ATRAC3plus
 Format tag: uses WAVE_FORMAT_EXTENSIBLE with the "SubFormat" field set to the following GUID: E923AABFCB584471A119FFFA01E4CE62
 Company: Sony
 Samples: http://samples.mplayerhq.hu/Acodecs/ATRAC3+/
 Stored in: WAV and Oma/Omg containers.
 Official information: http://www.sony.net/Products/ATRAC3/tech/atrac3plus.html
Contents
 1 ATRAC3plus introduction
 2 ATRAC3plus technical documentation
 2.1 Available bitrates
 2.2 Coding techniques
 2.3 Multichannel ATRAC3plus (ATRACX)
 2.4 Bitstream overview
 2.5 Annex A: Decoding tables
ATRAC3plus introduction
ATRAC3plus is a proprietary audio compression algorithm developed by Sony. As in the case of ATRAC3 ATRAC3plus represents the next generation of the ATRAC codec introduced in 1992 with the MiniDisc. Common use of that codec is in nowel Minidisc players and Portable Playstations made by Sony.
Streams coded with ATRAC3plus are usually stored either in the WAV container (those files have the ".at3" extension though) or in the Sony's proprietary Oma/Omg container. In the case of the WAV container the undocumented GUID:
E923AABFCB584471A119FFFA01E4CE62
is used in order to indicate the ATRAC3plus codec.
There is very limited number of software products supporting encoding/decoding of the ATRAC3plus streams; most of them are unfortunately available for Microsoft Windows only. Those are:
 Sony's own SonicStage software (Windows only)
 ATRAC Codec Plugin for Sony Media Software (Windows only)
 Sonic Studio's expensive Ncode plugin for professionals (available for Windows and Mac OS X)
There is a multichannel version of ATRAC3plus called "ATRACX".
ATRAC3plus technical documentation
Available bitrates
ATRAC3plus operates on fixed bitrates only. The following bitrates are offered by the Sony Encoding software:
bitrate frame size (stereo)   48 Kbps 280 bytes 64 Kbps 376 bytes 96 Kbps 560 bytes 128 Kbps 744 bytes 160 Kbps 936 bytes 192 Kbps 1120 bytes 256 Kbps 1488 bytes 320 Kbps 1864 bytes 352 Kbps 2048 bytes
Coding techniques
ATRAC3plus is a hybrid subband/MDCT codec like MP3. The signal is split into 16 subbands using Quadrature Mirror Filter before MDCT and bit allocation. The sampleframe size is 2048 samples per channel.
After the subband splitting ATRAC3plus tries to extract sine waves from each subband using Generalized Harmonic Analysis (further GHA). GHA encodes parameters of extracted sine waves such as frequency, amplitude and phase into final bitstream.
After the sine waves extraction the remained signal (residual) will be transformed into frequency domain by a 128point Modified discrete cosine transform. The resultet MDCT spectrum will be devided into 32 quantization units of unequal width (higher frequencies  wider units). The relationship between QMF bands and quantization units (QU) is shown in the table below:
QMF subband  0  1  2  3  4  5  6  7  8  9  10  11  12  13  14  15  

