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Title:
SYSTEMS AND METHODS FOR ENCODING A DEEP NEURAL NETWORK
Document Type and Number:
WIPO Patent Application WO/2021/063559
Kind Code:
A1
Abstract:
The present disclosure relates to a method including encoding indexes of symbols of a codebook, the codebook and information representative of numbers of occurrences of the encoded indexes. The present disclosure relates to a method including decoding indexes of symbols of a codebook, the method including decoding the codebook and information representative of numbers of occurrences of the indexes. The present disclosure also relates to the corresponding devices, signal computer program products and media.

Inventors:
HAMIDI-RAD, Shahab (Inc.Bld 4, Ste 200, 3000 El Camino Rea, Palo Alto California, US)
RACAPE, Fabien (Inc.Bld 4, Ste 200, 3000 El Camino Rea, Palo Alto California, US)
JAIN, Swayambhoo (Inc.Bld 4, Ste 200, 3000 El Camino Rea, Palo Alto California, US)
Application Number:
EP2020/070969
Publication Date:
April 08, 2021
Filing Date:
July 24, 2020
Export Citation:
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Assignee:
INTERDIGITAL VC HOLDINGS FRANCE, SAS (Cesson Sevigne, FR)
International Classes:
H03M7/00; H04N19/13; H04N19/46
Attorney, Agent or Firm:
TARQUIS-GUILLOU, Anne et al. (20 rue Rouget de Lisl, Issy-les-Moulineaux FR, FR)
Download PDF:
Claims:
CLAIMS

1. An electronic device comprising at least one processor adapted for encoding indexes of symbols of a codebook, said codebook and information representative of numbers of occurrences of said encoded indexes.

2. A method comprising encoding indexes of symbols of a codebook, said codebook and information representative of numbers of occurrences of said encoded indexes.

3. The electronic device of claim 1, said at least one processor being adapted for, or the method of claim 2 comprising, sorting said representative information of said numbers of occurrences of said indexes.

4. The electronic device of claim 1 or 3 the method of claim 2 or 3 wherein said indexes are encoded in a bitstream, said codebook and/or said representative information being encoded in a header part of said bitstream.

5. The electronic device of claim 4, said at least one processor being adapted for, or the method of claim 4 comprising, serializing said header part.

6. The electronic device of any of claims 1 or 3 to 5 or the method of any of claims 2 to 5 wherein said encoding is performed by taking account of at least one of the following elements:

• -a size of encoded data

• a size of said codebook,

• a size of said representative information of said number of occurrences of said indexes,

• a size of said indexes ;

• a combination thereof.

7. The electronic device of claim any of claims 1 or 3 to 6, said at least one processor being adapted for, or the method of any of claims 2 to 6 comprising, encoding at least one parameter of at least one Deep Neural Network.

8. The electronic device of claim 7, said at least one processor being adapted for, or the method of claim 7 comprising, obtaining said codebook and/or said indexes by clustering said at least one parameter.

9. An electronic device comprising at least one processor adapted for decoding indexes of symbols of a codebook, said at least one processor being adapted for decoding said codebook and information representative of numbers of occurrences of said indexes.

10. A method comprising decoding indexes of symbols of a codebook, said method comprising decoding said codebook and information representative of numbers of occurrences of said indexes.

11. The electronic device of claim 1 or 9 or the method of claim 2 or 10 wherein said codebook and said representative information are encoded using an adaptive arithmetic coding

12. The electronic device of claim 1 or 9 or 11 , or the method of claim 2 or 10 or 11 wherein said indexes are encoded using conditional arithmetic coding

13. The electronic device of claim 1 or 10 or 11 or 12, or the method of any of claims 2 or 10 to 12 wherein a representative information of a first number of occurrences of at least first index of said codebook is a difference between said first number and a second number of occurrences of at least one second index of said codebook.

14. The electronic device of claim 9 or the method of claim 10 wherein said indexes are decoded in from a bitstream, said codebook and/or said representative information being decoded from in a header part of said bitstream.

15. A signal carrying data representative of indexes of symbols of a codebook, of said codebook and of numbers of occurrences of said indexes in said signal.

16. A computer program product including instructions which, when the program is executed by one or more processors, causes the one or more processors to carry out a method according to any of claims 2 to 8 or 10 to 14.

17. A non-transitory computer-readable medium including instructions for causing one or more processors to perform a method according to any of claims 2 to 8 or 10 to 14.

18. A non-transitory computer-readable medium storing a signal according to claim 15.

Description:
Systems and Methods for encoding a Deep Neural Network

This application claims the benefit of EP Patent Application No.19306220.5 filed on 30 September 2019

1. FIELD

Embodiments of the present disclosure can be implemented in many technical fields, for instance in the technical domain of multimedia processing, like for instance in image processing, video processing and/or audio processing.

For instance, the domain technical field of the one or more embodiments of the present disclosure is related to the use of Deep Learning techniques, like a use of a Deep Neural Network (DNN).

2. BACKGROUND SECTION

Deep Neural Networks (DNNs) have shown state of the art performance in variety of domains such as computer vision, speech recognition, natural language processing, etc. This performance however can come at the cost of massive computational cost as DNNs tend to have a huge number of parameters often running into millions, and sometimes even billions.

This can lead for instance to prohibitively high inference complexity. Inference complexity can be defined as the computational cost of applying trained DNN to test data for inference. The high inference complexity can be an important challenge for using DNNs, notably in environments involving an electronic device with limited hardware and/or software resource, for instance mobile or embedded devices with resource limitations like battery size, limited computational power, and memory capacity etc.

There is a need for a solution to facilitate transmission and/or storage of parameters.

3. SUMMARY

According to some aspects, the present principles enable at least one of the above disadvantages to be resolved by proposing a encoding method and/or a decoding method. The methods can be used for instance for encoding, respectively decoding, at least a part of a Deep Neural Network.

Generally, in an encoding process, data are quantized data and entropy coded to obtain compressed data. To reconstruct data, the compressed data are decoded by inverse processes corresponding to the entropy coding and quantization.

For instance, at least one embodiment of the method of the present disclosure relates to an encoding method including entropy coding of at least a part of a Deep Neural Network.

At least some embodiments of the present disclosure relate to a method comprising encoding indexes of symbols of a codebook, said codebook and information representative of numbers of occurrences of said encoded indexes. According to a second aspect, the present disclosure proposes a method for decoding a Deep Neural Network. For instance, at least one embodiment of the method of the present disclosure relates to a decoding method including entropy decoding at least one parameter of a Deep Neural Network.

