is important to run on the real Q12 coefficients that will be used during
+ reconstruction, because small changes in the coefficients can make a stable
+ filter unstable, but increasing the precision back to Q16 allows more accurate
+ computation of the reflection coefficients.
+Thus, let
+
+ be the Q16 representation of the Q12 version of the LPC coefficients that will
+ eventually be used.
+Then for each k from d_LPC1 down to 0, if
+ abs(a32_Q16[k][k]) > 65520, the filter is unstable and the
+ recurrence stops.
+Otherwise, the row k1 of a32_Q16 is computed from row k as
+
+Here, rc_Q30[k] are the reflection coefficients.
+div_Q30[k] is the denominator for each iteration, and mul_Q16[k] is its
+ multiplicative inverse.
+inv_Qb1[k], which ranges from 16384 to 32767, is a lowprecision version of
+ that inverse (with b1[k] fractional bits, where b1[k] ranges from 3 to 14).
+err_Q29[k] is the residual error, ranging from 32392 to 32763, which is used
+ to improve the accuracy.
+t_Q16[k1][n], 0 <= n < k, are the numerators for the
+ next row of coefficients in the recursion, and a32_Q16[k1][n] is the final
+ version of that row.
+Every multiply in this procedure except the one used to compute mul_Q16[k]
+ requires more than 32 bits of precision, but otherwise all intermediate
+ results fit in 32 bits or less.
+In practice, because each row only depends on the next one, an implementation
+ does not need to store them all.
+If abs(a32_Q16[k][k]) <= 65520 for
+ 0 <= k < d_LPC, then the filter is considered stable.
+
+
+On round i, 1 <= i <= 18, if the filter passes this
+ stability check, then this procedure stops, and the final LPC coefficients to
+ use for reconstruction are
+
+Otherwise, a round of bandwidth expansion is applied using the same procedure
+ as in , with
+
+If, after the 18th round, the filter still fails the stability check, then
+ a_Q12[k] is set to 0 for all k.
+
+
+
+
+
+
+
+After the normalized LSF indices and, for 20 ms frames, the LSF
+ interpolation index, voiced frames (see )
+ include additional LongTerm Prediction (LTP) parameters.
+There is one primary lag index for each SILK frame, but this is refined to
+ produce a separate lag index per subframe using a vector quantizer.
+Each subframe also gets its own prediction gain coefficient.
+
+
+
+
+The primary lag index is coded either relative to the primary lag of the prior
+ frame or as an absolute index.
+Like the quantization gains, the first LBRR frame, an LBRR frame where the
+ previous LBRR frame was not coded, and the first regular SILK frame in each
+ channel of an Opus frame all code the pitch lag as an absolute index.
+When the most recent coded frame in the current channel was not voiced, this
+ also forces absolute coding.
+In particular, unlike an LBRR frame where the previous frame is not coded, in a
+ 60 ms stereo Opus frame, if the first and third regular SILK frames
+ in the side channel are coded, voiced frames, but the second is not coded, the
+ third still uses relative coding.
+
+
+With absolute coding, the primary pitch lag may range from 2 ms
+ (inclusive) up to 18 ms (exclusive), corresponding to pitches from
+ 500 Hz down to 55.6 Hz, respectively.
+It is comprised of a high part and a low part, where the decoder reads the high
+ part using the 32entry codebook in
+ and the low part using the codebook corresponding to the current audio
+ bandwidth from .
+The final primary pitch lag is then
+
+ where lag_high is the high part, lag_low is the low part, and lag_scale
+ and lag_min are the values from the "Scale" and "Minimum Lag" columns of
+ , respectively.
+
+
+
+PDF
+{3, 3, 6, 11, 21, 30, 32, 19,
+ 11, 10, 12, 13, 13, 12, 11, 9,
+ 8, 7, 6, 4, 2, 2, 2, 1,
+ 1, 1, 1, 1, 1, 1, 1, 1}/256
+
+
+
+Audio Bandwidth
+PDF
+Scale
+Minimum Lag
+Maximum Lag
+NB{64, 64, 64, 64}/256416144
+MB{43, 42, 43, 43, 42, 43}/256624216
+WB{32, 32, 32, 32, 32, 32, 32, 32}/256832288
+
+
+
+All frames that do not use absolute coding for the primary lag index use
+ relative coding instead.
+The decoder reads a single delta value using the 21entry PDF in
+ .
+If the resulting value is zero, it falls back to the absolute coding procedure
+ from the prior paragraph.
+Otherwise, the final primary pitch lag is then
+
+ where lag_prev is the primary pitch lag from the most recent frame in the same
+ channel and delta_lag_index is the value just decoded.
+This allows a perframe change in the pitch lag of 8 to +11 samples.
+The decoder does no clamping at this point, so this value can fall outside the
+ range of 2 ms to 18 ms, and the decoder must use this unclamped
+ value when using relative coding in the next SILK frame (if any).
+However, because an Opus frame can use relative coding for at most two
+ consecutive SILK frames, integer overflow should not be an issue.
+
+
+
+PDF
+{46, 2, 2, 3, 4, 6, 10, 15,
+ 26, 38, 30, 22, 15, 10, 7, 6,
+ 4, 4, 2, 2, 2}/256
+
+
+
+After the primary pitch lag, a "pitch contour", stored as a single entry from
+ one of four small VQ codebooks, gives lag offsets for each subframe in the
+ current SILK frame.
+The codebook index is decoded using one of the PDFs in
+ depending on the current frame size
+ and audio bandwidth.
+ through
+ give the corresponding offsets
+ to apply to the primary pitch lag for each subframe given the decoded codebook
+ index.
+
+
+
+Audio Bandwidth
+SILK Frame Size
+Codebook Size
+PDF
+NB10 ms3
+{143, 50, 63}/256
+NB20 ms11
+{68, 12, 21, 17, 19, 22, 30, 24,
+ 17, 16, 10}/256
+MB or WB10 ms12
+{91, 46, 39, 19, 14, 12, 8, 7,
+ 6, 5, 5, 4}/256
+MB or WB20 ms34
+{33, 22, 18, 16, 15, 14, 14, 13,
+ 13, 10, 9, 9, 8, 6, 6, 6,
+ 5, 4, 4, 4, 3, 3, 3, 2,
+ 2, 2, 2, 2, 2, 2, 1, 1,
+ 1, 1}/256
+
+
+
+Index
+Subframe Offsets
+0 0 0
+1 1 0
+2 0 1
+
+
+
+Index
+Subframe Offsets
+ 0 0 0 0 0
+ 1 2 1 0 1
+ 21 0 1 2
+ 31 0 0 1
+ 41 0 0 0
+ 5 0 0 0 1
+ 6 0 0 1 1
+ 7 1 1 0 0
+ 8 1 0 0 0
+ 9 0 0 0 1
+10 1 0 0 1
+
+
+
+Index
+Subframe Offsets
+ 0 0 0
+ 1 0 1
+ 2 1 0
+ 31 1
+ 4 1 1
+ 51 2
+ 6 2 1
+ 72 2
+ 8 2 2
+ 92 3
+10 3 2
+113 3
+
+
+
+Index
+Subframe Offsets
+ 0 0 0 0 0
+ 1 0 0 1 1
+ 2 1 1 0 0
+ 31 0 0 0
+ 4 0 0 0 1
+ 5 1 0 0 0
+ 61 0 0 1
+ 7 0 0 0 1
+ 81 0 1 2
+ 9 1 0 0 1
+102 1 1 2
+11 2 1 0 1
+122 0 0 2
+132 0 1 3
+14 2 1 1 2
+153 1 1 3
+16 2 0 0 2
+17 3 1 0 2
+183 1 2 4
+194 1 1 4
+20 3 1 1 3
+214 1 2 5
+22 4 2 1 3
+23 4 1 1 4
+245 1 2 6
+25 5 2 1 4
+266 2 2 6
+275 2 2 5
+28 6 2 1 5
+297 2 3 8
+30 6 2 2 6
+31 5 2 2 5
+32 8 3 2 7
+339 3 3 9
+
+
+
+The final pitch lag for each subframe is assembled in silk_decode_pitch()
+ (silk_decode_pitch.c).
+Let lag be the primary pitch lag for the current SILK frame, contour_index be
+ index of the VQ codebook, and lag_cb[contour_index][k] be the corresponding
+ entry of the codebook from the appropriate table given above for the k'th
+ subframe.
+Then the final pitch lag for that subframe is
+
+ where lag_min and lag_max are the values from the "Minimum Lag" and
+ "Maximum Lag" columns of ,
+ respectively.
+
+
+
+
+
+
+SILK can use a separate 5tap pitch filter for each subframe.
+It selects the filter to use from one of three codebooks.
+The three codebooks each represent different ratedistortion tradeoffs, with
+ average rates of 1.61 bits/subframe, 3.68 bits/subframe, and
+ 4.85 bits/subframe, respectively.
+
+
+
+The importance of the filter coefficients generally depends on two factors: the
+ periodicity of the signal and relative energy between the current subframe and
+ the signal from one period earlier.
+Greater periodicity and decaying energy both lead to more important filter
+ coefficients, and thus should be coded with lower distortion and higher rate.
+These properties are relatively stable over the duration of a single SILK
+ frame, hence all of the subframes in a SILK frame must choose their filter
+ from the same codebook.
+This is signaled with an explicitlycoded "periodicity index".
+This immediately follows the subframe pitch lags, and is coded using the
+ 3entry PDF from .
+
+
+
+PDF
+{77, 80, 99}/256
+
+
+
+The index of the filter to use for each subframe follows.
+They are all coded using the PDF from
+ corresponding to the periodicity index.
+ through
+ contain the corresponding filter taps
+ as signed Q7 integers.
+
+
+
+Periodicity Index
+Codebook Size
+PDF
+08{185, 15, 13, 13, 9, 9, 6, 6}/256
+116{57, 34, 21, 20, 15, 13, 12, 13,
+ 10, 10, 9, 10, 9, 8, 7, 8}/256
+232{15, 16, 14, 12, 12, 12, 11, 11,
+ 11, 10, 9, 9, 9, 9, 8, 8,
+ 8, 8, 7, 7, 6, 6, 5, 4,
+ 5, 4, 4, 4, 3, 4, 3, 2}/256
+
+
+
+Index
+Filter Taps (Q7)
+ 0
+ 4 6 24 7 5
+ 1
+ 0 0 2 0 0
+ 2
+ 12 28 41 13 4
+ 3
+ 9 15 42 25 14
+ 4
+ 1 2 62 41 9
+ 5
+10 37 65 4 3
+ 6
+ 6 4 66 7 8
+ 7
+ 16 14 38 3 33
+
+
+
+Index
+Filter Taps (Q7)
+
+ 0
+ 13 22 39 23 12
+ 1
+ 1 36 64 27 6
+ 2
+ 7 10 55 43 17
+ 3
+ 1 1 8 1 1
+ 4
+ 6 11 74 53 9
+ 5
+12 55 76 12 8
+ 6
+ 3 3 93 27 4
+ 7
+ 26 39 59 3 8
+ 8
+ 2 0 77 11 9
+ 9
+ 8 22 44 6 7
+10
+ 40 9 26 3 9
+11
+ 7 20 101 7 4
+12
+ 3 8 42 26 0
+13
+15 33 68 2 23
+14
+ 2 55 46 2 15
+15
+ 3 1 21 16 41
+
+
+
+Index
+Filter Taps (Q7)
+ 0
+ 6 27 61 39 5
+ 1
+11 42 88 4 1
+ 2
+ 2 60 65 6 4
+ 3
+ 1 5 73 56 1
+ 4
+ 9 19 94 29 9
+ 5
+ 0 12 99 6 4
+ 6
+ 8 19 102 46 13
+ 7
+ 3 2 13 3 2
+ 8
+ 9 21 84 72 18
+ 9
+11 46 104 22 8
+10
+ 18 38 48 23 0
+11
+16 70 83 21 11
+12
+ 5 11 117 22 8
+13
+ 6 23 117 12 3
+14
+ 3 8 95 28 4
+15
+10 15 77 60 15
+16
+ 1 4 124 2 4
+17
+ 3 38 84 24 25
+18
+ 2 13 42 13 31
+19
+ 21 4 56 46 1
+20
+ 1 35 79 13 19
+21
+ 7 65 88 9 14
+22
+ 20 4 81 49 29
+23
+ 20 0 75 3 17
+24
+ 5 9 44 92 8
+25
+ 1 3 22 69 31
+26
+ 6 95 41 12 5
+27
+ 39 67 16 4 1
+28
+ 0 6 120 55 36
+29
+13 44 122 4 24
+30
+ 81 5 11 3 7
+31
+ 2 0 9 10 88
+
+
+
+
+
+
+In some circumstances an LTP scaling parameter appears after the LTP filter
+ coefficients.
+This allows the encoder to trade off the prediction gain between
+ packets against the recovery time after packet loss.
+Like the quantization gains, only the first LBRR frame in an Opus frame,
+ an LBRR frame where the prior LBRR frame was not coded, and the first regular
+ SILK frame in each channel of an Opus frame include this field, and, like all
+ of the other LTP parameters, only for frames that are also voiced.
+Unlike absolutecoding for pitch lags, a regular SILK frame other than the
+ first one in a channel will not include this field even if the prior frame was
+ not voiced.
+
+
+If present, the value is coded using the 3entry PDF in
+ .
+The three possible values represent Q14 scale factors of 15565, 12288, and
+ 8192, respectively (corresponding to approximately 0.95, 0.75, and 0.5).
+Frames that do not code the scaling parameter use the default factor of 15565
+ (approximately 0.95).
+
+
+
+PDF
+{128, 64, 64}/256
+
+
+
+
+
+
+
+
+SILK uses a linear congruential generator (LCG) to inject pseudorandom noise
+ into the quantized excitation.
+To ensure synchronization of this process between the encoder and decoder, each
+ SILK frame stores a 2bit seed after the LTP parameters (if any).
+The encoder may consider the choice of this seed during quantization, meaning
+ the flexibility to choose the LCG seed can reduce distortion.
+The seed is decoded with the uniform 4entry PDF in
+ , yielding a value between 0 and 3, inclusive.
+
+
+
+PDF
+{64, 64, 64, 64}/256
+
+
+
+
+
+
+SILK codes the excitation using a modified version of the Pyramid Vector
+ Quantization (PVQ) codebook .
+The PVQ codebook is designed for Laplacedistributed values and consists of all
+ sums of K signed, unit pulses in a vector of dimension N, where two pulses at
+ the same position are required to have the same sign.
+Thus the codebook includes all integer codevectors y of dimension N that
+ satisfy
+
+Unlike regular PVQ, SILK uses a variablelength, rather than fixedlength,
+ encoding.
+This encoding is better suited to the more Gaussianlike distribution of the
+ coefficient magnitudes and the nonuniform distribution of their signs (caused
+ by the quantization offset described below).
+SILK also handles large codebooks by coding the least significant bits (LSb's)
+ of each coefficient directly.
+This adds a small coding efficiency loss, but greatly reduces the computation
+ time and ROM size required for decoding, as implemented in
+ silk_decode_pulses() (silk_decode_pulses.c).
+
+
+
+SILK fixes the dimension of the codebook to N = 16.
+The excitation is made up of a number of "shell blocks", each 16 samples in
+ size.
+ lists the number of shell blocks
+ required for a SILK frame for each possible audio bandwidth and frame size.
+10 ms MB frames nominally contain 120 samples (10 ms at
+ 12 kHz), which is not a multiple of 16.
+This is handled by coding 8 shell blocks (128 samples) and discarding the final
+ 8 samples of the last block.
+The decoder contains no special case that prevents an encoder from placing
+ pulses in these samples, and they must be correctly parsed from the bitstream
+ if present, but they are otherwise ignored.
+
+
+
+Audio Bandwidth
+Frame Size
+Number of Shell Blocks
+NB10 ms5
+MB10 ms8
+WB10 ms10
+NB20 ms10
+MB20 ms15
+WB20 ms20
+
+
+
+
+The first symbol in the excitation is a "rate level", which is an index from 0
+ to 8, inclusive, coded using the PDF in
+ corresponding to the signal type of the current frame (from
+ ).
+The rate level selects the PDF used to decode the number of pulses in
+ the individual shell blocks.
+It does not directly convey any information about the bitrate or the number of
+ pulses itself, but merely changes the probability of the symbols in
+ .
+Level 0 provides a more efficient encoding at low rates generally, and
+ level 8 provides a more efficient encoding at high rates generally,
+ though the most efficient level for a particular SILK frame may depend on the
+ exact distribution of the coded symbols.
+An encoder should, but is not required to, use the most efficient rate level.
+
+
+
+Signal Type
+PDF
+Inactive or Unvoiced
+{15, 51, 12, 46, 45, 13, 33, 27, 14}/256
+Voiced
+{33, 30, 36, 17, 34, 49, 18, 21, 18}/256
+
+
+
+
+
+
+The total number of pulses in each of the shell blocks follows the rate level.
+The pulse counts for all of the shell blocks are coded consecutively, before
+ the content of any of the blocks.
+Each block may have anywhere from 0 to 16 pulses, inclusive, coded using the
+ 18entry PDF in corresponding to the
+ rate level from .
+The special value 17 indicates that this block has one or more additional
+ LSb's to decode for each coefficient.
+If the decoder encounters this value, it decodes another value for the actual
+ pulse count of the block, but uses the PDF corresponding to the special rate
+ level 9 instead of the normal rate level.
+This process repeats until the decoder reads a value less than 17, and it then
+ sets the number of extra LSb's used to the number of 17's decoded for that
+ block.
+If it reads the value 17 ten times, then the next iteration uses the special
+ rate level 10 instead of 9.
+The probability of decoding a 17 when using the PDF for rate level 10 is
+ zero, ensuring that the number of LSb's for a block will not exceed 10.
+The cumulative distribution for rate level 10 is just a shifted version of
+ that for 9 and thus does not require any additional storage.
+
+
+
+Rate Level
+PDF
+0
+{131, 74, 25, 8, 3, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1}/256
+1
+{58, 93, 60, 23, 7, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1}/256
+2
+{43, 51, 46, 33, 24, 16, 11, 8, 6, 3, 3, 3, 2, 1, 1, 2, 1, 2}/256
+3
+{17, 52, 71, 57, 31, 12, 5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1}/256
+4
+{6, 21, 41, 53, 49, 35, 21, 11, 6, 3, 2, 2, 1, 1, 1, 1, 1, 1}/256
+5
+{7, 14, 22, 28, 29, 28, 25, 20, 17, 13, 11, 9, 7, 5, 4, 4, 3, 10}/256
+6
+{2, 5, 14, 29, 42, 46, 41, 31, 19, 11, 6, 3, 2, 1, 1, 1, 1, 1}/256
+7
+{1, 2, 4, 10, 19, 29, 35, 37, 34, 28, 20, 14, 8, 5, 4, 2, 2, 2}/256
+8
+{1, 2, 2, 5, 9, 14, 20, 24, 27, 28, 26, 23, 20, 15, 11, 8, 6, 15}/256
+9
+{1, 1, 1, 6, 27, 58, 56, 39, 25, 14, 10, 6, 3, 3, 2, 1, 1, 2}/256
+10
+{2, 1, 6, 27, 58, 56, 39, 25, 14, 10, 6, 3, 3, 2, 1, 1, 2, 0}/256
+
+
+
+
+
+
+The locations of the pulses in each shell block follows the pulse counts,
+ as decoded by silk_shell_decoder() (silk_shell_coder.c).
+As with the pulse counts, these locations are coded for all the shell blocks
+ before any of the remaining information for each block.
+Unlike many other codecs, SILK places no restriction on the distribution of
+ pulses within a shell block.
+All of the pulses may be placed in a single location, or each one in a unique
+ location, or anything in between.
+
+
+
+The location of pulses is coded by recursively partitioning each block into
+ halves, and coding how many pulses fall on the left side of the split.
+All remaining pulses must fall on the right side of the split.
+The process then recurses into the left half, and after that returns, the
+ right half (preorder traversal).
+The PDF to use is chosen by the size of the current partition (16, 8, 4, or 2)
+ and the number of pulses in the partition (1 to 16, inclusive).
+ through
+ list the PDFs used for each partition
+ size and pulse count.
+This process skips partitions without any pulses, i.e., where the initial pulse
+ count from was zero, or where the split in
+ the prior level indicated that all of the pulses fell on the other side.
+These partitions have nothing to code, so they require no PDF.
+
+
+
+Pulse Count
+PDF
+ 1{126, 130}/256
+ 2{56, 142, 58}/256
+ 3{25, 101, 104, 26}/256
+ 4{12, 60, 108, 64, 12}/256
+ 5{7, 35, 84, 87, 37, 6}/256
+ 6{4, 20, 59, 86, 63, 21, 3}/256
+ 7{3, 12, 38, 72, 75, 42, 12, 2}/256
+ 8{2, 8, 25, 54, 73, 59, 27, 7, 1}/256
+ 9{2, 5, 17, 39, 63, 65, 42, 18, 4, 1}/256
+10{1, 4, 12, 28, 49, 63, 54, 30, 11, 3, 1}/256
+11{1, 4, 8, 20, 37, 55, 57, 41, 22, 8, 2, 1}/256
+12{1, 3, 7, 15, 28, 44, 53, 48, 33, 16, 6, 1, 1}/256
+13{1, 2, 6, 12, 21, 35, 47, 48, 40, 25, 12, 5, 1, 1}/256
+14{1, 1, 4, 10, 17, 27, 37, 47, 43, 33, 21, 9, 4, 1, 1}/256
+15{1, 1, 1, 8, 14, 22, 33, 40, 43, 38, 28, 16, 8, 1, 1, 1}/256
+16{1, 1, 1, 1, 13, 18, 27, 36, 41, 41, 34, 24, 14, 1, 1, 1, 1}/256
+
+
+
+Pulse Count
+PDF
+ 1{127, 129}/256
+ 2{53, 149, 54}/256
+ 3{22, 105, 106, 23}/256
+ 4{11, 61, 111, 63, 10}/256
+ 5{6, 35, 86, 88, 36, 5}/256
+ 6{4, 20, 59, 87, 62, 21, 3}/256
+ 7{3, 13, 40, 71, 73, 41, 13, 2}/256
+ 8{3, 9, 27, 53, 70, 56, 28, 9, 1}/256
+ 9{3, 8, 19, 37, 57, 61, 44, 20, 6, 1}/256
+10{3, 7, 15, 28, 44, 54, 49, 33, 17, 5, 1}/256
+11{1, 7, 13, 22, 34, 46, 48, 38, 28, 14, 4, 1}/256
+12{1, 1, 11, 22, 27, 35, 42, 47, 33, 25, 10, 1, 1}/256
+13{1, 1, 6, 14, 26, 37, 43, 43, 37, 26, 14, 6, 1, 1}/256
+14{1, 1, 4, 10, 20, 31, 40, 42, 40, 31, 20, 10, 4, 1, 1}/256
+15{1, 1, 3, 8, 16, 26, 35, 38, 38, 35, 26, 16, 8, 3, 1, 1}/256
+16{1, 1, 2, 6, 12, 21, 30, 36, 38, 36, 30, 21, 12, 6, 2, 1, 1}/256
+
+
+
+Pulse Count
+PDF
+ 1{127, 129}/256
+ 2{49, 157, 50}/256
+ 3{20, 107, 109, 20}/256
+ 4{11, 60, 113, 62, 10}/256
+ 5{7, 36, 84, 87, 36, 6}/256
+ 6{6, 24, 57, 82, 60, 23, 4}/256
+ 7{5, 18, 39, 64, 68, 42, 16, 4}/256
+ 8{6, 14, 29, 47, 61, 52, 30, 14, 3}/256
+ 9{1, 15, 23, 35, 51, 50, 40, 30, 10, 1}/256
+10{1, 1, 21, 32, 42, 52, 46, 41, 18, 1, 1}/256
+11{1, 6, 16, 27, 36, 42, 42, 36, 27, 16, 6, 1}/256
+12{1, 5, 12, 21, 31, 38, 40, 38, 31, 21, 12, 5, 1}/256
+13{1, 3, 9, 17, 26, 34, 38, 38, 34, 26, 17, 9, 3, 1}/256
+14{1, 3, 7, 14, 22, 29, 34, 36, 34, 29, 22, 14, 7, 3, 1}/256
+15{1, 2, 5, 11, 18, 25, 31, 35, 35, 31, 25, 18, 11, 5, 2, 1}/256
+16{1, 1, 4, 9, 15, 21, 28, 32, 34, 32, 28, 21, 15, 9, 4, 1, 1}/256
+
+
+
+Pulse Count
+PDF
+ 1{128, 128}/256
+ 2{42, 172, 42}/256
+ 3{21, 107, 107, 21}/256
+ 4{12, 60, 112, 61, 11}/256
+ 5{8, 34, 86, 86, 35, 7}/256
+ 6{8, 23, 55, 90, 55, 20, 5}/256
+ 7{5, 15, 38, 72, 72, 36, 15, 3}/256
+ 8{6, 12, 27, 52, 77, 47, 20, 10, 5}/256
+ 9{6, 19, 28, 35, 40, 40, 35, 28, 19, 6}/256
+10{4, 14, 22, 31, 37, 40, 37, 31, 22, 14, 4}/256
+11{3, 10, 18, 26, 33, 38, 38, 33, 26, 18, 10, 3}/256
+12{2, 8, 13, 21, 29, 36, 38, 36, 29, 21, 13, 8, 2}/256
+13{1, 5, 10, 17, 25, 32, 38, 38, 32, 25, 17, 10, 5, 1}/256
+14{1, 4, 7, 13, 21, 29, 35, 36, 35, 29, 21, 13, 7, 4, 1}/256
+15{1, 2, 5, 10, 17, 25, 32, 36, 36, 32, 25, 17, 10, 5, 2, 1}/256
+16{1, 2, 4, 7, 13, 21, 28, 34, 36, 34, 28, 21, 13, 7, 4, 2, 1}/256
+
+
+
+
+
+
+After the decoder reads the pulse locations for all blocks, it reads the LSb's
+ (if any) for each block in turn.
+Inside each block, it reads all the LSb's for each coefficient in turn, even
+ those where no pulses were allocated, before proceeding to the next one.
+They are coded from most significant to least significant, and they all use the
+ PDF in .
+
+
+
+PDF
+{136, 120}/256
+
+
+
+The number of LSb's read for each coefficient in a block is determined in
+ .
+The magnitude of the coefficient is initially equal to the number of pulses
+ placed at that location in .
+As each LSb is decoded, the magnitude is doubled, and then the value of the LSb
+ added to it, to obtain an updated magnitude.
+
+
+
+
+
+After decoding the pulse locations and the LSb's, the decoder knows the
+ magnitude of each coefficient in the excitation.
+It then decodes a sign for all coefficients with a nonzero magnitude, using
+ one of the PDFs from .
+If the value decoded is 0, then the coefficient magnitude is negated.
+Otherwise, it remains positive.
+
+
+
+The decoder chooses the PDF for the sign based on the signal type and
+ quantization offset type (from ) and the
+ number of pulses in the block (from ).
+The number of pulses in the block does not take into account any LSb's.
+If a block has no pulses, even if it has some LSb's (and thus may have some
+ nonzero coefficients), then no signs are decoded.
+In that case, any nonzero coefficients use a positive sign.
+
+
+
+Signal Type
+Quantization Offset Type
+Pulse Count
+PDF
+InactiveLow1{207, 49}/256
+InactiveLow2{189, 67}/256
+InactiveLow3{179, 77}/256
+InactiveLow4{174, 82}/256
+InactiveLow5{163, 93}/256
+InactiveLow6 or more{157, 99}/256
+InactiveHigh1{245, 11}/256
+InactiveHigh2{238, 18}/256
+InactiveHigh3{232, 24}/256
+InactiveHigh4{225, 31}/256
+InactiveHigh5{220, 36}/256
+InactiveHigh6 or more{211, 45}/256
+UnvoicedLow1{210, 46}/256
+UnvoicedLow2{190, 66}/256
+UnvoicedLow3{178, 78}/256
+UnvoicedLow4{169, 87}/256
+UnvoicedLow5{162, 94}/256
+UnvoicedLow6 or more{152, 104}/256
+UnvoicedHigh1{242, 14}/256
+UnvoicedHigh2{235, 21}/256
+UnvoicedHigh3{224, 32}/256
+UnvoicedHigh4{214, 42}/256
+UnvoicedHigh5{205, 51}/256
+UnvoicedHigh6 or more{190, 66}/256
+VoicedLow1{162, 94}/256
+VoicedLow2{152, 104}/256
+VoicedLow3{147, 109}/256
+VoicedLow4{144, 112}/256
+VoicedLow5{141, 115}/256
+VoicedLow6 or more{138, 118}/256
+VoicedHigh1{203, 53}/256
+VoicedHigh2{187, 69}/256
+VoicedHigh3{176, 80}/256
+VoicedHigh4{168, 88}/256
+VoicedHigh5{161, 95}/256
+VoicedHigh6 or more{154, 102}/256
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+The CELT layer is decoded based on the following symbols and sets of symbols:
+
+
+
+Symbol(s)
+PDF
+Condition
+silence{32767, 1}/32768
+postfilter{1, 1}/2
+octaveuniform (6)postfilter
+periodraw bits (4+octave)postfilter
+gainraw bits (3)postfilter
+tapset{2, 1, 1}/4postfilter
+transient{7, 1}/8
+intra{7, 1}/8
+coarse energy
+tf_change
+tf_select{1, 1}/2
+spread{7, 2, 21, 2}/32
+dyn. alloc.
+alloc. trim{2, 2, 5, 10, 22, 46, 22, 10, 5, 2, 2}/128
+skip{1, 1}/2
+intensityuniform
+dual{1, 1}/2
+fine energy
+residual
+anticollapse{1, 1}/2
+finalize
+Order of the symbols in the CELT section of the bitstream.
+
+
+
+The decoder extracts information from the rangecoded bitstream in the order
+described in the figure above. In some circumstances, it is
+possible for a decoded value to be out of range due to a very small amount of redundancy
+in the encoding of large integers by the range coder.
+In that case, the decoder should assume there has been an error in the coding,
+decoding, or transmission and SHOULD take measures to conceal the error and/or report
+to the application that a problem has occurred.
+
+
+
+
+The "transient" flag encoded in the bitstream has a probability of 1/8.
+When it is set, then the MDCT coefficients represent multiple
+short MDCTs in the frame. When not set, the coefficients represent a single
+long MDCT for the frame. In addition to the global transient flag is a perband
+binary flag to change the timefrequency (tf) resolution independently in each band. The
+change in tf resolution is defined in tf_select_table[][] in celt.c and depends