Quant unit  0  1  2  3  4  5  6  7  8  9  10  11  12  13  14  15  16  17  18  19  20  21  22  23  24  25  26  27  28  29  30  31 
The flowchart of the ATRAC3plus decoding process is shown below:
"Bitstream decoder" decodes various sound parameters from supplied frame data. First the residual signal will be decoded by applying inverse quantization, power compensation, inverse MDCT and gain compensation. Then the sine waves will be synthesized according with their parameters such as frequency, amplitude and phase. Then the residual and the synthesized sine waves will be added together. Optionally, some white noise can be added if specified in the bitstream.
This processing will be repeated for each of 16 subbands. Finally the QMF synthesis filter will be applied in order to sum all subbands together and reconstruct the encoded audio signal.
Various algorithms are used to improve compression results:
 gain control for reducing preecho artifacts
 power compensation for better quality at low bitrates
The following techniques are used in order to make the compressed data smaller:
 variablelenght (Huffman) coding
 vector quantization based on trained tables
 differential coding
Probably the most interesting part of the ATRAC3plus codec is the Generalized Harmonic Analysis (GHA)  an inharmonic frequency analysis proposed by Norbert Wiener in 1930. The main advantage of that is an excellent frequency resolution that surpasses the shorttime Discrete Furier transformation. However it requires huge amount of calculations. Several algorithms to work around that problem were introduced during last 20 years, for example the one proposed by Dr.Hirata.
Coding methods for compressing bitstream parameters
Coding methods described in this section serve the purpose of representing different bitstream parameters like wordlength, scale factor etc. using a smaller number of bits. It will be achieved by exploring and removing redundancy from the signals being encoded. The coding techniques described here are lossless.
Huffman coding
ATRAC3plus uses this coding technique widely. There are more than 130 different huffman tables in total for coding bitstream signals. Usually more frequently occuring values will have shorter codes. ATRAC3plus huffman trees are canonical ones. That means those can be stored very compactly by specifying the following parameters:
 number of bits of the shortest codeword
 number of bits of the longest codeword
 number of items for every bit length
 order of items
In my code I'm using the following descriptor in order to specify a canonical huffman table:
uint8_t min; /* shortest codeword length */ uint8_t max; /* longest codeword length */ uint8_t num_items[max  min + 1]; /* number of items for every bit length */
For example, the huffman table vlc_tab_index = 3 here will be described as follows:
min = 1 max = 5 num_items[1, 0, 2, 3, 2]
The 2nd element of the array "num_items" is set to "0" because there is no codeword with the length of 2 bits.
The following Cpseudocode can be used for generating huffman tables from the descriptor described above during decoder initialization:
code = 0; index = 0; for (num_bits = min; num_bits <= max; num_bits++) { for (i = num_items[num_bits]; i > 0; i) { bits [index] = num_bits; codes[index] = code++; index++; } code <<= 1; }
The array "bits" receives length in bits for each codeword, "codes" receives codeword itself.
Finally, the order of codes need to be specified. A simple remapping table will be used to translate the code index into final code. For the table described above the translation table will look as follows:
0, 1, 7, 2, 3, 6, 4, 5
Delta coding
ATRAC3plus utilizes various deltacoding schemes in order to remove linear correlation from the signal. It often uses the modular arithmetic as well. The main advantage of this coding is that only the half of the range of the difference values is required. An example: wordlength information coefficients in the range 0...7 need to be transmitted compactly. Using delta coding this would require to code difference values in the range 7...+7, also 15 values.
In the case of modular arithmetic the range of the difference values can be reduced to 0...7 by introducing a "wraparound" so that the final equation looks like this:
B = (A + delta) & 7;
Below an example with "wrap around":
Consider we need to code the value B = "1" and the reference value A = "6". Then the difference value (delta) will be = "5". According with equation above the delta value of "3" can be used instead of "5":
(6 + 3) & 7 = 1;
Another example without "wrap around":
Consider we need to code the value B = "7" and the reference value A = "2". Then the difference value (delta) will be = "5":
(2 + 5) & 7 = 7;
Further variablelength codes will be used to reduce amount of bits of difference values in accordance with their probability.
The following is a description of the deltacoding methods used in ATRAC3plus:
Method A: huffmancoded modulo difference to previous
Consider the following signal:
3, 6, 6, 3, 3, 3, 4, 2, 2, 1, 1, 1, 3
Now code it using delta coding:
Coefficient  Modulo delta value  Huffman code  Number of bits 