At least some embodiments of the present disclosure relate to a method comprising decoding indexes of symbols of a codebook, said method comprising decoding said codebook and information representative of numbers of occurrences of said indexes.

According to another aspect, there is provided an apparatus. The apparatus comprises a processor. The processor can be configured to execute any of the aforementioned methods.

According to another general aspect of at least one embodiment, there is provided a device comprising an apparatus according to any of the decoding embodiments; and at least one of (i) an antenna configured to receive a signal, (ii) a band limiter configured to limit the received signal to a band of frequencies that includes a part of the signal, or (iii) a display configured to display an output representative of a part of the signal.

According to another general aspect of at least one embodiment, there is provided a non-transitory computer readable medium containing data content generated according to any of the described encoding embodiments or variants.

According to another general aspect of at least one embodiment, there is provided a signal comprising data generated according to any of the described encoding embodiments or variants.

According to another general aspect of at least one embodiment, a bitstream is formatted to include data content generated according to any of the described encoding embodiments or variants.

According to another general aspect of at least one embodiment, there is provided a computer program product comprising instructions which, when the program is executed by a computer, cause the computer to carry out any of the described decoding embodiments or variants.

4. BRIEF DESCRIPTION OF THE DRAWINGS

Fig. 1 shows a generic, standard encoding scheme.

Fig. 2 shows a generic, standard decoding scheme.

Fig. 3 shows a typical processor arrangement in which the described embodiments may be implemented;

Fig. 4a illustrates a DNN encoding scheme using at least some embodiments of the encoding method of the present disclosure; Fig. 4b illustrates with more details the way entropy encoding is performed, in at least some embodiment of the present disclosure compatible with the illustrated embodiment of Fig. 4a;

Fig. 5a illustrates a DNN decoding scheme using at least some embodiment of the decoding method of the present disclosure;

Fig. 5b illustrates with more details the way entropy decoding is performed, in at least some embodiment of the present disclosure compatible with the illustrated embodiment of Fig. 5a;

It is to be noted that the drawings illustrate example embodiments and that the embodiments of the present disclosure are not limited to the illustrated embodiments.

5. DETAILED DESCRIPTION

Deep Neural Networks are made up of several layers. A layer is associated with a set of parameters that can be obtained during a training of the DNN. These parameters (like Weights and/or Biases) are stored as multi-dimensional arrays (also referred to herein as “tensors”).

At least some embodiments of the present disclosure apply to compression of at least some parameters of at least one DNN. Indeed, compression can facilitate transmission and/or storage of the parameters of the at least one DNN. For instance, as illustrated by Fig. 4a and 4B, at least some embodiments of the present disclosure apply to the compression of parameters of at least one tensor associated with at least one layer of at least one Deep Neural Network. In some embodiments, the compression can be performed iteratively on two or more layers of a same DNN (as illustrated by Fig. 4a) and, notably, in some embodiments, on each layer of the same DNN.

Depending upon embodiments of the present disclosure, all the at least one layer can be convolutional layer(s), or fully connecter layer(s), or the at least one layer can comprise at least one convolutional layer and/or at least one fully connecter layer.

In the exemplary embodiment of the compression method 400 of Fig. 4A, the method 400 can comprise obtaining 410 (or in other words getting) parameters of at least one tensor associated with a layer to be compressed. The obtaining can for instance be performed by retrieving the parameters of at least one layer from a storage unit, or by receiving the parameters from a data source via a communication interface.

In at least one embodiment of the present disclosure, performing a compression of a layer of a Neural Network can comprise:

- Quantization 430 of parameters (like Weights and Biases) of the layer of the Neural Network to represent them with a smaller number of bits;

- Lossless entropy coding 440 of the quantized information. In some embodiments, the compression 400 can further comprise, prior to the quantization 430, a step of reducing 420 the number of parameters (like Weights and Biases) of the Neural Network by utilizing the inherent redundancies in the Neural Network. The reducing 420 thus provides a tensor of reduced dimensions, compared to the dimension of the tensor associated with a layer. This reducing 420 is optional and can thus be omitted in some embodiments.

In the exemplary embodiment described, quantization is performed on parameters of a tensor (also called herein “original tensor”, or “tensor to be quantized”) associated with one layer. Quantization can for instance be performed by using a method like “trained quantization”.

As illustrated by Fig. 4a, the parameters input to the quantization can be of floating point type, while the element output by the quantization can be of integer type and/or floating point type.

In the exemplary embodiment described, the output of quantization 430 can comprise following elements:

- at least one codebook,

- symbol counts (also called hereinafter “parameter Counts”), and

- indexes.

In the exemplary embodiment of Fig. 4a, the at least one codebook can be a single codebook.

A Codebook is a set of values (like floating-point values) that the parameters of a layer can have, after quantization. For instance, in an exemplary embodiment, where the K-Means algorithm is used for the quantization of the network parameters, the values of a codebook can be the centers of clusters calculated by the K-Means Quantization algorithm.

K-Means is a simple algorithm for clustering n-dimensional vectors. The goal of the K- Means algorithm is to partition data that are similar into “k” well-separated clusters. In quantization context, the number k can be a power of 2. The group of clusters is referred to hereinafter as the “Codebook”. Each entry in the codebook is a number specifying the “center” of that cluster. For example, for 5-bit quantization of numbers, the codebook has 2 5 =32 entries and each number can be represented by a 5-bit index value that corresponds to the codebook entry that is closest to this number.

Symbol Counts provide, for each value of the codebook, the number of quantized parameters having the corresponding codebook value. For instance, the symbol counts can correspond to a set of integer values, comprising one integer value for each value of the codebook. The i th item in this symbol counts set gives the number of times the i th symbol of the codebook occurs in the quantified tensor, or in other words the number of times the i th symbol of the codebook is used for quantizing a value of the original tensor. Symbol Counts set and the corresponding codebook have the same dimension.

Indexes correspond to the codebook values assigned to the parameters of original tensor by the quantizing. In some embodiment, a codebook value can be assigned to each of the parameters of the same cluster (thus the set of quantized parameters can be seen as a tensor of a same shape than the original tensor). In some other embodiments, instead of assigning a codebook value to each of the parameters of the same cluster, an index can be derived, which can correspond to a list with a length equal to the size of the original tensor, (i.e. the length of the flattened version of the original tensor). Each item in this list can be an index to the item in the codebook whose value is closest to the value of the corresponding parameter in the original tensor.