+on the frame size, whether the transient flag is set, and the value of tf_select.
+The tf_select flag uses a 1/2 probability, but is only decoded
+if it can have an impact on the result knowing the value of all perband
+tf_change flags.
+
+
+
+
+
+
+It is important to quantize the energy with sufficient resolution because
+any energy quantization error cannot be compensated for at a later
+stage. Regardless of the resolution used for encoding the shape of a band,
+it is perceptually important to preserve the energy in each band. CELT uses a
+threestep coarsefinefine strategy for encoding the energy in the base2 log
+domain, as implemented in quant_bands.c
+
+
+
+Coarse quantization of the energy uses a fixed resolution of 6 dB
+(integer part of base2 log). To minimize the bitrate, prediction is applied
+both in time (using the previous frame) and in frequency (using the previous
+bands). The part of the prediction that is based on the
+previous frame can be disabled, creating an "intra" frame where the energy
+is coded without reference to prior frames. The decoder first reads the intra flag
+to determine what prediction is used.
+The 2D ztransform of
+the prediction filter is:
+
+where b is the band index and l is the frame index. The prediction coefficients
+applied depend on the frame size in use when not using intra energy and are alpha=0, beta=4915/32768
+when using intra energy.
+The timedomain prediction is based on the final fine quantization of the previous
+frame, while the frequency domain (within the current frame) prediction is based
+on coarse quantization only (because the fine quantization has not been computed
+yet). The prediction is clamped internally so that fixed point implementations with
+limited dynamic range do not suffer desynchronization.
+We approximate the ideal
+probability distribution of the prediction error using a Laplace distribution
+with separate parameters for each frame size in intra and interframe modes. The
+coarse energy quantization is performed by unquant_coarse_energy() and
+unquant_coarse_energy_impl() (quant_bands.c). The encoding of the Laplacedistributed values is
+implemented in ec_laplace_decode() (laplace.c).
+
+
+
+
+
+
+The number of bits assigned to fine energy quantization in each band is determined
+by the bit allocation computation described in .
+Let B_i be the number of fine energy bits
+for band i; the refinement is an integer f in the range [0,2**B_i1]. The mapping between f
+and the correction applied to the coarse energy is equal to (f+1/2)/2**B_i  1/2. Fine
+energy quantization is implemented in quant_fine_energy() (quant_bands.c).
+
+
+When some bits are left "unused" after all other flags have been decoded, these bits
+are assigned to a "final" step of fine allocation. In effect, these bits are used
+to add one extra fine energy bit per band per channel. The allocation process
+determines two "priorities" for the final fine bits.
+Any remaining bits are first assigned only to bands of priority 0, starting
+from band 0 and going up. If all bands of priority 0 have received one bit per
+channel, then bands of priority 1 are assigned an extra bit per channel,
+starting from band 0. If any bits are left after this, they are left unused.
+This is implemented in unquant_energy_finalise() (quant_bands.c).
+
+
+
+
+
+
+
+Many codecs transmit significant amounts of side information for
+the purpose of controlling bit allocation within a frame. Often this
+side information controls bit usage indirectly and must be carefully
+selected to achieve the desired rate constraints.
+
+The bandenergy normalized structure of Opus MDCT mode ensures that a
+constant bit allocation for the shape content of a band will result in a
+roughly constant tone to noise ratio, which provides for fairly consistent
+perceptual performance. The effectiveness of this approach is the result of
+two factors: that the band energy, which is understood to be perceptually
+important on its own, is always preserved regardless of the shape precision, and because
+the constant tonetonoise ratio implies a constant intraband noise to masking ratio.
+Intraband masking is the strongest of the perceptual masking effects. This structure
+means that the ideal allocation is more consistent from frame to frame than
+it is for other codecs without an equivalent structure.
+
+Because the bit allocation is used to drive the decoding of the rangecoder
+stream, it MUST be recovered exactly so that identical coding decisions are
+made in the encoder and decoder. Any deviation from the reference's resulting
+bit allocation will result in corrupted output, though implementers are
+free to implement the procedure in any way which produces identical results.
+
+Because all of the information required to decode a frame must be derived
+from that frame alone in order to retain robustness to packet loss, the
+overhead of explicitly signaling the allocation would be considerable,
+especially for lowlatency (small frame size) applications,
+even though the allocation is relatively static.
+
+For this reason, in the MDCT mode Opus uses a primarily implicit bit
+allocation. The available bitstream capacity is known in advance to both
+the encoder and decoder without additional signaling, ultimately from the
+packet sizes expressed by a higherlevel protocol. Using this information
+the codec interpolates an allocation from a hardcoded table.
+
+While the bandenergy structure effectively models intraband masking,
+it ignores the weaker interband masking, bandtemporal masking, and
+other less significant perceptual effects. While these effects can
+often be ignored, they can become significant for particular samples. One
+mechanism available to encoders would be to simply increase the overall
+rate for these frames, but this is not possible in a constant rate mode
+and can be fairly inefficient. As a result three explicitly signaled
+mechanisms are provided to alter the implicit allocation:
+
+
+
+Band boost
+Allocation trim
+Band skipping
+
+
+
+The first of these mechanisms, band boost, allows an encoder to boost
+the allocation in specific bands. The second, allocation trim, works by
+biasing the overall allocation towards higher or lower frequency bands. The third, band
+skipping, selects which lowprecision high frequency bands
+will be allocated no shape bits at all.
+
+In stereo mode there are two additional parameters
+potentially coded as part of the allocation procedure: a parameter to allow the
+selective elimination of allocation for the 'side' in jointly coded bands,
+and a flag to deactivate joint coding. These values are not signaled if
+they would be meaningless in the overall context of the allocation.
+
+Because every signaled adjustment increases overhead and implementation
+complexity, none were included speculatively: the reference encoder makes use
+of all of these mechanisms. While the decision logic in the reference was
+found to be effective enough to justify the overhead and complexity, further
+analysis techniques may be discovered which increase the effectiveness of these
+parameters. As with other signaled parameters, an encoder is free to choose the
+values in any manner, but unless a technique is known to deliver superior
+perceptual results the methods used by the reference implementation should be
+used.
+
+The allocation process consists of the following steps: determining the perband
+maximum allocation vector, decoding the boosts, decoding the tilt, determining
+the remaining capacity of the frame, searching the mode table for the
+entry nearest but not exceeding the available space (subject to the tilt, boosts, band
+maximums, and band minimums), linear interpolation, reallocation of
+unused bits with concurrent skip decoding, determination of the
+fineenergy vs. shape split, and final reallocation. This process results
+in a perband shape allocation (in 1/8th bit units), a perband fineenergy
+allocation (in 1 bit per channel units), a set of band priorities for
+controlling the use of remaining bits at the end of the frame, and a
+remaining balance of unallocated space, which is usually zero except
+at very high rates.
+
+The maximum allocation vector is an approximation of the maximum space
+that can be used by each band for a given mode. The value is
+approximate because the shape encoding is variable rate (due
+to entropy coding of splitting parameters). Setting the maximum too low reduces the
+maximum achievable quality in a band while setting it too high
+may result in waste: bitstream capacity available at the end
+of the frame which can not be put to any use. The maximums
+specified by the codec reflect the average maximum. In the reference
+the maximums are provided in partially computed form, in order to fit in less
+memory as a static table (XXX cache.caps). Implementations are expected
+to simply use the same table data, but the procedure for generating
+this table is included in rate.c as part of compute_pulse_cache().
+
+To convert the values in cache.caps into the actual maximums: first
+set nbBands to the maximum number of bands for this mode, and stereo to
+zero if stereo is not in use and one otherwise. For each band set N
+to the number of MDCT bins covered by the band (for one channel), set LM
+to the shift value for the frame size (e.g. 0 for 120, 1 for 240, 3 for 480),
+then set i to nbBands*(2*LM+stereo). Then set the maximum for the band to
+the ith index of cache.caps + 64 and multiply by the number of channels
+in the current frame (one or two) and by N, then divide the result by 4
+using truncating integer division. The resulting vector will be called
+cap[]. The elements fit in signed 16bit integers but do not fit in 8 bits.
+This procedure is implemented in the reference in the function init_caps() in celt.c.
+
+
+The band boosts are represented by a series of binary symbols which
+are coded with very low probability. Each band can potentially be boosted
+multiple times, subject to the frame actually having enough room to obey
+the boost and having enough room to code the boost symbol. The default
+coding cost for a boost starts out at six bits, but subsequent boosts
+in a band cost only a single bit and every time a band is boosted the
+initial cost is reduced (down to a minimum of two). Since the initial
+cost of coding a boost is 6 bits, the coding cost of the boost symbols when
+completely unused is 0.48 bits/frame for a 21 band mode (21*log2(11/2**6)).
+
+To decode the band boosts: First set 'dynalloc_logp' to 6, the initial
+amount of storage required to signal a boost in bits, 'total_bits' to the
+size of the frame in 8th bits, 'total_boost' to zero, and 'tell' to the total number
+of 8th bits decoded
+so far. For each band from the coding start (0 normally, but 17 in hybrid mode)
+to the coding end (which changes depending on the signaled bandwidth): set 'width'
+to the number of MDCT bins in this band for all channels. Take the larger of width
+and 64, then the minimum of that value and the width times eight and set 'quanta'
+to the result. This represents a boost step size of six bits subject to limits
+of 1/bit/sample and 1/8th bit/sample. Set 'boost' to zero and 'dynalloc_loop_logp'
+to dynalloc_logp. While dynalloc_loop_log (the current worst case symbol cost) in
+8th bits plus tell is less than total_bits plus total_boost and boost is less than cap[] for this
+band: Decode a bit from the bitstream with a with dynalloc_loop_logp as the cost
+of a one, update tell to reflect the current used capacity, if the decoded value
+is zero break the loop otherwise add quanta to boost and total_boost, subtract quanta from
+total_bits, and set dynalloc_loop_log to 1. When the while loop finishes
+boost contains the boost for this band. If boost is nonzero and dynalloc_logp
+is greater than 2, decrease dynalloc_logp. Once this process has been
+executed on all bands, the band boosts have been decoded. This procedure
+is implemented around line 2352 of celt.c.
+
+At very low rates it is possible that there won't be enough available
+space to execute the inner loop even once. In these cases band boost
+is not possible but its overhead is completely eliminated. Because of the
+high cost of band boost when activated, a reasonable encoder should not be
+using it at very low rates. The reference implements its dynalloc decision
+logic around line 1269 of celt.c.
+
+The allocation trim is a integer value from 010. The default value of
+5 indicates no trim. The trim parameter is entropy coded in order to
+lower the coding cost of less extreme adjustments. Values lower than
+5 bias the allocation towards lower frequencies and values above 5
+bias it towards higher frequencies. Like other signaled parameters, signaling
+of the trim is gated so that it is not included if there is insufficient space
+available in the bitstream. To decode the trim, first set
+the trim value to 5, then iff the count of decoded 8th bits so far (ec_tell_frac)
+plus 48 (6 bits) is less than or equal to the total frame size in 8th
+bits minus total_boost (a product of the above band boost procedure),
+decode the trim value using the inverse CDF {127, 126, 124, 119, 109, 87, 41, 19, 9, 4, 2, 0}.
+
+Stereo parameters
+
+Anticollapse reservation
+
+The allocation computation begins by setting up some initial conditions.
+'total' is set to the remaining available 8th bits, computed by taking the
+size of the coded frame times 8 and subtracting ec_tell_frac(). From this value, one (8th bit)
+is subtracted to ensure that the resulting allocation will be conservative. 'anti_collapse_rsv'
+is set to 8 (8th bits) iff the frame is a transient, LM is greater than 1, and total is
+greater than or equal to (LM+2) * 8. Total is then decremented by anti_collapse_rsv and clamped
+to be equal to or greater than zero. 'skip_rsv' is set to 8 (8th bits) if total is greater than
+8, otherwise it is zero. Total is then decremented by skip_rsv. This reserves space for the
+final skipping flag.
+
+If the current frame is stereo, intensity_rsv is set to the conservative log2 in 8th bits
+of the number of coded bands for this frame (given by the table LOG2_FRAC_TABLE). If
+intensity_rsv is greater than total then intensity_rsv is set to zero. Otherwise total is
+decremented by intensity_rsv, and if total is still greater than 8, dual_stereo_rsv is
+set to 8 and total is decremented by dual_stereo_rsv.
+
+The allocation process then computes a vector representing the hard minimum amounts allocation
+any band will receive for shape. This minimum is higher than the technical limit of the PVQ
+process, but very low rate allocations produce an excessively sparse spectrum and these bands
+are better served by having no allocation at all. For each coded band, set thresh[band] to
+twentyfour times the number of MDCT bins in the band and divide by 16. If 8 times the number
+of channels is greater, use that instead. This sets the minimum allocation to one bit per channel
+or 48 128th bits per MDCT bin, whichever is greater. The bandsize dependent part of this
+value is not scaled by the channel count, because at the very low rates where this limit is
+applicable there will usually be no bits allocated to the side.
+
+The previously decoded allocation trim is used to derive a vector of perband adjustments,
+'trim_offsets[]'. For each coded band take the alloc_trim and subtract 5 and LM. Then multiply
+the result by the number of channels, the number of MDCT bins in the shortest frame size for this mode,
+the number of remaining bands, 2**LM, and 8. Then divide this value by 64. Finally, if the
+number of MDCT bins in the band per channel is only one, 8 times the number of channels is subtracted
+in order to diminish the allocation by one bit, because width 1 bands receive greater benefit
+from the coarse energy coding.
+
+
+
+
+
+
+In each band, the normalized "shape" is encoded
+using a vector quantization scheme called a "pyramid vector quantizer".
+
+
+In
+the simplest case, the number of bits allocated in
+ is converted to a number of pulses as described
+by . Knowing the number of pulses and the
+number of samples in the band, the decoder calculates the size of the codebook
+as detailed in . The size is used to decode
+an unsigned integer (uniform probability model), which is the codeword index.
+This index is converted into the corresponding vector as explained in
+. This vector is then scaled to unit norm.
+
+
+
+
+Although the allocation is performed in 1/8th bit units, the quantization requires
+an integer number of pulses K. To do this, the encoder searches for the value
+of K that produces the number of bits nearest to the allocated value
+(rounding down if exactly halfway between two values), not to exceed
+the total number of bits available. For efficiency reasons, the search is performed against a
+precomputed allocation table which only permits some K values for each N. The number of
+codebook entries can be computed as explained in . The difference
+between the number of bits allocated and the number of bits used is accumulated to a
+"balance" (initialized to zero) that helps adjust the
+allocation for the next bands. One third of the balance is applied to the
+bit allocation of each band to help achieve the target allocation. The only
+exceptions are the band before the last and the last band, for which half the balance
+and the whole balance are applied, respectively.
+
+
+
+
+
+
+The codeword is decoded as a uniformlydistributed integer value
+by decode_pulses() (cwrs.c).
+The codeword is converted from a unique index in the same way specified in
+. The indexing is based on the calculation of V(N,K)
+(denoted N(L,K) in ), which is the number of possible
+combinations of K pulses
+in N samples. The number of combinations can be computed recursively as
+V(N,K) = V(N1,K) + V(N,K1) + V(N1,K1), with V(N,0) = 1 and V(0,K) = 0, K != 0.
+There are many different ways to compute V(N,K), including precomputed tables and direct
+use of the recursive formulation. The reference implementation applies the recursive
+formulation one line (or column) at a time to save on memory use,
+along with an alternate,
+univariate recurrence to initialize an arbitrary line, and direct
+polynomial solutions for small N. All of these methods are
+equivalent, and have different tradeoffs in speed, memory usage, and
+code size. Implementations MAY use any methods they like, as long as
+they are equivalent to the mathematical definition.
+
+
+
+The decoding of the codeword from the index is performed as specified in
+, as implemented in function
+decode_pulses() (cwrs.c). The decoded codeword is then normalised such that it's
+L2norm equals one.
+
+
+
+
+
+The normalised vector decoded in is then rotated
+for the purpose of avoiding tonal artefacts. The rotation gain is equal to
+
+
+where N is the number of dimensions, K is the number of pulses, and f_r depends on
+the value of the "spread" parameter in the bitstream.
+
+
+
+Spread value
+f_r
+ 0infinite (no rotation)
+ 115
+ 210
+ 35
+
+
+
+The rotation angle is then calculated as
+
+A 2D rotation R(i,j) between points x_i and x_j is defined as:
+
+
+An ND rotation is then achieved by applying a series of 2D rotations back and forth, in the
+following order: R(x_1, x_2), R(x_2, x_3), ..., R(x_N2, X_N1), R(x_N1, X_N),
+R(x_N2, X_N1), ..., R(x_1, x_2).
+
+
+
+If the decoded vector represents more
+than one time block, then the following process is applied separately on each time block.
+
+
+
+
+
+To avoid the need for multiprecision calculations when decoding PVQ codevectors,
+the maximum size allowed for codebooks is 32 bits. When larger codebooks are
+needed, the vector is instead split in two subvectors of size N/2.
+A quantized gain parameter with precision
+derived from the current allocation is entropy coded to represent the relative
+gains of each side of the split, and the entire decoding process is recursively
+applied. Multiple levels of splitting may be applied up to a frame size
+dependent limit. The same recursive mechanism is applied for the joint coding
+of stereo audio.
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+When the frame has the transient bit set, an anticollapse bit is decoded.
+When anticollapse is set, the energy in each small MDCT is prevented
+from collapsing to zero. For each band of each MDCT where a collapse is
+detected, a pseudorandom signal is inserted with an energy corresponding
+to the min energy over the two previous frames. A renormalization step is
+then required to ensure that the anticollapse step did not alter the
+energy preservation property.
+
+
+
+
+
+Just like each band was normalized in the encoder, the last step of the decoder before
+the inverse MDCT is to denormalize the bands. Each decoded normalized band is
+multiplied by the square root of the decoded energy. This is done by denormalise_bands()
+(bands.c).
+
+
+
+
+
+
+The MDCT implementation has no special characteristics. The
+input is a windowed signal (after preemphasis) of 2*N samples and the output is N
+frequencydomain samples. A "lowoverlap" window is used to reduce the algorithmic delay.
+It is derived from a basic (full overlap) window that is the same as the one used in the Vorbis codec:
+
+The lowoverlap window is created by zeropadding the basic window and inserting ones in the middle, such that the resulting window still satisfies power complementarity. The MDCT is computed in mdct_forward() (mdct.c), which includes the windowing operation and a scaling of 2/N.
+
+
+
+The inverse MDCT implementation has no special characteristics. The
+input is N frequencydomain samples and the output is 2*N timedomain
+samples, while scaling by 1/2. A "lowoverlap" window is used to reduce the algorithmic delay.
+It is derived from a basic (full overlap) 240sample version of the window used by the Vorbis codec:
+
+The lowoverlap window is created by zeropadding the basic window and inserting ones in the
+middle, such that the resulting window still satisfies power complementarity. The IMDCT and
+windowing are performed by mdct_backward (mdct.c).
+
+
+
+
+The output of the inverse MDCT (after weighted overlapadd) is sent to the
+postfilter. Although the postfilter is applied at the end, the postfilter
+parameters are encoded at the beginning, just after the silence flag.
+The postfilter can be switched on or off using one bit (logp=1).
+If the postfilter is enabled, then the octave is decoded as an integer value
+between 0 and 6 of uniform probability. Once the octave is known, the fine pitch
+within the octave is decoded using 4+octave raw bits. The final pitch period
+is equal to (16<<octave)+fine_pitch1 so it is bounded between 15 and 1022,
+inclusively. Next, the gain is decoded as three raw bits and is equal to
+G=3*(int_gain+1)/32. The set of postfilter taps is decoded last, using
+a pdf equal to {2, 1, 1}/4. Tapset zero corresponds to the filter coefficients
+g0 = 0.3066406250, g1 = 0.2170410156, g2 = 0.1296386719. Tapset one
+corresponds to the filter coefficients g0 = 0.4638671875, g1 = 0.2680664062,
+g2 = 0, and tapset two uses filter coefficients g0 = 0.7998046875,
+g1 = 0.1000976562, g2 = 0.
+
+
+
+The postfilter response is thus computed as:
+
+
+During a transition between different gains, a smooth transition is calculated
+using the square of the MDCT window. It is important that values of y(n) be
+interpolated one at a time such that the past value of y(n) used is interpolated.
+
+
+
+
+
+After the postfilter,
+the signal is deemphasized using the inverse of the preemphasis filter
+used in the encoder:
+
+where alpha_p=0.8500061035.
+
+
+
+
Two frames of different compressed size:
+Packet loss concealment (PLC) is an optional decoderside feature which
+SHOULD be included when transmitting over an unreliable channel. Because
+PLC is not part of the bitstream, there are several possible ways to
+implement PLC with different complexity/quality tradeoffs. The PLC in
+the reference implementation finds a periodicity in the decoded
+signal and repeats the windowed waveform using the pitch offset. The windowed
+waveform is overlapped in such a way as to preserve the timedomain aliasing
+cancellation with the previous frame and the next frame. This is implemented
+in celt_decode_lost() (mdct.c).
+
+
+
+