3      3 
6  3  11110  5 
6  0  0  1 
3  5  1101  4 
3  0  0  1 
3  0  0  1 
4  1  100  3 
2  6  1110  4 
2  0  0  1 
1  7  101  3 
1  0  0  1 
1  0  0  1 
3  2  1100  4 
The 1st coefficient has no delta value associated with it because there is no previous value. It will be coded "as is" using fixed length of 3 bits. The following delta values get a variablelength code from the table val_tab_index = 2 here so the final number of bits to be transmitted will be = 32. Compared to the unpacked version (13 x 3 bits = 39 bits) the coding method described above will yield a bitreduction of 7 bits (18% smaller).
Method B: huffmancoded modulo difference to master
In a stereo mix the signal of the left channel is often very similar to the signal of the right channel (i.e. there is a high crosscorrelation between the channels). In this case the estimated sound parameters like wordlength or scale factor will have a high similarity as well. Then coding the differential signal between the channels can lead to a significant bit reduction. Surely at least the one of the channels must be coded independently. Such a channel will be called "master" (it's usually the left channel but ATRAC3plus has the possibility to make the right channel act like a master as well). For the 2nd channel only the difference to master will be coded. The 2nd channel will be called "slave" in this case.
Below an example of such a highcorrelated signal:
Left : 6, 5, 6, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1 Right: 6, 5, 6, 2, 2, 2, 3, 1, 1, 1, 2, 1, 1 Diff : 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0
Coding the difference signal using the table val_tab_index = 0 here will result in another signal 15 bits long. Compared to the unpacked version (13 x 3 bits = 39 bits) that coding method will yield a bitreduction of 24 bits (62% smaller).
Method C: shorter delta to min
Sometimes coefficients in a signal are very close to each other, so subtracting the minimum value from each coefficient will result in smaller deltas whose can be coded using fewer bits.
An example:
2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1
As one can see the values in the sequence above are very similar to each other. Let us find minimum and maximum values and then determine the number of delta bits:
min = 1; max = 2; num_delta_bits = ilog2(max  min + 1) = 1 bit
Now let us encode the sequence above using shorter deltas:
num_delta_bits = 1 will be coded as a 2bit value min = 1 will be coded as a 3bit value deltas: 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0
The encoded signal is 5 + 1 x 15 = 20 bits long while the unpacked one is 15 x 3 = 45 bits long. The bitreduction is thereafter 25 bits (55% smaller).
Another example:
1, 2, 3, 2, 4, 2, 1, 2, 3, 3, 1, 4, 4, 1, 1
min = 1; max = 4; num_delta_bits = ilog2(max  min + 1) = 2 bits
Now the encoded signal:
num_delta_bits = 2 (will be coded as a 2bit value) min = 1 (will be coded as a 3bit value) deltas: 0, 1, 2, 1, 3, 1, 0, 1, 2, 2, 0, 3, 3, 0, 0
The encoded signal is 5 + 2 x 15 = 35 bits long while the unpacked one is 15 x 3 = 45 bits long. The bitreduction is thereafter 10 bits (22% smaller).
Method D: sequence of numbers in ascending order
Sometimes ATRAC3plus have to deal with sequences of numbers (i.e. gain control position information) where all items are known to be in ascending order (i.e. satisfy the following equation: V_{n+1} > V_{n}). Such sequences can be packed without any additional bitstream information by examining previous value (predecessor), calculating magnitude between it and the maximum value and making the decision about number of bits of the next delta value.
Consider the following sequence:
Position index: 0, 1, 2, 3, 4, 5, 6, 7  Position info : 5, 7, 14, 15, 18, 25, 29, 30  Num delta bits: 5, 5, 5, 4, 4, 3, 1, 0
1st coefficient (position index = 0) will be coded directly using 5 bits because the sequence should start somewhere. The following coefficients (except one with the value of "30") will be coded according to the following pseudocode:
num_delta_bits = ilog2(31  prev_val); if (num_delta_bits == 5) new_val = get_bits(5); else new_val = prev_val + get_bits(num_delta_bits) + 1;
Let us return to our sequence. The 2nd value will be coded directly as well using 5 bits because ilog2(31  5) = 5. Similar for the 3rd one. No delta coding is applied in that case. The 4th value will be deltacoded using 4 bits:
num_delta_bits = ilog2(31  15) = 4 bits; delta = 18  15  1 = 2
And so on until we reach the last value = 30. In this case there is only one value that meets our condition V_{n+1} > V_{n}: the value of "31". In this case no delta will be transmitted and the coming value will be calculated just as:
new_val = prev_val + 1;
Therefore the resulting sequence will be 27 bits long. Compared to the unpacked version (8 x 5 bits = 40 bits) this packing method will yield a bitreduction of 13 bits (32% smaller).
Vector quantization with residual encoding
One further packing technique used in ATRAC3plus is based on socalled "shape prediction vectors". Encoder decomposes a signal (wordlength or scale factor info) into "shape prediction" + residual. Then only the index of the "shape prediction vector" and the huffmancoded residual will be transmitted. The main advantage of this method is when the shape matches the coded signal closely, the residual can be represented very compactly (usually 12 bits per value). Moreover, the majority of values of the residual will turn into zeroes, which can be further packed.
Each entry of the "shape prediction tables" contain an average value over 3 coefficients. This helps to keep those tables comparable small. For example, for a signal of 32 values each "shape table" will have 10 entries (last entry contains usually an average value over 5 coefficients).
Consider the following signal to be encoded:
7, 7, 6, 5, 4, 4, 3, 2, 2, 2, 1, 1
Let us "quantize" that signal by diving it into 4 * 3 groups and find the averaged value in each group:
floor((7 + 7 + 6) / 3 + 0.5) = 7, floor((5 + 4 + 4) / 3 + 0.5) = 4, floor((3 + 2 + 2) / 3 + 0.5) = 2, floor((2 + 1 + 1) / 3 + 0.5) = 1
Find a "shape table" in the trained set that closely matches our "quantized" version. It will be (for example):
7, 5, 2, 1
Now compute the residual:
Original signal  7  7  6  5  4  4  3  2  2  2  1  1 