According to at least one embodiment of the present disclosure, at least some of the elements output by the quantization 430 are used as input for performing a lossless entropy coding 440. Other elements can be input to the entropy coding 440. For instance, as in the illustrated embodiment, a shape of the original tensor can be input to the entropy coding 440. The shape gives information about the dimensionality of the original tensor. For instance, the shape can be a set of numbers. A 2-D, 64x32 weight matrix can for example be represented by a shape comprising two values [64, 32] As another example, a 4-D weight tensor for a convolution layer with kernel size 3x3 and input and channel 16 and output channel 32, can be represented by a shape comprising four values [3, 3, 16, 32]

Entropy coding is a lossless data compression which works based on the fact that any data can be compressed if some data symbols are more likely to happen than others.

For instance, for the best possible compression code (minimum average code length) the output length contains a contribution of “-log p” bits from the encoding of each symbol whose probability of occurrence is p.

Thus, at least one embodiment of the present disclosure can take account of a probability of occurrence of at least one of the data symbols . As an exemplar, at least one embodiment of the present disclosure takes account of a probability model of occurrence for all the data symbols. Indeed, having an accurate probability model of occurrence of all the data symbols can be helpful to improve the efficiency of the encoding.

According to at least one embodiment of the present disclosure, the information input to the entropy coding 440 can be broken down into a header part and a body part, which can each be encoded differently. Indeed, information contained in the header (like information related to the symbol counts for instance) can be used for obtaining a probability model for the body part. More precisely, in at least one exemplary embodiment of the present disclosure, the header can comprise the shape, at least one codebook, and information related to symbol counts corresponding to the at least one codebook (like the symbol counts set described above).

In at least some embodiments of the present disclosure, the body part can comprise the indexes output by the quantization of the at least codebook contained in the header.

The size of header can differ upon embodiments, compared to the size of the indexes output by the quantization. Notably, in some embodiments, the header size can be insignificant compared to the indexes size, or at least much smaller than the whole size of indexes. Indeed, the indexes can contain millions of integer values for instance, while the header size can be less or equal to 0.01%, 0.1%, 1%, 5% or 10% of the whole size of indexes, for instance.

Fig. 4b illustrates in more details the entropy coding 440 of Fig. 4A.

According to at least one embodiment of the present disclosure, the entropy coding 440 can be performed differently for the header and for the indexes. For instance, entropy coding 446 of the header can be based on adaptive arithmetic coding for the header, as no probability of occurrence is associated to the header information. Entropy coding 448 of the body (or indexes) can be based on conditional arithmetic coding for the indexes. For instance, the body can be compressed using conditional arithmetic coding using the Symbol Counts introduced above as an initial value of the probability model, the probability model being then updated as symbols are encoded.

As explained above, in the compression framework of at least some embodiments of the present disclosure, which is adapted to compress a DNN, a quantization is performed before the entropy coding. When using the K-means based quantization, for instance, the probability distribution can be automatically available as a byproduct of quantization process.

Arithmetic Coding works for instance with a probability model (the probability of each symbol happening in the data). In some real applications, the probability model is not constant during the compression process. Adaptive Arithmetic Coding creates a probability model based on actual occurrences of symbols in the data stream and updates this model continuously during the process. This can be especially useful when a probability model is not available for the compressed data, as it is the case for the header data of at least some embodiments of the present disclosure for instance.

In the exemplary embodiment illustrated, the encoding step 440 comprises sorting 442 at least some of the elements output by the quantization 430. The sorting 442 can be performed as a preliminary stage of the encoding 444. For instance, the entries of the codebook can be sorted based on the frequency of occurrences of each symbol (or entry) in the indexes. The Symbol Counts can be sorted similarly (to correspond to the sorted codebook). Depending on the embodiments, the sorting can be performed differently (like in an increasing or decreasing order).

For instance, in the exemplary embodiment illustrated, the Symbol Counts and the corresponding codebook can both be reordered in decreasing order of the Symbol Counts, the first item in the codebook corresponding to the most frequent value in the quantized tensor, and thus to the most probable symbol. In the exemplary embodiment illustrated, once sorted, symbol counts correspond to a set of integers in descending order.

As, in at least some embodiments of the present disclosure, indexes can contain millions of integer values, the symbol counts values can be very large numbers. Thus, in at least some embodiments of the present disclosure, instead of storing actual values of symbol counts in the header, absolute values of differences between values of symbol counts can be stored (except for some values like the first and/or the last values for instance). As an exemplar, instead of storing a current value of a symbol counts set ordered in a descending order, we can store the difference between the current value and its previous (or preceding) value, except for the first value (which is the largest value, in this exemplar). Such an embodiment can help obtaining smaller numbers in the portion of the header associated to “symbol count”, compared to a storage of the symbol counts themselves, and can thus help to reduce the size of the header.

According to Fig. 4b, the encoding 440 can further comprise serializing 444 the header part. For instance, the shape, the at least one codebook, and the information related to the corresponding symbol counts can be gathered (e.g. serialized) into an array of bytes. The shape can be stored as an array of integer values. In the exemplary embodiment of Fig. 4b, the codebook can contain floating-point values assumed to be 32-bits format (e.g. in 32-bits IEEE-754 format). Each floating-point value can be serialized to a list of 4 bytes. Appendix A gives more details on how the floating-point numbers can be converted to 4- byte integers and how integer numbers can be stored using variable number of bytes.

In the illustrated embodiment, after the serialization 444 of the header, all header information can correspond to an array of bytes. This array of bytes can be processed with an adaptive arithmetic coding algorithm. As explained before, adaptive arithmetic coding does not require a probability model as it can automatically create an initial model (with equal probability for all symbols) and updates it as each symbol is seen in the data.

Conditional Arithmetic Coding can provide the Arithmetic Coding with a real-time probability model. In the illustrated exemplary embodiment of the present disclosure, the symbol counts output by the quantization give the exact number of occurrences for each symbol (or value) of the codebook. Thus, at the beginning of the encoding of the indexes, the probability of occurrence for each symbol in the codebook can be proportional to its number of occurrences in the indexes. As the data is encoded, the actual occurrence of the already encoded indexes can impact the probability of occurrences of the codebook values for the indexes not yet encoded. Thus, the probability of occurrence can evolve during the encoding. In other words, at each stage, we use the original probability conditioned by the counts of each symbol already consumed by the encoding. Conditional Arithmetic Coding can be expected to provide a good compression ratio because it is expected to use the most accurate probability model when encoding/decoding each index of the body (as explained above in link with Shannon's source coding theorem.) .