+Switching between the Opus coding modes requires careful consideration. More
+specifically, the transitions that cannot be easily handled are the ones where
+the lower frequencies have to switch between the SILK LPbased model and the CELT
+transform model. If nothing is done, a glitch will occur for these transitions.
+On the other hand, switching between the SILKonly modes and the hybrid mode
+does not require any special treatment.
Three frames of different durations:
+There are two ways to avoid or reduce glitches during the problematic mode
+transitions: with side information or without it. Only transitions with side
+information are normatively specified. For transitions with no side
+information, it is RECOMMENDED for the decoder to use a concealment technique
+(e.g. make use of the PLC algorithm) to "fill in"
+the gap or discontinuity caused by the mode transition. Note that this
+concealment MUST NOT be applied when switching between the SILK mode and the
+hybrid mode or vice versa. Similarly, it MUST NOT be applied when merely
+changing the bandwidth within the same mode.
+
+
+
+Switching with side information involves transmitting inband a 5ms
+"redundant" CELT frame within the Opus frame.
+This frame is designed to fill in the gap or discontinuity without requiring
+the decoder to conceal it. For transitions from a CELTonly frame to a
+SILKonly or hybrid frame, the redundant frame is inserted in the frame
+following the transition (i.e. the SILKonly/hybrid frame). For transitions
+from a SILKonly/hybrid frame to a CELTonly frame, the redundant frame is
+inserted in the first frame. For all SILKonly and hybrid frames (not only
+those involved in a mode transition), a binary symbol of probability 2^12
+needs to be decoded just after the SILK part of the bitstream. When the
+symbol value is 1, the frame then includes an embedded redundant frame. The
+redundant frame always starts and ends on a byte boundary. For SILKonly
+frames, the number of bytes is simply the number of whole remaining bytes.
+For hybrid frames, the number of bytes is equal to 2, plus a decoded unsigned
+integer (ec_dec_uint()) between 0 and 255. For hybrid frames, the redundant
+frame is placed at the end of the frame, after the CELT layer of the
+hybrid frame. The redundant frame is decoded like any other CELTonly frame,
+with the exception that it does not contain a TOC byte. The bandwidth
+is instead set to the same bandwidth of the current frame (for MB
+frames, the redundant frame is set to WB).