Unpacked shape table  7  7  7  5  5  5  2  2  2  1  1  1 
Residual  0  0  1  0  1  1  1  0  0  1  0  0 
Now select a huffman table that represents the residual above as small as possible. The following huffman tree assigns the shortest code (1 bit) to the most frequently occuring symbol = "0" and 2bit codes to the others: "1" and "1":
Huffman code  Number of bits  Delta value 

0  1  0 
10  2  1 
11  2  1 
The packed signal will occupy 21 bits: 4 bits "shape table" index + 17 bits residual(7 bits for "zeroes" + 10 bits for "nonzeroes"). Compared to the unpacked version (12 x 3 bits = 36 bits) this packing method will yield a bitreduction of 15 bits (42% smaller).
Value grouping with "group coded" flag
If a signal contains lots of zeroes, grouping several values together and assigning the "group coded" flag to each group will achieve a significant bitreduction. Consider the following sequence of numbers to be encoded:
0, 0, 1, 2, 0, 0, 3, 3, 0, 0, 0, 7, 0, 6, 0, 0
Let us cluster each two values together and assign the "coded" flag (1 bit) to each group:
(0, 0); flag = 0 (group not coded) (1, 2); flag = 1 (group coded) (0, 0); flag = 0 (group not coded) (3, 3); flag = 1 (group coded) (0, 0); flag = 0 (group not coded) (0, 7); flag = 1 (group coded) (0, 6); flag = 1 (group coded) (0, 0); flag = 0 (group not coded)
Thereafter, each "not coded" group requires only one bit to be transmitted indicating that all values in that group are zero. On the other hand, each "coded" group requires one extra bit to be transmitted indicating that at least one value in that group is nonzero. In the case above that overhead is worthwhile because the half of the signal contains zeroes.
The encoded signal is 4 x 1 + 4 x 7 = 32 bits long while the unpacked one is 16 x 3 = 48 bits long. The bitreduction is thereafter 16 bits (33% smaller).
Multichannel ATRAC3plus (ATRACX)
ATRAC3plus supports multichannel streams (up to 8 channels). Such streams are encoded in units customary called "channel block"; each block contains max. 2 channels (ie can be MONO or STEREO). For example, taking the channel_id = 3 and looking at the table below we have a stream containing 2 channel blocks: 1 stereo + 1 mono and thus 3 channels. The base codec operates on either MONO or STEREO channel blocks only.
ATRACX channel configurations
channel_id  total channels  number of channel blocks  speaker mapping 