In some embodiments; when several layers can be encoded by the encoding method 400, after encoding parameters associated to a layer, the method can be performed iteratively layer per layer, until (450) the end of the encoding of parameters of the last layerto be encoded.

In some embodiments, the method 400 can comprise obtaining (or calculating) (not illustrated) the size of quantized elements (including for instance codebook, symbol counts, and/or indexes) and the size of the raw (un-quantized) elements, the encoding being performed by taking account of those obtained sizes. For instance, the encoding can use the output of the quantizing as described above only when the size of the raw elements is bigger than the size of the quantified elements. When the size of the raw elements is smaller than the size of the quantified elements, the encoding can use directly values of the original tensor, instead of their corresponding approximated, quantized values, as the original tensor values take less space in the bitstream than the quantified values and are furthermore exact values.

Figures 5a and 5b depict a decoding method 500 that can be used for decoding a bitstream obtained by the encoding method 400 already described, according to at least one exemplary embodiment of the present disclosure.

As illustrated by Fig. 5A, the method 500 can comprise parsing and decoding 510 a bitstream corresponding to a layer of the DNN. More precisely, the parsing and decoding 510 can comprise decoding 512 the header part of the bitstream. The decoded header information, obtained by decoding the header, can comprise for instance the codebook previously used for quantizing the values of the corresponding original tensor and parameter counts (or in other words “symbol counts”) for items of the codebooks. The method 500 can further comprise decoding 514 the body of the bitstream. The decoding 514 of the body can use the decoded header information to arithmetically decode the body.

For instance, in the exemplary embodiment described, the decoding 512 of the header is performed prior to the decoding 514 of the body. The decoding 512 of the header can be performed using an arithmetic decoder corresponding to the arithmetic encoder used for encoding the header. The decoding of the header can permit to retrieve the shape, the codebook values as well as the symbol counts in their encoded version. Indeed, according to some embodiments detailed above in link with figures 4a and 4b, the encoded symbol counts can comprise the first value v 0 of the symbol counts and encoded differences between values of the symbol counts. In such an embodiment, the method 500 can comprise obtaining actual values of the symbol counts, from the encoded symbol counts, an actual value v k (with k: integer strictly positive) of the symbol counts being derived from the current decoded difference d k , for instance by adding the previously obtained actual value v k -i of the symbol counts to the current decoded difference d k .

The initial probability model, derived by the obtained actual values of the symbol counts, can then be used during the decoding 514 of the body of the bitstream. The indexes comprised in the decoded body can then be reshaped (if needed) to the original shape (i.e. the shape of the original tensor) using the decoded shape information (obtained when decoding the header). The method can further comprise performing inverse quantization 520, using the decoded information (like the indexes reshaped in the original shape and the codebook).

When several layers can be decoded by the decoding method 500, the method 500 can be performed iteratively layer per layer, until (550) parameters of the last layer are encoded.

Experimental results

Some experimental results are detailed below for some exemplary embodiments tested on network structures of LeNet-5 (handwritten digit classification network) and VGG16 (for Image Classification network) and using Adaptive Arithmetic Coding for header part and Conditional Arithmetic Coding for the body part, as in the exemplary embodiment detailed above. In the tested exemplary embodiments, LeNet-5 and VGG16 network structures have the following network configuration:

Configuration for LeNet-5

Scope InShape Comments OutShape Activ. Post Act. # of Params

L1_CONV 2828 1 KSP: 5 1 s 14 146 Tanh MP(KSP):22 s 156 L2_CONV 14 146 KSP: 5 1 v 5 5 16 Tanh MP(KSP):22 v 2,416

L3_FC 5 5 16 120 Tanh 48,120

L4_FC 120 84 Tanh 10,164

L5 FC 84 10 Softmax 850

Total Number of parameters: 61 ,706

Configuration for VGG16

Scope InShape Comments OutShape Activ. Post Act. # of Params

S1_L1_CONV 224224 3 KSP: 3 1 s 224 22464 ReLU 1 ,792

S1_L2_CONV 22422464 KSP: 3 1 s 112 11264 ReLU MP(KSP):22 s 36,928

S2 L1 CONV 112 11264 KSP: 3 1 s 112 112 128 ReLU 73,856 S2_L2_CONV 112 112 128 KSP: 3 1 s 5656 128 ReLU MP(KSP):22 s 147,584

S3_L1_CONV 5656 128 KSP: 3 1 s 56 56256 ReLU 295,168

S3_L2_CONV 5656256 KSP: 3 1 s 56 56256 ReLU 590,080

S3_L3_CONV 5656256 KSP: 3 1 s 2828256 ReLU MP(KSP):22 s 590,080

S4_L1_CONV 2828256 KSP: 3 1 s 2828 512 ReLU 1 ,180,160

S4_L2_CONV 2828 512 KSP: 3 1 s 2828 512 ReLU 2,359,808

S4_L3_CONV 2828 512 KSP: 3 1 s 14 14 512 ReLU MP(KSP):22 s 2,359,808

S5_L1_CONV 14 14 512 KSP: 3 1 s 14 14 512 ReLU 2,359,808

S5_L2_CONV 14 14 512 KSP: 3 1 s 14 14 512 ReLU 2,359,808

S5_L3_CONV 14 14 512 KSP: 3 1 s 7 7 512 ReLU MP(KSP):22 s 2,359,808

S6_L1_FC 7 7 512 4096 ReLU 102,764,544

S6_L2_FC 4096 4096 ReLU 16,781 ,312

S6 L3 FC 4096 1000 Softmax 4,097,000

Total Number of parameters: 138,357,544

The tested exemplary embodiments can lead to better results than some known solutions based only adaptive arithmetic coding, or on one of its variation, like solutions known as CABAC (for encoding video and image information) or DeepCABAC, as shown by the following table.

The following table compares the results of entropy coding for actual network parameters of 4 different tensors from VGG16 or LeNet-5 networks. These tensors are first quantized and then the results of the quantization are provided to two different entropy coding unit: a unit using a DeepCABAC algorithms and a unit using at least one embodiment of the method in the present disclosure).

Additional Embodiments and Information

This application describes a variety of aspects, including tools, features, embodiments, models, approaches, etc. Many of these aspects are described with specificity and, at least to show the individual characteristics, are often described in a manner that may sound limiting. However, this is for purposes of clarity in description, and does not limit the application or scope of those aspects. Indeed, all of the different aspects can be combined and interchanged to provide further aspects. Moreover, the aspects can be combined and interchanged with aspects described in earlier filings as well.