+For CELTonly to SILKonly/hybrid transitions, the first
+2.5 ms of the redundant frame is used asis for the reconstructed
+output. The remaining 2.5 ms is overlapped and added (crossfaded using
+the square of the MDCT powercomplementary window) to the decoded SILK/hybrid
+signal, ensuring a smooth transition. For SILKonly/hyrid to CELTonly
+transitions, only the second half of the 5ms decoded redundant frame is used.
+In that case, only a 2.5ms crossfade is applied, still using the
+powercomplementary window.
+
+
+
+
+
+
Opus encoder block diagram.
+
Opus uses an entropy coder based upon ,
which is itself a rediscovery of the FIFO arithmetic code introduced by .
It is very similar to arithmetic encoding, except that encoding is done with
digits in any base instead of with bits,
so it is faster when using larger bases (i.e.: an octet). All of the
calculations in the range coder must use bitexact integer arithmetic.



The range coder also acts as the bitpacker for Opus. It is
used in three different ways, to encode:
entropycoded symbols with a fixed probability model using ec_encode(), (rangeenc.c)
integers from 0 to 2^M1 using ec_enc_uint() or ec_enc_bits(), (entenc.c)
+entropycoded symbols with a fixed probability model using ec_encode(), (entenc.c)
+integers from 0 to 2**M1 using ec_enc_uint() or ec_enc_bits(), (entenc.c)integers from 0 to N1 (where N is not a power of two) using ec_enc_uint(). (entenc.c)
The range encoder maintains an internal state vector composed of the
fourtuple (low,rng,rem,ext), representing the low end of the current
+fourtuple (low,rng,rem,ext) representing the low end of the current
range, the size of the current range, a single buffered output octet,
and a count of additional carrypropagating output octets. Both rng
and low are 32bit unsigned integer values, rem is an octet value or
the special value 1, and ext is an integer with at least 16 bits.
This state vector is initialized at the start of each each frame to
the value (0,2^31,1,0).