0  0  undefined 

1  1  1 

2  2  1 

3  3  2 

4  4  3 

5  5+1  4 

6  6+1  5 

7  7+1  5 

Bitstream overview
The table below shows the bitstream organization of ATRAC3plus at the toplevel. Depends on channel configuration a typical frame may contain more than one channel block. In this case the additional fields channel_block_type and channel_block_data will be included for each block.
name  number of bits  value  description 

start_marker  1  0 
marks the start of the ATRAC3plus bitstream 
channel_block_type  2 

type of the channel block 
channel_block_data  variable  contains encoded sound information  
terminator  2  11b  indicates the end of the bitstream 
Channel block types
There are following channel block types in ATRAC3plus:
 Mono channel block: contains monaural sound data.
 Stereo channel block: contains stereophonic sound data.
 Extension block: as indicated by its name it's intended to carry some extension information. Its purpose is unknown though due to the lack of an official description. All existing decoder implementations are programmed to ignore blocks of that type.
Channel block layout
ATRAC3plus was designed to provide a highquality sound compression. Therefore it tries to save as much bits as possible. It uses a new coding scheme for channel blocks compared to ATRAC3: channels in a stereo sound are no more coded separately but rather in one stereo channel block. The bitstream for such a block provides the possibility for both channels to share several sound parameters so that there is no need to transmit the same things twice. Depends on correlation between the channels this can lead to a significant bit reduction and thus improve coding quality.
A mono/stereo channel block contains the following pieces of sound information:
name  size in bits  description 

sound_header  6  defines some global sound parameters 
wordlength_info  variable  quantization word length information for each quant unit 
scalefactor_info  variable  quantization scale factor indexes for each coded quant unit 
codetable_info  variable  code table table information for each coded quant unit 
spectra  variable  huffmancoded spectral information for each coded quant unit 
window_info  variable  tells which IMDCT window shape should be used during the sound reconstruction 
gain_info  variable  gain envelope used by the gain compensation 
gha_info  variable  information about sinelike waves in the compressed sound obtained by the GHA. It contains quantized frequency, amplitude and phase for each wave to be synthesized in the decoder. 
noise_info  1/9  contains noise flag, level index and table selector for the white noise to be added during decoding. 
Sound header
At the start of each channel block the sound header is located. It contains the following fields:
size in bits  name  value(s)  comments 

5  num_quant_units  valid values: 0...27,31  number of coded quantization units  1. The value of "0" indicates one coded unit, the value of "31"  32 ones. The values 28, 29 and 30 are invalid. 
1  x_flag  to be figured out 
Wordlength information
Coding summary
Wordlength (or quantization precision) information follows the sound header. It defines the wordlength parameter for each coded quantization unit. This parameter is in the range 0...7, where the value of "7" indicates the highest quantization precision and the value of "1"  the lowest one. The value of "0" means no data, i.e. the corresponding quantization unit was not coded.
In the case of the stereo channel block the wordlength parameters for the channel 1(L) will be transmitted first followed by the the wordlength parameters for the channel 2(R). The wordlengths for the channel 1 are always coded independently. The wordlengths for the channel 2 can be coded either independently or relative to the channel 1. In this case the 1st channel is called "master" and the 2nd one  "slave". The wordlengths for the mono block will be coded just like the channel 1 in the stereo block.
In order to keep the wordlength data as small as possible ATRAC3plus uses several coefficient packing techniques achieving different amount of bits needed for transmission:
 the coefficients are coded directly (3 bits value). This means no packing and used at high bitrates because the frame size is big enough to keep the infomation unpacked.
 differential coding + huffmancoded delta: the first coefficient is coded directly; all others are huffmancoded deltas to the previous coefficient.
 prediction + huffmancoded residual: this techniques offers the best packing and used at low bitrates. It's analogous to the lossless coding and based on trained shape tables serving as prediction. Later the huffmancoded residual will be added to the prediction prefectly reconstructing the coefficients.
Reconstruction of trimmed wordlength coefficients
Wordlength coefficient of the trailing quantization units corresponding to the high spectral bands tend to be either 1 (lowprecision) or 0 (not coded). Such coefficients will be ommited and one the following modes will be used in order to reconstruct their values during decoding:
mode code(2 bits)  num_coded_vals  split_point_delta  Action(master)  Action(slave) 