The aspects described and contemplated in this application can be implemented in many different forms. Figures 1 , 2 and 3 below provide some embodiments, but other embodiments are contemplated and the discussion of Figures 1, 2 and 3 does not limit the breadth of the implementations. At least one of the aspects generally relates to an encoding and decoding framework, that can be applied to encoding or decoding data related to a DNN, and at least one other aspect generally relates to transmitting a bitstream generated or encoded. These and other aspects can be implemented as a method, an apparatus, a computer readable storage medium having stored thereon instructions for encoding or decoding data, like data related to a DNN, according to any of the methods described, and/or a computer readable storage medium having stored thereon a bitstream generated according to any of the methods described.

In the present application, the terms “reconstructed” and “decoded” may be used interchangeably, Usually, but not necessarily, the term “reconstructed” is used at the encoder side while “decoded” is used at the decoder side.

Various methods are described herein, and each of the methods comprises one or more steps or actions for achieving the described method. Unless a specific order of steps or actions is required for proper operation of the method, the order and/or use of specific steps and/or actions may be modified or combined.

Various methods and other aspects described in this application can be used to modify modules, for example, entropy coding, and/or decoding modules (360, 150, 330), of a video encoder 100 and decoder 200 as shown in FIG. 1 and FIG. 2. Moreover, the present aspects are not limited to a given standard and can be applied, for example, to other standards and recommendations, whether pre-existing or future-developed, and extensions of any such standards and recommendations. Unless indicated otherwise, or technically precluded, the aspects described in this application can be used individually or in combination.

Various numeric values are used in the present application. The specific values are for example purposes and the aspects described are not limited to these specific values.

Fig. 1 illustrates an encoder 100. Variations of this encoder 100 are contemplated, but the encoder 100 is described below for purposes of clarity without describing all expected variations.

Before being encoded, the data sequence may go through pre-encoding processing (110), for example in order to get a signal distribution more resilient to compression. Metadata can be associated with the pre-processing and attached to the bitstream. In the encoder 100, data is encoded by the encoder elements as described below. The data to be encoded can be partitioned (120) and processed in units of, for example, CUs. Each unit is encoded . The data can be transformed (130) and quantized (140). The quantized (and optionally transform) coefficients, as well other syntax elements, are entropy coded (150) to output a bitstream. The encoder can skip the transform and apply quantization directly to the non-transformed data. The encoder can bypass both transform and quantization, i.e., the data is coded directly without the application of the transform or quantization processes.

Fig. 2 illustrates a block diagram of a decoder 200. In the decoder 200, a bitstream is decoded by the decoder elements as described below. Decoder 200 generally performs a decoding pass reciprocal to the encoding pass as described in FIG. 1. The encoder 100 also generally performs decoding as part of encoding data.

In particular, the input of the decoder includes a bitstream, which can be generated by encoder 100. The bitstream is first entropy decoded (210) to obtain transform coefficients, and other coded information (for instance coded information regarding a number of encoded layers of a DNN and/or an identification of an encoded layer of a DNN). The partition information indicates how data is partitioned. The decoder may therefore divide (220) the data according to the decoded partitioning information. The transform coefficients are de-quantized (230) and inverse transformed (240).

The decoded data can further go through post-decoding processing (250), for example, for performing the inverse of the process performed in the pre-encoding processing (110). The post-decoding processing can use metadata derived in the pre-encoding processing and signaled in the bitstream.

Fig. 3 illustrates a block diagram of an example of a system in which various aspects and embodiments are implemented. System 1000 can be embodied as a device including the various components described below and is configured to perform one or more of the aspects described in this document. Examples of such devices include, but are not limited to, various electronic devices such as personal computers, laptop computers, smartphones, tablet computers, digital multimedia set top boxes, digital television receivers, personal video recording systems, connected home appliances, and servers. Elements of system 1000, singly or in combination, can be embodied in a single integrated circuit (IC), multiple ICs, and/or discrete components. For example, in at least one embodiment, the processing and encoder/decoder elements of system 1000 are distributed across multiple ICs and/or discrete components. In various embodiments, the system 1000 is communicatively coupled to one or more other systems, or other electronic devices, via, for example, a communications bus or through dedicated input and/or output ports. In various embodiments, the system 1000 is configured to implement one or more of the aspects described in this document. The system 1000 includes at least one processor 1010 configured to execute instructions loaded therein for implementing, for example, the various aspects described in this document. Processor 1010 can include embedded memory, input output interface, and various other circuitries as known in the art. The system 1000 includes at least one memory 1020 (e.g., a volatile memory device, and/or a non-volatile memory device). System 1000 includes a storage device 1040, which can include non-volatile memory and/or volatile memory, including, but not limited to, Electrically Erasable Programmable Read-Only Memory (EEPROM), Read-Only Memory (ROM), Programmable Read-Only Memory (PROM), Random Access Memory (RAM), Dynamic Random-Access Memory (DRAM), Static Random- Access Memory (SRAM), flash, magnetic disk drive, and/or optical disk drive. The storage device 1040 can include an internal storage device, an attached storage device (including detachable and non-detachable storage devices), and/ora network accessible storage device, as non-limiting examples.

System 1000 includes an encoder/decoder module 1030 configured, for example, to process data to provide an encoded DNN layer or decoded DNN layer, and the encoder/decoder module 1030 can include its own processor and memory. The encoder/decoder module 1030 represents module(s) that can be included in a device to perform the encoding and/or decoding functions. As is known, a device can include one or both of the encoding and decoding modules. Additionally, encoder/decoder module 1030 can be implemented as a separate element of system 1000 or can be incorporated within processor 1010 as a combination of hardware and software as known to those skilled in the art.

Program code to be loaded onto processor 1010 or encoder/decoder 1030 to perform the various aspects described in this document can be stored in storage device 1040 and subsequently loaded onto memory 1020 for execution by processor 1010. In accordance with various embodiments, one or more of processor 1010, memory 1020, storage device 1040, and encoder/decoder module 1030 can store one or more of various items during the performance of the processes described in this document. Such stored items can include, but are not limited to, the input tensors, decoded tensors or portions of the decoded tensors, the bitstream, matrices, variables, and intermediate or final results from the processing of equations, formulas, operations, and operational logic.