Each symbol is drawn from a finite alphabet and coded in a separate
context which describes the size of the alphabet and the relative
frequency of each symbol in that alphabet. Opus only uses static
contexts; they are not adapted to the statistics of the data that is
coded.
+the value (0,2**31,1,0). The reference implementation reuses the
+'val' field of the entropy coder structure to hold low, in order to
+allow the same structure to be used for encoding and decoding, but
+we maintain the distinction here for clarity.
 The main encoding function is ec_encode() (rangeenc.c),
+ The main encoding function is ec_encode() (entenc.c),
which takes as an argument a threetuple (fl,fh,ft)
describing the range of the symbol to be encoded in the current
context, with 0 <= fl < fh <= ft <= 65535. The values of this tuple
are derived from the probability model for the symbol. Let f(i) be
 the frequency of the ith symbol in the current context. Then the
 threetuple corresponding to the kth symbol is given by
+ the frequency of the i'th symbol in the current context. Then the
+ threetuple corresponding to the k'th symbol is given by
ec_encode() updates the state of the encoder as follows. If fl is
 greater than zero, then low = low + rng  (rng/ft)*(ftfl) and
+ greater than zero, then low = low + rng  (rng/ft)*(ftfl) and
rng = (rng/ft)*(fhfl). Otherwise, low is unchanged and
rng = rng  (rng/ft)*(fhfl). The divisions here are exact integer
division. After this update, the range is normalized.
To normalize the range, the following process is repeated until
 rng > 2^23. First, the top 9 bits of low, (low>>23), are placed into
+ rng > 2**23. First, the top 9 bits of low, (low>>23), are placed into
a carry buffer. Then, low is set to . This process is carried out by
 ec_enc_normalize() (rangeenc.c).
+ ec_enc_normalize() (entenc.c).
The 9 bits produced in each iteration of the normalization loop
@@ 358,9 +4616,9 @@ fl=sum(f(i),i
 The function ec_enc_carry_out() (rangeenc.c) performs
 this buffering. It takes a 9bit input value, c, from the normalization
 8bit output and a carry bit. If c is 0xFF, then ext is incremented
+ The function ec_enc_carry_out() (entenc.c) performs
+ this buffering. It takes a 9bit input value, c, from the normalization:
+ 8 bits of output and a carry bit. If c is 0xFF, then ext is incremented
and no octets are output. Otherwise, if rem is not the special value
1, then the octet (rem+(c>>8)) is output. Then ext octets are output
with the value 0 if the carry bit is set, or 0xFF if it is not, and
@@ 368,29 +4626,36 @@ fl=sum(f(i),i
In the reference implementation, a special version of ec_encode()
 called ec_encode_bin() (rangeenc.c) is defined to
 take a twotuple (fl,ftb), where , but avoids using division.

+
 Functions ec_enc_uint() or ec_enc_bits() are based on ec_encode() and
 encode one of N equiprobable symbols, each with a frequency of 1,
 where N may be as large as 2^321. Because ec_encode() is limited to
 a total frequency of 2^161, this is done by encoding a series of
 symbols in smaller contexts.
+ The CELT layer also allows directly encoding a series of raw bits, outside
+ of the range coder, implemented in ec_enc_bits() (entenc.c).
+ The raw bits are packed at the end of the packet, starting by storing the
+ least significant bit of the value to be packed in the least significant bit
+ of the last byte, filling up to the most significant bit in
+ the last byte, and then continuing in the least significant bit of the
+ penultimate byte, and so on.
+ This packing may continue into the last byte output by the range coder,
+ though the format should render it impossible to overwrite any set bit
+ produced by the range coder when the procedure in
+ is followed to finalize the stream.
+
+
+
 ec_enc_bits() (entenc.c) is defined, like
 ec_encode_bin(), to take a twotuple (fl,ftb), with >ftb8&0xFF) using ec_encode_bin() and
 subtracts 8 from ftb. Then, it encodes the remaining bits of fl, e.g.,
 (fl&(1<, again using ec_encode_bin().
+ The function ec_enc_uint() is based on ec_encode() and encodes one of N
+ equiprobable symbols, each with a frequency of 1, where N may be as large as
+ 2**321. Because ec_encode() is limited to a total frequency of 2**161, this
+ is done by encoding a series of symbols in smaller contexts.
ec_enc_uint() (entenc.c) takes a twotuple (fl,ft),
@@ 399,9 +4664,8 @@ fl=sum(f(i),i8, then the top 8 bits of fl
are encoded using ec_encode() with the threetuple
(fl>>ftb8,(fl>>ftb8)+1,(ft1>>ftb8)+1), and the remaining bits
 are encoded with ec_enc_bits using the twotuple
 .
+ are encoded as raw bits. Otherwise, fl is encoded with ec_encode() directly
+ using the threetuple (fl,fl+1,ft).
@@ 410,15 +4674,17 @@ fl=sum(f(i),i>23), are sent to the carry buffer, and end is replaced by
(end<<8&0x7FFFFFFF). Finally, if the value in carry buffer, rem, is]]>
neither zero nor the special value 1, or the carry count, ext, is
greater than zero, then 9 zero bits are sent to the carry buffer.
After the carry buffer is finished outputting octets, the rest of the
 output buffer is padded with zero octets. Finally, rem is set to the
+ output buffer (if any) is padded with zero bits, until it reaches the raw
+ bits. Finally, rem is set to the
special value 1. This process is implemented by ec_enc_done()
 (rangeenc.c).
+ (entenc.c).
@@ 427,285 +4693,683 @@ fl=sum(f(i),i


Copy from SILK draft.