0  not present  not present  no trimmed coefficients  
1  5 bits  set all trimmed coefficients to "0"  
2  set all trimmed coefficients to "1"  for each trimmed coefficient read one bit of its direct value  
3  2 bits  set all trimmed coefficients up to split point to "1" and after split point  to "0". The split point is calculated differently for master and slave channels (see below) 
To calculate the split point from split_point_delta do the following:
 for the master channel: number of zeroes = split_point_delta + 1
 for the slave channel: number of ones = split_point_delta + 3
The following Cpseudocode shows how to parse a bitstream according with the table above:
mode = get_bits(2); if (mode) { num_coded_vals = get_bits(5); if (mode == 3) split_point_delta = get_bits(2); } else { num_coded_vals = num_quant_units; }
The following Cpseudocode shows how to reconstruct trimmed wordlength coefficients according with the table above:
switch (mode) { case 0: /* no further action */ break; case 1: for (pos = num_coded_vals; pos < num_quant_units; pos++) wl_coeffs[pos] = 0; break; case 2: for (pos = num_coded_vals; pos < num_quant_units; pos++) { if (channel == master) wl_coeffs[pos] = 1; else wl_coeffs[pos] = get_bits(1); } break; case 3: if (channel == master) split_point = num_quant_units  split_point_delta  1; else split_point = num_coded_vals + split_point_delta + 3; for (pos = num_coded_vals; pos < split_point; pos++) wl_coeffs[pos] = 1; for (; pos < num_quant_units; pos++) wl_coeffs[pos] = 0; }
Wordlength coding in detail
The wordlength information for each channel will be coded as follows:
size in bits  name  comments 