In some embodiments, memory inside of the processor 1010 and/or the encoder/decoder module 1030 is used to store instructions and to provide working memory for processing that is needed during encoding or decoding. In other embodiments, however, a memory external to the processing device (for example, the processing device can be either the processor 1010 or the encoder/decoder module 1030) is used for one or more of these functions. The external memory can be the memory 1020 and/or the storage device 1040, for example, a dynamic volatile memory and/or a non-volatile flash memory. In several embodiments, an external non-volatile flash memory is used to store the operating system of, for example, a television. In at least one embodiment, a fast external dynamic volatile memory such as a RAM is used as working memory for video coding and decoding operations, such as for MPEG-2 (MPEG refers to the Moving Picture Experts Group, MPEG-2 is also referred to as ISO/IEC 13818, and 13818-1 is also known as H.222, and 13818-2 is also known as H.262), HE VC (HEVC refers to High Efficiency Video Coding, also known as H.265 and MPEG- H Part 2), or WC (Versatile Video Coding, a new standard being developed by JVET, the Joint Video Experts Team).

The input to the elements of system 1000 can be provided through various input devices as indicated in block 1130. Such input devices include, but are not limited to, (i) a radio frequency (RF) portion that receives an RF signal transmitted, for example, over the air by a broadcaster, (ii) a Component (COMP) input terminal (or a set of COMP input terminals), (iii) a Universal Serial Bus (USB) input terminal, and/or (iv) a High Definition Multimedia Interface (HDMI) input terminal. Other examples, not shown in Fig. 3, include composite video.

In various embodiments, the input devices of block 1130 have associated respective input processing elements as known in the art. For example, the RF portion can be associated with elements suitable for (i) selecting a desired frequency (also referred to as selecting a signal, or band-limiting a signal to a band of frequencies), (ii) down converting the selected signal, (iii) band-limiting again to a narrower band of frequencies to select (for example) a signal frequency band which can be referred to as a channel in certain embodiments, (iv) demodulating the down converted and band-limited signal, (v) performing error correction, and (vi) demultiplexing to select the desired stream of data packets. The RF portion of various embodiments includes one or more elements to perform these functions, for example, frequency selectors, signal selectors, band-limiters, channel selectors, filters, downconverters, demodulators, error correctors, and demultiplexers. The RF portion can include a tuner that performs various of these functions, including, for example, down converting the received signal to a lower frequency (for example, an intermediate frequency or a near-baseband frequency) or to baseband. In one set-top box embodiment, the RF portion and its associated input processing element receives an RF signal transmitted over a wired (for example, cable) medium, and performs frequency selection by filtering, down converting, and filtering again to a desired frequency band. Various embodiments rearrange the order of the above-described (and other) elements, remove some of these elements, and/or add other elements performing similar or different functions. Adding elements can include inserting elements in between existing elements, such as, for example, inserting amplifiers and an analog-to-digital converter. In various embodiments, the RF portion includes an antenna. Additionally, the USB and/or HDMI terminals can include respective interface processors for connecting system 1000 to other electronic devices across USB and/or HDMI connections. It is to be understood that various aspects of input processing, for example, Reed-Solomon error correction, can be implemented, for example, within a separate input processing IC or within processor 1010 as necessary. Similarly, aspects of USB or HDMI interface processing can be implemented within separate interface ICs or within processor 1010 as necessary. The demodulated, error corrected, and demultiplexed stream is provided to various processing elements, including, for example, processor 1010, and encoder/decoder 1030 operating in combination with the memory and storage elements to process the data stream as necessary for presentation on an output device.

Various elements of system 1000 can be provided within an integrated housing, Within the integrated housing, the various elements can be interconnected and transmit data therebetween using suitable connection arrangement 1140, for example, an internal bus as known in the art, including the Inter-IC (I2C) bus, wiring, and printed circuit boards.

The system 1000 includes communication interface 1050 that enables communication with other devices via communication channel 1060. The communication interface 1050 can include, but is not limited to, a transceiver configured to transmit and to receive data over communication channel 1060. The communication interface 1050 can include, but is not limited to, a modem or network card and the communication channel 1060 can be implemented, for example, within a wired and/or a wireless medium.

Data is streamed, or otherwise provided, to the system 1000, in various embodiments, using a wireless network such as a Wi-Fi network, for example IEEE 802.11 (IEEE refers to the Institute of Electrical and Electronics Engineers). The Wi-Fi signal of these embodiments is received over the communications channel 1060 and the communications interface 1050 which are adapted for Wi-Fi communications. The communications channel 1060 of these embodiments is typically connected to an access point or router that provides access to external networks including the Internet for allowing streaming applications and other over-the- top communications. Other embodiments provide streamed data to the system 1000 using a set-top box that delivers the data over the HDMI connection of the input block 1130. Still other embodiments provide streamed data to the system 1000 using the RF connection of the input block 1130. As indicated above, various embodiments provide data in a non-streaming manner. Additionally, various embodiments use wireless networks other than Wi-Fi, for example a cellular network or a Bluetooth network.

The system 1000 can provide an output signal to various output devices, including a display 1100, speakers 1110, and other peripheral devices 1120. The display 1100 of various embodiments includes one or more of, for example, a touchscreen display, an organic light- emitting diode (OLED) display, a curved display, and/or a foldable display. The display 1100 can be for a television, a tablet, a laptop, a cell phone (mobile phone), or another device. The display 1100 can also be integrated with other components (for example, as in a smart phone), or separate (for example, an external monitor for a laptop). The other peripheral devices 1120 include, in various examples of embodiments, one or more of a stand-alone digital video disc (or digital versatile disc) (DVR, for both terms), a disk player, a stereo system, and/or a lighting system. Various embodiments use one or more peripheral devices 1120 that provide a function based on the output of the system 1000. For example, a disk player performs the function of playing the output of the system 1000.

In various embodiments, control signals are communicated between the system 1000 and the display 1100, speakers 1110, or other peripheral devices 1120 using signaling such as AV. Link, Consumer Electronics Control (CEC), or other communications protocols that enable device-to-device control with or without user intervention. The output devices can be communicatively coupled to system 1000 via dedicated connections through respective interfaces 1070, 1080, and 1090. Alternatively, the output devices can be connected to system 1000 using the communications channel 1060 via the communications interface 1050. The display 1100 and speakers 1110 can be integrated in a single unit with the other components of system 1000 in an electronic device such as, for example, a television. In various embodiments, the display interface 1070 includes a display driver, such as, for example, a timing controller (T Con) chip.