+
+
+ In the following, we focus on the core encoder and describe its components. For simplicity, we will refer to the core encoder simply as the encoder in the remainder of this document. An overview of the encoder is given in .
+


Copy from CELT draft.


+
+1: Input speech signal
+2: High passed input signal
+3: Voice activity estimate
+4: Pitch lags (per 5 ms) and voicing decision (per 20 ms)
+5: Noise shaping quantization coefficients
+  Short term synthesis and analysis
+ noise shaping coefficients (per 5 ms)
+  Long term synthesis and analysis noise
+ shaping coefficients (per 5 ms and for voiced speech only)
+  Noise shaping tilt (per 5 ms)
+  Quantizer gain/step size (per 5 ms)
+6: Input signal filtered with analysis noise shaping filters
+7: Short and long term prediction coefficients
+ LTP (per 5 ms) and LPC (per 20 ms)
+8: LSF quantization indices
+9: LSF coefficients
+10: Quantized LSF coefficients
+11: Processed gains, and synthesis noise shape coefficients
+12: LTP state scaling coefficient. Controlling error propagation
+ / prediction gain tradeoff
+13: Quantized signal
+14: Range encoded bitstream


Opus decoder block diagram.

+]]>
+
+ Encoder block diagram.
+


The range decoder extracts the symbols and integers encoded using the range encoder in
. The range decoder maintains an internal
state vector composed of the twotuple (dif,rng), representing the
difference between the high end of the current range and the actual
coded value, and the size of the current range, respectively. Both
dif and rng are 32bit unsigned integer values. rng is initialized to
2^7. dif is initialized to rng minus the top 7 bits of the first
input octet. Then the range is immediately normalized, using the
procedure described in the following section.

+
+
+ The input signal is processed by a Voice Activity Detector (VAD) to produce a measure of voice activity, spectral tilt, and signaltonoise estimates for each frame. The VAD uses a sequence of halfband filterbanks to split the signal into four subbands: 0  Fs/16, Fs/16  Fs/8, Fs/8  Fs/4, and Fs/4  Fs/2, where Fs is the sampling frequency (8, 12, 16, or 24 kHz). The lowest subband, from 0  Fs/16, is highpass filtered with a firstorder moving average (MA) filter (with transfer function H(z) = 1z**(1)) to reduce the energy at the lowest frequencies. For each frame, the signal energy per subband is computed. In each subband, a noise level estimator tracks the background noise level and a SignaltoNoise Ratio (SNR) value is computed as the logarithm of the ratio of energy to noise level. Using these intermediate variables, the following parameters are calculated for use in other SILK modules:
+
+
+ Average SNR. The average of the subband SNR values.
+


 Decoding symbols is a twostep process. The first step determines
 a value fs that lies within the range of some symbol in the current
 context. The second step updates the range decoder state with the
 threetuple (fl,fh,ft) corresponding to that symbol, as defined in
 .


 The first step is implemented by ec_decode()
 (rangedec.c),
 and computes fs = ftmin((dif1)/(rng/ft)+1,ft), where ft is
 the sum of the frequency counts in the current context, as described
 in . The divisions here are exact integer division.


 In the reference implementation, a special version of ec_decode()
 called ec_decode_bin() (rangeenc.c) is defined using
 the parameter ftb instead of ft. It is mathematically equivalent to
 calling ec_decode() with ft = (1<<ftb), but avoids one of the
 divisions.

+
+ Smoothed subband SNRs. Temporally smoothed subband SNR values.
+
+
+
+ Speech activity level. Based on the average SNR and a weighted average of the subband energies.
+
+
+
+ Spectral tilt. A weighted average of the subband SNRs, with positive weights for the low subbands and negative weights for the high subbands.
+
+
+
+
+
+
+
+ The input signal is filtered by a highpass filter to remove the lowest part of the spectrum that contains little speech energy and may contain background noise. This is a second order Auto Regressive Moving Average (ARMA) filter with a cutoff frequency around 70 Hz.
+
+
+ In the future, a music detector may also be used to lower the cutoff frequency when the input signal is detected to be music rather than speech.
+
+
+
+
+
+ The highpassed input signal is processed by the open loop pitch estimator shown in .
+
+ The pitch analysis finds a binary voiced/unvoiced classification, and, for frames classified as voiced, four pitch lags per frame  one for each 5 ms subframe  and a pitch correlation indicating the periodicity of the signal. The input is first whitened using a Linear Prediction (LP) whitening filter, where the coefficients are computed through standard Linear Prediction Coding (LPC) analysis. The order of the whitening filter is 16 for best results, but is reduced to 12 for medium complexity and 8 for low complexity modes. The whitened signal is analyzed to find pitch lags for which the time correlation is high. The analysis consists of three stages for reducing the complexity:
+
+ In the first stage, the whitened signal is downsampled to 4 kHz (from 8 kHz) and the current frame is correlated to a signal delayed by a range of lags, starting from a shortest lag corresponding to 500 Hz, to a longest lag corresponding to 56 Hz.
+
+
+ The second stage operates on an 8 kHz signal (downsampled from 12, 16, or 24 kHz) and measures time correlations only near the lags corresponding to those that had sufficiently high correlations in the first stage. The resulting correlations are adjusted for a small bias towards short lags to avoid ending up with a multiple of the true pitch lag. The highest adjusted correlation is compared to a threshold depending on:
+
+
+ Whether the previous frame was classified as voiced
+
+
+ The speech activity level
+
+
+ The spectral tilt.
+
+
+ If the threshold is exceeded, the current frame is classified as voiced and the lag with the highest adjusted correlation is stored for a final pitch analysis of the highest precision in the third stage.
+
+
+ The last stage operates directly on the whitened input signal to compute time correlations for each of the four subframes independently in a narrow range around the lag with highest correlation from the second stage.
+
+
+
+
+
+
+
+ The noise shaping analysis finds gains and filter coefficients used in the prefilter and noise shaping quantizer. These parameters are chosen such that they will fulfill several requirements:
+
+ Balancing quantization noise and bitrate. The quantization gains determine the step size between reconstruction levels of the excitation signal. Therefore, increasing the quantization gain amplifies quantization noise, but also reduces the bitrate by lowering the entropy of the quantization indices.
+ Spectral shaping of the quantization noise; the noise shaping quantizer is capable of reducing quantization noise in some parts of the spectrum at the cost of increased noise in other parts without substantially changing the bitrate. By shaping the noise such that it follows the signal spectrum, it becomes less audible. In practice, best results are obtained by making the shape of the noise spectrum slightly flatter than the signal spectrum.
+ Deemphasizing spectral valleys; by using different coefficients in the analysis and synthesis part of the prefilter and noise shaping quantizer, the levels of the spectral valleys can be decreased relative to the levels of the spectral peaks such as speech formants and harmonics. This reduces the entropy of the signal, which is the difference between the coded signal and the quantization noise, thus lowering the bitrate.
+ Matching the levels of the decoded speech formants to the levels of the original speech formants; an adjustment gain and a first order tilt coefficient are computed to compensate for the effect of the noise shaping quantization on the level and spectral tilt.
+
+
+
+
+ shows an example of an input signal spectrum (1). After deemphasis and level matching, the spectrum has deeper valleys (2). The quantization noise spectrum (3) more or less follows the input signal spectrum, while having slightly less pronounced peaks. The entropy, which provides a lower bound on the bitrate for encoding the excitation signal, is proportional to the area between the deemphasized spectrum (2) and the quantization noise spectrum (3). Without deemphasis, the entropy is proportional to the area between input spectrum (1) and quantization noise (3)  clearly higher.
+
+
+
+ The transformation from input signal to deemphasized signal can be described as a filtering operation with a filter
+
+ having an adjustment gain G, a first order tilt adjustment filter with
+ tilt coefficient c_tilt, and where
+
+ is the analysis part of the deemphasis filter, consisting of the shortterm shaping filter with coefficients a_ana(k), and the longterm shaping filter with coefficients b_ana(k) and pitch lag L. The parameter d determines the number of longterm shaping filter taps.
+
+
+
+ Similarly, but without the tilt adjustment, the synthesis part can be written as
+
+
+
+ All noise shaping parameters are computed and applied per subframe of 5 ms. First, an LPC analysis is performed on a windowed signal block of 15 ms. The signal block has a lookahead of 5 ms relative to the current subframe, and the window is an asymmetric sine window. The LPC analysis is done with the autocorrelation method, with an order of 16 for best quality or 12 in low complexity operation. The quantization gain is found by taking the square root of the residual energy from the LPC analysis and multiplying it by a value inversely proportional to the coding quality control parameter and the pitch correlation.
+
+
+ Next we find the two sets of shortterm noise shaping coefficients a_ana(k) and a_syn(k), by applying different amounts of bandwidth expansion to the coefficients found in the LPC analysis. This bandwidth expansion moves the roots of the LPC polynomial towards the origin, using the formulas
+
+ where a(k) is the k'th LPC coefficient, and the bandwidth expansion factors g_ana and g_syn are calculated as
+
+ where C is the coding quality control parameter between 0 and 1. Applying more bandwidth expansion to the analysis part than to the synthesis part gives the desired deemphasis of spectral valleys in between formants.
+
+
+
+ The longterm shaping is applied only during voiced frames. It uses three filter taps, described by
+
+ For unvoiced frames these coefficients are set to 0. The multiplication factors F_ana and F_syn are chosen between 0 and 1, depending on the coding quality control parameter, as well as the calculated pitch correlation and smoothed subband SNR of the lowest subband. By having F_ana less than F_syn, the pitch harmonics are emphasized relative to the valleys in between the harmonics.
+
+
+
+ The tilt coefficient c_tilt is for unvoiced frames chosen as
+
+ for voiced frames, where C again is the coding quality control parameter and is between 0 and 1.
+
+
+ The adjustment gain G serves to correct any level mismatch between the original and decoded signals that might arise from the noise shaping and deemphasis. This gain is computed as the ratio of the prediction gain of the shortterm analysis and synthesis filter coefficients. The prediction gain of an LPC synthesis filter is the square root of the output energy when the filter is excited by a unitenergy impulse on the input. An efficient way to compute the prediction gain is by first computing the reflection coefficients from the LPC coefficients through the stepdown algorithm, and extracting the prediction gain from the reflection coefficients as
+
+ where r_k is the k'th reflection coefficient.
+
+
+
+ Initial values for the quantization gains are computed as the squareroot of the residual energy of the LPC analysis, adjusted by the coding quality control parameter. These quantization gains are later adjusted based on the results of the prediction analysis.
+
+
+
+
+
+ In the prefilter the input signal is filtered using the spectral valley deemphasis filter coefficients from the noise shaping analysis (see ). By applying only the noise shaping analysis filter to the input signal, it provides the input to the noise shaping quantizer.
+
+
+
+
+ The prediction analysis is performed in one of two ways depending on how the pitch estimator classified the frame. The processing for voiced and unvoiced speech is described in and , respectively. Inputs to this function include the prewhitened signal from the pitch estimator (see ).
+
+
+
+
+ For a frame of voiced speech the pitch pulses will remain dominant in the prewhitened input signal. Further whitening is desirable as it leads to higher quality at the same available bitrate. To achieve this, a LongTerm Prediction (LTP) analysis is carried out to estimate the coefficients of a fifthorder LTP filter for each of four subframes. The LTP coefficients are used to find an LTP residual signal with the simulated output signal as input to obtain better modeling of the output signal. This LTP residual signal is the input to an LPC analysis where the LPCs are estimated using Burg's method, such that the residual energy is minimized. The estimated LPCs are converted to a Line Spectral Frequency (LSF) vector and quantized as described in . After quantization, the quantized LSF vector is converted back to LPC coefficients using the full procedure in . By using LPC coefficients derived from the quantized LSF coefficients, the encoder remains fully synchronized with the decoder. The LTP coefficients are quantized using a method described in . The quantized LPC and LTP coefficients are then used to filter the highpass filtered input signal and measure residual energy for each of the four subframes.
+
+
+
+
+ For a speech signal that has been classified as unvoiced, there is no need for LTP filtering, as it has already been determined that the prewhitened input signal is not periodic enough within the allowed pitch period range for LTP analysis to be worth the cost in terms of complexity and rate. The prewhitened input signal is therefore discarded, and instead the highpass filtered input signal is used for LPC analysis using Burg's method. The resulting LPC coefficients are converted to an LSF vector and quantized as described in the following section. They are then transformed back to obtain quantized LPC coefficients, which are then used to filter the highpass filtered input signal and measure residual energy for each of the four subframes.
+
+
+
+
+
+ In general, the purpose of quantization is to significantly lower the bitrate at the cost of introducing some distortion. A higher rate should always result in lower distortion, and lowering the rate will generally lead to higher distortion. A commonly used but generally suboptimal approach is to use a quantization method with a constant rate, where only the error is minimized when quantizing.
+
+ Instead, we minimize an objective function that consists of a weighted sum of rate and distortion, and use a codebook with an associated nonuniform rate table. Thus, we take into account that the probability mass function for selecting the codebook entries is by no means guaranteed to be uniform in our scenario. This approach has several advantages. It ensures that rarely used codebook vector centroids, which are modeling statistical outliers in the training set, are quantized with low error at the expense of a high rate. At the same time, it allows modeling frequently used centroids with low error and a relatively low rate. This approach leads to equal or lower distortion than the fixedrate codebook at any given average rate, provided that the data is similar to that used for training the codebook.
+
+
+
+
+ Instead of minimizing the error in the LSF domain, we map the errors to better approximate spectral distortion by applying an individual weight to each element in the error vector. The weight vectors are calculated for each input vector using the Inverse Harmonic Mean Weighting (IHMW) function proposed by Laroia et al. (see ).
+ Consequently, we solve the following minimization problem, i.e.,
+
+ where LSF_q is the quantized vector, LSF is the input vector to be quantized, and c is the quantized LSF vector candidate taken from the set C of all possible outcomes of the codebook.
+
+
+
+
+ We arrange the codebook in a multiplestage structure to achieve a quantizer that is both memory efficient and highly scalable in terms of computational complexity (see, e.g., ). In the first stage the input is the LSF vector to be quantized, and in any other stage s > 1, the input is the quantization error from the previous stage (see ).
+
+
+
+
+ By storing a total of M codebook vectors, i.e.,
+
+ where M_s is the number of vectors in stage s, we obtain a total of
+
+ possible combinations for generating the quantized vector. It is, for example, possible to represent 2**36 uniquely combined vectors using only 216 vectors in memory, as is done in SILK for voiced speech at all sample frequencies above 8 kHz.
+
+
+
+
+ This number of possible combinations is far too high to carry out a full search for each frame, so for all stages but the last (i.e., s smaller than S), only the best min(L, Ms) centroids are carried over to stage s+1. In each stage, the objective function (i.e., the weighted sum of accumulated bitrate and distortion) is evaluated for each codebook vector entry and the results are sorted. Only the best paths and their corresponding quantization errors are considered in the next stage. In the last stage, S, the single best path through the multistage codebook is determined. By varying the maximum number of survivors from each stage to the next, L, the complexity can be adjusted in real time, at the cost of a potential increase when evaluating the objective function for the resulting quantized vector. This approach scales all the way between the two extremes, L=1 being a greedy search, and the desirable but infeasible full search, L=T/MS. Performance almost as good as that of the infeasible full search can be obtained at substantially lower complexity by using this approach (see, e.g., ).
+
+
+
+ If the input is stable, finding the best candidate usually results in a quantized vector that is also stable. Due to the multistage approach, however, it is theoretically possible that the best quantization candidate is unstable. Because of this, it is necessary to explicitly ensure that the quantized vectors are stable. Therefore we apply an LSF stabilization method which ensures that the LSF parameters are within valid range, increasingly sorted, and have minimum distances between each other and the border values that have been predetermined as the 0.01 percentile distance values from a large training set.
+
+
+
+ The vectors and rate tables for the multistage codebook have been trained by minimizing the average of the objective function for LSF vectors from a large training set.
+
+
+
+
+
+
+ For voiced frames, the prediction analysis described in resulted in four sets (one set per subframe) of five LTP coefficients, plus four weighting matrices. The LTP coefficients for each subframe are quantized using entropy constrained vector quantization. A total of three vector codebooks are available for quantization, with different ratedistortion tradeoffs. The three codebooks have 10, 20, and 40 vectors and average rates of about 3, 4, and 5 bits per vector, respectively. Consequently, the first codebook has larger average quantization distortion at a lower rate, whereas the last codebook has smaller average quantization distortion at a higher rate. Given the weighting matrix W_ltp and LTP vector b, the weighted ratedistortion measure for a codebook vector cb_i with rate r_i is give by
+
+ where u is a fixed, heuristicallydetermined parameter balancing the distortion and rate. Which codebook gives the best performance for a given LTP vector depends on the weighting matrix for that LTP vector. For example, for a low valued W_ltp, it is advantageous to use the codebook with 10 vectors as it has a lower average rate. For a large W_ltp, on the other hand, it is often better to use the codebook with 40 vectors, as it is more likely to contain the best codebook vector.
+ The weighting matrix W_ltp depends mostly on two aspects of the input signal. The first is the periodicity of the signal; the more periodic, the larger W_ltp. The second is the change in signal energy in the current subframe, relative to the signal one pitch lag earlier. A decaying energy leads to a larger W_ltp than an increasing energy. Both aspects fluctuate relatively slowly, which causes the W_ltp matrices for different subframes of one frame often to be similar. Because of this, one of the three codebooks typically gives good performance for all subframes, and therefore the codebook search for the subframe LTP vectors is constrained to only allow codebook vectors to be chosen from the same codebook, resulting in a rate reduction.
+
+
+
+ To find the best codebook, each of the three vector codebooks is used to quantize all subframe LTP vectors and produce a combined weighted ratedistortion measure for each vector codebook. The vector codebook with the lowest combined ratedistortion over all subframes is chosen. The quantized LTP vectors are used in the noise shaping quantizer, and the index of the codebook plus the four indices for the four subframe codebook vectors are passed on to the range encoder.
+
+
+
+
+
+
+ The noise shaping quantizer independently shapes the signal and coding noise spectra to obtain a perceptually higher quality at the same bitrate.
+
+
+ The prefilter output signal is multiplied with a compensation gain G computed in the noise shaping analysis. Then the output of a synthesis shaping filter is added, and the output of a prediction filter is subtracted to create a residual signal. The residual signal is multiplied by the inverse quantized quantization gain from the noise shaping analysis, and input to a scalar quantizer. The quantization indices of the scalar quantizer represent a signal of pulses that is input to the pyramid range encoder. The scalar quantizer also outputs a quantization signal, which is multiplied by the quantized quantization gain from the noise shaping analysis to create an excitation signal. The output of the prediction filter is added to the excitation signal to form the quantized output signal y(n). The quantized output signal y(n) is input to the synthesis shaping and prediction filters.
+
+
+
+
+
+
+ Range encoding is a well known method for entropy coding in which a bitstream sequence is continually updated with every new symbol, based on the probability for that symbol. It is similar to arithmetic coding, but rather than being restricted to generating binary output symbols, it can generate symbols in any chosen number base. In SILK all side information is range encoded. Each quantized parameter has its own cumulative density function based on histograms for the quantization indices obtained by running a training database.
+
+
+
+
+ TBD.
+
+
+
+
+
+
+
 The decoder then identifies the symbol in the current context
 corresponding to fs; i.e., the one whose threetuple (fl,fh,ft)
 satisfies fl <= fs < fh. This tuple is used to update the decoder
 state according to dif = dif  (rng/ft)*(ftfh), and if fl is greater
 than zero, rng = (rng/ft)*(fhfl), or otherwise rng = rng  (rng/ft)*(ftfh). After this update, the range is normalized.
+Most of the aspects of the CELT encoder can be directly derived from the description
+of the decoder. For example, the filters and rotations in the encoder are simply the
+inverse of the operation performed by the decoder. Similarly, the quantizers generally
+optimize for the mean square error (because noise shaping is part of the bitstream itself),
+so no special search is required. For this reason, only the less straightforward aspects of the
+encoder are described here.