2  coding_mode  indicates the coding mode used. 
variable  coeff_info  wordlength coefficients coded according with the coding_mode. 
The coding_mode parameter may be interpreted differently depends on the channel number. The following pseudocode examples explain the coding modes in detail:
Mode 0 (master and slave)
All coefficients will be directly coded as follows:
for (i = 0; i < num_quant_units; i++) wl_coeffs[i] = get_bits(3);
Mode 1 (master)
Leading "n" values are stored directly while trailing ones are packed using Method C: shorter delta to min method.
Data stored in the bitstream:
 2 bits: index of the table of weigths, "0"  indicates "no table used"
 2/7/9 or more bits (depending on mode): info for the reconstruction of trimmed coefficients
 5 bits: number of directly coded coefficients (num_direct_coeffs). This value must be < num_coded_vals
 2 bits: size of deltas in bits (delta_bits)
 3 bits: minimum value (min_value)
 for each num_direct_coeffs
 3 bits: coefficient value
 if delta_bits > 0: for each (num_coded_vals  num_direct_coeffs)
 delta_bits: delta value to be added to the min_value
The following Cpseudocode summarizes all above:
weigths_tab_indx = get_bits(2); /* get index of weights table to be added after decoding */ /* parse mode/num_coded_vals/split_point_delta parameters for trimmed coefficients */ num_direct_coeffs = get_bits(5); if (num_direct_coeffs > num_coded_vals) ABORT("Invalid number of directly coded coefficients"); delta_bits = get_bits(2); min_value = get_bits(3); for (pos = 0; pos < num_direct_coeffs; pos++) wl_coeffs[pos] = get_bits(3); for (; pos < num_coded_vals; pos++) { if (delta_bits) wl_coeffs[pos] = min_value + get_bits(delta_bits); else wl_coeffs[pos] = min_value; } /* reconstruct trimmed coefficients as described here */ /* add weighting coefficients if requested */ if (weigths_tab_indx) { for (pos = 0; pos < num_quant_units; pos++) wl_coeffs[pos] += wl_weights[channel_num][weights_tab_indx  1][pos]; }
Mode 1 (slave)
Coding method: Huffmancoded modulo difference to master.
Data stored in the bitstream:
 2/7/9 or more bits (depending on mode): info for the reconstruction of trimmed coefficients
 2 bits: indicates which huffman table from this set should be used for decoding
 for each num_coded_vals
 huffmancoded delta value to be added to the corresponding value of the master channel
/* parse mode/num_coded_vals/split_point_delta parameters for trimmed coefficients */ vlc_sel = get_bits(2); /* selects a huffman table from this set */ for (i = 0; i < num_coded_vals; i++) { delta = get_vlc(vlc_sel); wl_coeffs[i] = (master_ch>wl_coeffs[i] + delta) & 7; }
Mode 2 (master)
Coding method: Vector quantization with residual encoding and Value grouping with "group coded" flag.
Data stored in the bitstream:
 2/7/9 or more bits (depending on mode): info for the reconstruction of trimmed coefficients.
 1 bit: enable_grouping flag. "1" indicates that residual values were coded pairwise (in groups of two).
 1 bit: selects one of the first two huffman tables from this set.
 3 bits: start_value selecting a subset of "shape tables" from the trained set.
 4 bits: shape_index selecting a "shape table" within the subset indicated by start_value.
 for each num_coded_vals
 if enable_grouping == 1:
 1 bit: group_coded flag
 if group_coded == 1:
 2 huffmancoded residual values to be added to the unpacked "shape table" using modular arithmetic
 if enable_grouping == 0:
 one huffmancoded residual value to be added to the unpacked "shape table" using modular arithmetic
 if enable_grouping == 1:
Annex A: Decoding tables
Tables of weights
The weights below will be added to the decoded wordlength coefficients. The tables are organized as follows:
 [channel_number: 0 or 1][index: 0...2][coeff_indx: 0...31]
wl_weights[2][3][32] = { { {5, 5, 4, 4, 3, 3, 2, 2, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {5, 5, 5, 4, 4, 4, 3, 3, 3, 2, 2, 2, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {6, 5, 5, 5, 4, 4, 4, 4, 3, 3, 3, 3, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0}, }, { {5, 5, 4, 4, 3, 3, 2, 2, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {5, 5, 5, 4, 4, 4, 3, 3, 3, 2, 2, 2, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {6, 5, 5, 5, 5, 5, 5, 5, 3, 3, 3, 3, 2, 2, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0} } };
Huffman tables for delta coding
PLEASE NOTE: delta values indicated in the tables below will be added using modular arithmetic as described here, so in the case of "wrap around" the value of "7" will be treated as "1", the value of "6" = "2" and so on.
 vlc_tab_index = 0, delta range 1...1
Huffman code  Number of bits  Delta value 

0  1  0 
10  2  1 
11  2  7 
 vlc_tab_index = 1, delta range 2...2
Huffman code  Number of bits  Delta value 

0  1  0 
100  3  1 
101  3  2 
110  3  6 
111  3  7 
 vlc_tab_index = 2, delta range 0...7 (4...3)
Huffman code  Number of bits  Delta value 

0  1  0 
100  3  1 
101  3  7 
1100  4  2 
1101  4  5 
1110  4  6 
11110  5  3 
11111  5  4 
 vlc_tab_index = 3, delta range 0...7 (4...3)
Huffman code  Number of bits  Delta value 

0  1  0 
100  3  1 
101  3  7 
1100  4  2 
1101  4  3 
1110  4  6 
11110  5  4 
11111  5  5 