The display 1100 and speaker 1110 can alternatively be separate from one or more of the other components, for example, if the RF portion of input 1130 is part of a separate set-top box. In various embodiments in which the display 1100 and speakers 1110 are external components, the output signal can be provided via dedicated output connections, including, for example, HDMI ports, USB ports, or COMP outputs.

The embodiments can be carried out by computer software implemented by the processor 1010 or by hardware, or by a combination of hardware and software. As a nonlimiting example, the embodiments can be implemented by one or more integrated circuits. The memory 1020 can be of any type appropriate to the technical environment and can be implemented using any appropriate data storage technology, such as optical memory devices, magnetic memory devices, semiconductor-based memory devices, fixed memory, and removable memory, as non-limiting examples. The processor 1010 can be of any type appropriate to the technical environment, and can encompass one or more of microprocessors, general purpose computers, special purpose computers, and processors based on a multicore architecture, as non-limiting examples. Various implementations involve decoding. “Decoding”, as used in this application, can encompass all or part of the processes performed, for example, on a received encoded sequence in order to produce a final output suitable for display. In various embodiments, such processes include one or more of the processes typically performed by a decoder, for example, entropy decoding, inverse quantization, inverse transformation, and differential decoding. In various embodiments, such processes also, or alternatively, include processes performed by a decoder of various implementations described in this application.

As further examples, in one embodiment “decoding” refers only to entropy decoding, in another embodiment “decoding” refers only to differential decoding, and in another embodiment “decoding” refers to a combination of entropy decoding and differential decoding. Whether the phrase “decoding process” is intended to refer specifically to a subset of operations or generally to the broader decoding process will be clear based on the context of the specific descriptions and is believed to be well understood by those skilled in the art.

Various implementations involve encoding. In an analogous way to the above discussion about “decoding”, “encoding” as used in this application can encompass all or part of the processes performed, for example, on an input data sequence in order to produce an encoded bitstream. In various embodiments, such processes include one or more of the processes typically performed by an encoder, for example, partitioning, differential encoding, transformation, quantization, and entropy encoding. In various embodiments, such processes also, or alternatively, include processes performed by an encoder of various implementations described in this application.

As further examples, in one embodiment “encoding” refers only to entropy encoding, in another embodiment “encoding” refers only to differential encoding, and in another embodiment “encoding” refers to a combination of differential encoding and entropy encoding. Whether the phrase “encoding process” is intended to refer specifically to a subset of operations or generally to the broader encoding process will be clear based on the context of the specific descriptions and is believed to be well understood by those skilled in the art.

Note that the syntax elements as used herein, are descriptive terms. As such, they do not preclude the use of other syntax element names.

When a figure is presented as a flow diagram, it should be understood that it also provides a block diagram of a corresponding apparatus. Similarly, when a figure is presented as a block diagram, it should be understood that it also provides a flow diagram of a corresponding method/process.

Various embodiments refer to parametric models or rate distortion optimization. In particular, during the encoding process, the balance or trade-off between the rate and distortion is usually considered, often given the constraints of computational complexity. It can be measured through a Rate Distortion Optimization (RDO) metric, or through Least Mean Square (LMS), Mean of Absolute Errors (MAE), or other such measurements. The rate distortion optimization is usually formulated as minimizing a rate distortion function, which is a weighted sum of the rate and of the distortion. There are different approaches to solve the rate distortion optimization problem. For example, the approaches may be based on an extensive testing of all encoding options, including all considered modes or coding parameters values, with a complete evaluation of their coding cost and related distortion of the reconstructed signal after coding and decoding. Faster approaches may also be used, to save encoding complexity, in particular with computation of an approximated distortion based on the prediction or the prediction residual signal, not the reconstructed one. Mix of these two approaches can also be used, such as by using an approximated distortion for only some of the possible encoding options, and a complete distortion for other encoding options. Other approaches only evaluate a subset of the possible encoding options. More generally, many approaches employ any of a variety of techniques to perform the optimization, but the optimization is not necessarily a complete evaluation of both the coding cost and related distortion.

The implementations and aspects described herein can be implemented in, for example, a method or a process, an apparatus, a software program, a data stream, or a signal. Even if only discussed in the context of a single form of implementation (for example, discussed only as a method), the implementation of features discussed can also be implemented in other forms (for example, an apparatus or program). An apparatus can be implemented in, for example, appropriate hardware, software, and firmware. The methods can be implemented in, for example, a processor, which refers to processing devices in general, including, for example, a computer, a microprocessor, an integrated circuit, or a programmable logic device. Processors also include communication devices, such as, for example, computers, cell phones, portable/personal digital assistants ("PDAs"), and other devices that facilitate communication of information between end-users.

Reference to “one embodiment” or “an embodiment” or “one implementation” or “an implementation”, as well as other variations thereof, means that a particular feature, structure, characteristic, and so forth described in connection with the embodiment is included in at least one embodiment. Thus, the appearances of the phrase “in one embodiment” or “in an embodiment” or “in one implementation” or “in an implementation”, as well any other variations, appearing in various places throughout this application are not necessarily all referring to the same embodiment.

Additionally, this application may refer to “determining” various pieces of information. Determining the information can include one or more of, for example, estimating the information, calculating the information, predicting the information, or retrieving the information from memory.

Further, this application may refer to “accessing” various pieces of information. Accessing the information can include one or more of, for example, receiving the information, retrieving the information (for example, from memory), storing the information, moving the information, copying the information, calculating the information, determining the information, predicting the information, or estimating the information.

Additionally, this application may refer to “receiving” various pieces of information. Receiving is, as with “accessing”, intended to be a broad term. Receiving the information can include one or more of, for example, accessing the information, or retrieving the information (for example, from memory). Further, “receiving” is typically involved, in one way or another, during operations such as, for example, storing the information, processing the information, transmitting the information, moving the information, copying the information, erasing the information, calculating the information, determining the information, predicting the information, or estimating the information.

It is to be appreciated that the use of any of the following 7”, “and/or”, and “at least one of, for example, in the cases of “A/B”, “A and/or B” and “at least one of A and B”, is intended to encompass the selection of the first listed option (A) only, or the selection of the second listed option (B) only, or the selection of both options (A and B). As a further example, in the cases of “A, B, and/or C” and “at least one of A, B, and C”, such phrasing is intended to encompass the selection of the first listed option (A) only, or the selection of the second listed option (B) only, or the selection of the third listed option (C) only, or the selection of the first and the second listed options (A and B) only, or the selection of the first and third listed options (A and C) only, or the selection of the second and third listed options (B and C) only, or the selection of all three options (A and B and C). This may be extended, as is clear to one of ordinary skill in this and related arts, for as many items as are listed.