 To normalize the range, the following process is repeated until
 rng > 2^23. First, rng is set to (rng<8)&0xFFFFFFFF. Then the next
 8 bits of input are read into sym, using the remaining bit from the
 previous input octet as the high bit of sym, and the top 7 bits of the
 next octet for the remaining bits of sym. If no more input octets
 remain, zero bits are used instead. Then, dif is set to
 (dif<<8)sym&0xFFFFFFFF (i.e., using wraparound if the subtraction
 overflows a 32bit register). Finally, if dif is larger than 2^31,
 dif is then set to dif  2^31. This process is carried out by
 ec_dec_normalize() (rangedec.c).
+
+
+The pitch prefilter is applied after the preemphasis and before the deemphasis. It's applied
+in such a way as to be the inverse of the decoder's postfilter. The main nonobvious aspect of the
+prefilter is the selection of the pitch period. The pitch search should be optimised for the
+following criteria:
+
+continuity: it is important that the pitch period
+does not change abruptly between frames; and
+avoidance of pitch multiples: when the period used is a multiple of the real period
+(lower frequency fundamental), the postfilter loses most of its ability to reduce noise
+

+
 Functions ec_dec_uint() or ec_dec_bits() are based on ec_decode() and
 decode one of N equiprobable symbols, each with a frequency of 1,
 where N may be as large as 2^321. Because ec_decode() is limited to
 a total frequency of 2^161, this is done by decoding a series of
 symbols in smaller contexts.


 ec_dec_bits() (entdec.c) is defined, like
 ec_decode_bin(), to take a single parameter ftb, with ftb < 32.
 and ftb < 32, and produces an ftbbit decoded integer value, t,
 initialized to zero. While ftb is greater than 8, it decodes the next
 8 most significant bits of the integer, s = ec_decode_bin(8), updates
 the decoder state with the 3tuple (s,s+1,256), adds those bits to
 the current value of t, t = t<<8  s, and subtracts 8 from ftb. Then
 it decodes the remaining bits of the integer, s = ec_decode_bin(ftb),
 updates the decoder state with the 3 tuple (s,s+1,1<<ftb), and adds
 those bits to the final values of t, t = t<<ftb  s.


 ec_dec_uint() (entdec.c) takes a single parameter,
 ft, which is not necessarily a power of two, and returns an integer,
 t, with a value between 0 and ft1, inclusive, which is initialized to zero. Let
 ftb be the location of the highest 1 bit in the two'scomplement
 representation of (ft1), or 1 if no bits are set. If ftb>8, then
 the top 8 bits of t are decoded using t = ec_decode((ft1>>ftb8)+1),
 the decoder state is updated with the threetuple
 (s,s+1,(ft1>>ftb8)+1), and the remaining bits are decoded with
 t = t<<ftb8ec_dec_bits(ftb8). If, at this point, t >= ft, then
 the current frame is corrupt, and decoding should stop. If the
 original value of ftb was not greater than 8, then t is decoded with
 t = ec_decode(ft), and the decoder state is updated with the
 threetuple (t,t+1,ft).
+The MDCT output is divided into bands that are designed to match the ear's critical
+bands for the smallest (2.5 ms) frame size. The larger frame sizes use integer
+multiples of the 2.5 ms layout. For each band, the encoder
+computes the energy that will later be encoded. Each band is then normalized by the
+square root of the unquantized energy, such that each band now forms a unit vector X.
+The energy and the normalization are computed by compute_band_energies()
+and normalise_bands() (bands.c), respectively.

+
+
 The bit allocation routines in CELT need to be able to determine a
 conservative upper bound on the number of bits that have been used
 to decode from the current frame thus far. This drives allocation
 decisions which must match those made in the encoder. This is
 computed in the reference implementation to fractional bit precision
 by the function ec_dec_tell() (rangedec.c). Like all
 operations in the range decoder, it must be implemented in a
 bitexact manner, and must produce exactly the same value returned by
 ec_enc_tell() after encoding the same symbols.
+Energy quantization (both coarse and fine) can be easily understood from the decoding process.
+The quantizer simply minimizes the log energy error for each band, with the exception that at
+very low rate, larger errors are allowed in the coarse energy to minimize the bitrate. When the
+avaialble CPU requirements allow it, it is best to try encoding the coarse energy both with and without
+interframe prediction such that the best prediction mode can be selected. The optimal mode depends on
+the coding rate, the available bitrate, and the current rate of packet loss.

+



Copy from SILK draft.
+
+CELT uses a Pyramid Vector Quantization (PVQ)
+codebook for quantizing the details of the spectrum in each band that have not
+been predicted by the pitch predictor. The PVQ codebook consists of all sums
+of K signed pulses in a vector of N samples, where two pulses at the same position
+are required to have the same sign. Thus the codebook includes
+all integer codevectors y of N dimensions that satisfy sum(abs(y(j))) = K.


Insert decoder figure.
+In bands where there are sufficient bits allocated the PVQ is used to encode
+the unit vector that results from the normalization in
+ directly. Given a PVQ codevector y,
+the unit vector X is obtained as X = y/y, where . denotes the
+L2 norm.
+
+
+
The decoder extracts information from the rangecoded bitstream in the same order
as it was encoded by the encoder. In some circumstances, it is
possible for a decoded value to be out of range due to a very small amount of redundancy
in the encoding of large integers by the range coder.
In that case, the decoder should assume there has been an error in the coding,
decoding, or transmission and SHOULD take measures to conceal the error and/or report
to the application that a problem has occurred.
+The search for the best codevector y is performed by alg_quant()
+(vq.c). There are several possible approaches to the
+search, with a tradeoff between quality and complexity. The method used in the reference
+implementation computes an initial codeword y1 by projecting the residual signal
+R = X  p' onto the codebook pyramid of K1 pulses:


The energy of each band is extracted from the bitstream in two steps according
to the same coarsefine strategy used in the encoder. First, the coarse energy is
decoded in unquant_coarse_energy() (quant_bands.c)
based on the probability of the Laplace model used by the encoder.
+y0 = round_towards_zero( (K1) * R / sum(abs(R)))
After the coarse energy is decoded, the same allocation function as used in the
encoder is called. This determines the number of
bits to decode for the fine energy quantization. The decoding of the fine energy bits
is performed by unquant_fine_energy() (quant_bands.c).
Finally, like the encoder, the remaining bits in the stream (that would otherwise go unused)
are decoded using unquant_energy_finalise() (quant_bands.c).
+Depending on N, K and the input data, the initial codeword y0 may contain from
+0 to K1 nonzero values. All the remaining pulses, with the exception of the last one,
+are found iteratively with a greedy search that minimizes the normalized correlation
+between y and R:
+


If the pitch bit is set, then the pitch period is extracted from the bitstream. The pitch
gain bits are extracted within the PVQ decoding as encoded by the encoder. When the folding
bit is set, the folding prediction is computed in exactly the same way as the encoder,
with the same gain, by the function intra_fold() (vq.c).
+The search described above is considered to be a good tradeoff between quality
+and computational cost. However, there are other possible ways to search the PVQ
+codebook and the implementers MAY use any other search methods.



In order to correctly decode the PVQ codewords, the decoder must perform exactly the same
bits to pulses conversion as the encoder.



The decoding of the codeword from the index is performed as specified in
, as implemented in function
decode_pulses() (cwrs.c).



The spherical codebook is decoded by alg_unquant() (vq.c).
The index of the PVQ entry is obtained from the range coder and converted to
a pulse vector by decode_pulses() (cwrs.c).

The decoded normalized vector for each band is equal to
X' = y/y,

This operation is implemented in mix_pitch_and_residual() (vq.c),
which is the same function as used in the encoder.




Just like each band was normalized in the encoder, the last step of the decoder before
the inverse MDCT is to denormalize the bands. Each decoded normalized band is
multiplied by the square root of the decoded energy. This is done by denormalise_bands()
(bands.c).


The inverse MDCT implementation has no special characteristics. The
input is N frequencydomain samples and the output is 2*N timedomain
samples, while scaling by 1/2. The output is windowed using the same window
as the encoder. The IMDCT and windowing are performed by mdct_backward
(mdct.c). If a timedomain preemphasis
window was applied in the encoder, the (inverse) timedomain deemphasis window
is applied on the IMDCT result. After the overlapadd process,
the signal is deemphasized using the inverse of the preemphasis filter
used in the encoder: 1/A(z)=1/(1alpha_p*z^1).


+

Packet loss concealment (PLC) is an optional decoderside feature which
SHOULD be included when transmitting over an unreliable channel. Because
PLC is not part of the bitstream, there are several possible ways to
implement PLC with different complexity/quality tradeoffs. The PLC in
the reference implementation finds a periodicity in the decoded
signal and repeats the windowed waveform using the pitch offset. The windowed
waveform is overlapped in such a way as to preserve the timedomain aliasing
cancellation with the previous frame and the next frame. This is implemented
in celt_decode_lost() (mdct.c).
+It is the intention to allow the greatest possible choice of freedom in
+implementing the specification. For this reason, outside of a few exceptions
+noted in this section, conformance is defined through the reference
+implementation of the decoder provided in .
+Although this document includes an English description of the codec, should
+the description contradict the source code of the reference implementation,
+the latter shall take precedence.


+
+Compliance with this specification means that a decoder's output MUST be
+ within the thresholds specified by the opus_compare.c tool in
+ compared to the reference implementation.
+
+
+
+To complement the Opus specification, the "Opus Custom" codec is defined to
+handle special sampling rates and frame rates that are not supported by the
+main Opus specification. Use of Opus Custom is discouraged for all but very
+special applications for which a frame size different from 2.5, 5, 10, or 20 ms is
+needed (for either complexity or latency reasons). Such applications will not
+be compatible with the "main" Opus codec. In Opus Custom operation,
+only the CELT layer is available, which is available using the celt_* function
+calls in celt.h.
+
The codec needs to take appropriate security considerations
+Implementations of the Opus codec need to take appropriate security considerations
into account, as outlined in and .
It is extremely important for the decoder to be robust against malicious
payloads. Malicious payloads must not cause the decoder to overrun its
allocated memory or to take much more resources to decode. Although problems
+payloads.
+Malicious payloads must not cause the decoder to overrun its allocated memory
+ or to take an excessive amount of resources to decode.
+Although problems
in encoders are typically rarer, the same applies to the encoder. Malicious
audio stream must not cause the encoder to misbehave because this would
+audio streams must not cause the encoder to misbehave because this would
allow an attacker to attack transcoding gateways.
In its current version, the Opus codec likely does NOT meet these
security considerations, so it should be used with caution.
+The reference implementation contains no known buffer overflow or cases where
+ a specially crafted packet or audio segment could cause a significant increase
+ in CPU load.
+However, on certain CPU architectures where denormalized floatingpoint
+ operations are much slower than normal floatingpoint operations, it is
+ possible for some audio content (e.g., silence or nearsilence) to cause a certain
+ an increase in CPU load.
+Denormals can be introduced by reordering operations in the compiler and depend
+ on the target architecture, so it is difficult to guarantee that an implementation
+ avoids them.
+For architectures on which denormals are problematic, it is RECOMMENDED to
+add very small floatingpoint offsets to the affected signals
+to prevent significant numbers of denormalized
+ operations. Alternatively, it is often possible to configure the hardware to treat
+ denormals as zero (DAZ).
+No such issue exists for the fixedpoint reference implementation.

+The reference implementation was validated in the following conditions:
+
+Sending the decoder valid packets generated by the reference encoder and
+verifying that the decoder's final range coder state matches that of the encoder.
+Sending the decoder packets generated by the reference encoder, after random corruption.
+Sending the decoder random packets to the decoder.
+Altering the encoder to make random coding decisions (internal fuzzing), including
+mode switching and verifying that the range coder final states match.
+
+In all of the conditions above, both the encoder and the decoder were run inside
+the Valgrind memory debugger, which tracks reads and writes to invalid memory
+regions, as well as use of uninitialized memory. There were no error reported
+on any of the tested conditions.
+
+
@@ 716,10 +5380,14 @@ This document has no actions for IANA.
Thanks to all other developers, including Raymond Chen, Soeren Skak Jensen, Gregory Maxwell,
Christopher Montgomery, Karsten Vandborg Soerensen, and Timothy Terriberry.
+Thanks to all other developers, including Raymond Chen, Soeren Skak Jensen, Gregory Maxwell,
+Christopher Montgomery, and Karsten Vandborg Soerensen. We would also
+like to thank Igor Dyakonov and Jan Skoglund for their help with subjective testing of the
+Opus codec. Thanks to John Ridges, Keith Yan, and many others on the Opus and CELT mailing lists
+for their bug reports and feedback, as well as Ralph Giles, Christian Hoene, and
+Kat Walsh, for their feedback on the draft.

+
@@ 744,6 +5412,62 @@ Christopher Montgomery, Karsten Vandborg Soerensen, and Timothy Terriberry.
+
+
+
+ Robust and Efficient Quantization of Speech LSP Parameters Using Structured Vector Quantization
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+ Evaluation of Split and Multistage Techniques in LSF Quantization
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+ Efficient Search and Design Procedures for Robust MultiStage VQ of LPC Parameters for 4 kb/s Speech Coding
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
ConstrainedEnergy Lapped Transform (CELT) Codec
@@ 803,7 +5527,7 @@ Christopher Montgomery, Karsten Vandborg Soerensen, and Timothy Terriberry.

+
@@ 821,15 +5545,15 @@ Christopher Montgomery, Karsten Vandborg Soerensen, and Timothy Terriberry.

+

+
This appendix contains the complete source code for the
reference implementation of the Opus codec written in C. This
implementation can be compiled for
+implementation can be compiled for
either floatingpoint or fixedpoint architectures.
@@ 847,16 +5571,27 @@ following command line:
opus_source.tar.gz
+cat draftietfcodecopus.txt  grep '^\ \ \ ###'  sed 's/\s\s\s###//'  base64 d > opus_source.tar.gz
]]>
tar xzvf opus_source.tar.gz
+cd opus_source
+make
+
+
+The current development version of the source code is available in a
+ Git repository.
+Development snapshots are provided at
+ .
+
+
+
@@ 865,6 +5600,185 @@ tar xzvf opus_source.tar.gz
+
+
+
+
+
+
+
+
+To use the internal framing described in , the decoder
+ must know the total length of the Opus packet, in bytes.
+This section describes a simple variation of that framing which can be used
+ when the total length of the packet is not known.
+Nothing in the encoding of the packet itself allows a decoder to distinguish
+ between the regular, undelimited framing and the selfdelimiting framing
+ described in this appendix.
+Which one is used and where must be established by context at the transport
+ layer.
+It is RECOMMENDED that a transport layer choose exactly one framing scheme,
+ rather than allowing an encoder to signal which one it wants to use.
+
+
+
+For example, although a regular Opus stream does not support more than two
+ channels, a multichannel Opus stream may be formed from several one and
+ twochannel streams.
+To pack an Opus packet from each of these streams together in a single packet
+ at the transport layer, one could use the selfdelimiting framing for all but
+ the last stream, and then the regular, undelimited framing for the last one.
+Reverting to the undelimited framing for the last stream saves overhead
+ (because the total size of the transportlayer packet will still be known),
+ and ensures that a "multichannel" stream which only has a single Opus stream
+ uses the same framing as a regular Opus stream does.
+This avoids the need for signaling to distinguish these two cases.
+
+
+
+The selfdelimiting framing is identical to the regular, undelimited framing
+ from , except that each Opus packet contains one extra
+ length field, encoded using the same one or twobyte scheme from
+ .
+This extra length immediately precedes the compressed data of the first Opus
+ frame in the packet, and is interpreted in the various modes as follows:
+
+
+Code 0 packets: It is the length of the single Opus frame (see
+ ).
+
+
+Code 1 packets: It is the length used for both of the Opus frames (see
+ ).
+
+
+Code 2 packets: It is the length of the second Opus frame (see
+ ).
+
+CBR Code 3 packets: It is the length used for all of the Opus frames (see
+ ).
+
+VBR Code 3 packets: It is the length of the last Opus frame (see
+ ).
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+