Also, as used herein, the word “signal” refers to, among other things, indicating something to a corresponding decoder. For example, in certain embodiments the encoder signals at least one of a plurality of transforms, coding modes or flags. In this way, in an embodiment the same parameter is used at both the encoder side and the decoder side. Thus, for example, an encoder can transmit (explicit signaling) a particular parameter to the decoder so that the decoder can use the same particular parameter. Conversely, if the decoder already has the particular parameter as well as others, then signaling can be used without transmitting (implicit signaling) to simply allow the decoder to know and select the particular parameter. By avoiding transmission of any actual functions, a bit savings is realized in various embodiments. It is to be appreciated that signaling can be accomplished in a variety of ways. For example, one or more syntax elements, flags, and so forth are used to signal information to a corresponding decoder in various embodiments. While the preceding relates to the verb form of the word “signal”, the word “signal” can also be used herein as a noun.

As will be evident to one of ordinary skill in the art, implementations can produce a variety of signals formatted to carry information that can be, for example, stored or transmitted. The information can include, for example, instructions for performing a method, or data produced by one of the described implementations. For example, a signal can be formatted to carry the bitstream of a described embodiment. Such a signal can be formatted, for example, as an electromagnetic wave (for example, using a radio frequency portion of spectrum) or as a baseband signal. The formatting can include, for example, encoding a data stream and modulating a carrier with the encoded data stream. The information that the signal carries can be, for example, analog or digital information. The signal can be transmitted over a variety of different wired or wireless links, as is known. The signal can be stored on a processor-readable medium.

We describe a number of embodiments. Features of these embodiments can be provided alone or in any combination, across various claim categories and types. Further, embodiments can include one or more of the following features, devices, or aspects, alone or in any combination, across various claim categories and types:

• A process or device to perform encoding and decoding of at least one parameter of a pre-trained deep neural network, to implement deep neural network compression.

• A process or device to perform encoding and decoding with inserted information in a bitstream representative of parameters to implement deep neural network compression of a pre-trained deep neural network comprising one or more layers.

• A process or device to perform encoding and decoding with inserted information in a bitstream representative of parameters to implement deep neural network compression of a pre-trained deep neural network until a compression criterion is reached.

• A bitstream or signal that includes one or more of the described syntax elements, or variations thereof.

• A bitstream or signal that includes syntax conveying information generated according to any of the embodiments described.

• Creating and/or transmitting and/or receiving and/or decoding according to any of the embodiments described.

• A method, process, apparatus, medium storing instructions, medium storing data, or signal according to any of the embodiments described.

• Inserting in the signaling syntax elements that enable the decoder to determine coding mode in a manner corresponding to that used by an encoder. • Creating and/or transmitting and/or receiving and/or decoding a bitstream or signal that includes one or more of the described syntax elements, or variations thereof.

• A TV, set-top box, cell phone, tablet, or other electronic device that performs transform method(s) according to any of the embodiments described.

• A TV, set-top box, cell phone, tablet, or other electronic device that performs transform method(s) determination according to any of the embodiments described, and that displays (e.g. using a monitor, screen, or other type of display) a resulting image.

• A TV, set-top box, cell phone, tablet, or other electronic device that selects, bandlimits, or tunes (e.g. using a tuner) a channel to receive a signal including an encoded image, and performs transform method(s) according to any of the embodiments described.

• A TV, set-top box, cell phone, tablet, or other electronic device that receives (e.g. using an antenna) a signal over the air that includes an encoded image, and performs transform method(s).

As can be appreciated by one skilled in the art, aspects of the present principles can be embodied as a system, device, method, signal or computer readable product or medium.

The present disclosure for instance relates to a method comprising encoding indexes of symbols of a codebook, said codebook and information representative of numbers of occurrences of said encoded indexes.

According to at least one embodiment of the present disclosure, said codebook and said representative information are encoded using an adaptive arithmetic coding.

According to at least one embodiment of the present disclosure, said indexes are encoded using conditional arithmetic coding.

According to at least one embodiment of the present disclosure, said method comprises sorting said representative information of said numbers of occurrences of said indexes. The representative information can be sorted decreasingly for instance.

According to at least one embodiment of the present disclosure, a representative information of a first number of occurrences of at least first index of said codebook is a difference between said first number and a second number of occurrences of at least one second index of said codebook.

According to at least one embodiment of the present disclosure, said indexes are encoded in a bitstream, said codebook and/or said representative information being encoded in a header part of said bitstream.

According to at least one embodiment of the present disclosure, said method comprises serializing said header part.

According to at least one embodiment of the present disclosure, said encoding is performed by taking account of at least one of the following elements : • -a size of encoded data

• a size of said codebook,

• a size of said representative information of said number of occurrences of said indexes,

• a size of said indexes ;

• a combination thereof.

According to at least one embodiment of the present disclosure, said method comprises encoding at least one parameter of at least one Deep Neural Network.

According to at least one embodiment of the present disclosure, said method comprises obtaining said codebook and/or said indexes by clustering said parameter(s).

The present disclosure also relates to an electronic device comprising at least one processor adapted for encoding indexes of symbols of a codebook, said codebook and information representative of numbers of occurrences of said encoded indexes. The processor can be configured to perform any embodiments of the aforementioned method.

The present disclosure also relates to a method comprising decoding indexes of symbols of a codebook, said method comprising decoding said codebook and information representative of numbers of occurrences of said indexes.

According to at least one embodiment of the present disclosure, said indexes are decoded in from a bitstream, said codebook and/or said representative information being decoded from in a header part of said bitstream.

The present disclosure also relates to an electronic device comprising at least one processor adapted for decoding indexes of symbols of a codebook, said at least one processor being adapted for decoding said codebook and information representative of numbers of occurrences of said indexes. The processor can be configured to perform any embodiments of the aforementioned method.

The present disclosure also relates to a computer program product including instructions which, when the program is executed by one or more processors, causes the one or more processors to carry out a method according to any of the aforementioned methods.

The present disclosure also relates to a non-transitory computer-readable medium including instructions for causing one or more processors to perform a method according to any of the aforementioned methods.

The present disclosure also relates to a signal carrying data representative of indexes of symbols of a codebook, of said codebook and of numbers of occurrences of said indexes in said signal.

The present disclosure also relates to a non-transitory computer-readable medium storing said signal.