EP1709743A1 - Dimensional vector and variable resolution quantisation - Google Patents

Abstract

The invention relates to compression coding and/ or decoding of digital signals, in particular by vector variable-rate quantisation defining a variable resolution. For this purpose an impulsion dictionary comprises: for a given dimension, increasing resolution dictionaries imbricated into each other and, for a given dimension, a union of: a totality (D'iN) of code-vectors produced, by inserting elements taken in a final set (A) into smaller dimension code-vectors according to a final set of predetermined insertion rules (F1) and a second totality of code-vectors (Y') which are not obtainable by insertion into the smaller dimension code vectors according to said set of the insertion rules.

Description

 VECTOR QUANTIFICATION IN VARIABLE DIMENSION AND RESOLUTION

The present invention relates to the coding and / or decoding in compression of digital signals such as audio, video signals, and more generally multimedia signals for their storage and / or their transmission.

A very widespread solution in compression of digital signals is vector quantization. A first incentive to use vector quantization can be found in the theory of block coding developed by Shannon according to which better performance can be achieved by increasing the size of the vectors to be coded. Vector quantization consists in representing an input vector by a vector of the same dimension chosen from a finite set. Thus, providing a quantifier at M levels (or code vectors) amounts to creating a non-bijective application of the set of input vectors (generally the real Euclidean space with dimensions R ⁿ , or even a subset of R ⁿ ) in a finite subset Y of R ⁿ . The subset Y then has M distinct elements:

Y is called the reproduction alphabet, or dictionary, or even directory. The elements of Y are called "vector-codes", "code words", "exit points", or even "representatives".

The flow rate by dimension (r) of the quantifier (or its "resolution") is defined by r = - log2 M n

In vector quantization, a block of n samples is treated as a vector of dimension n. The vector is coded by choosing a vector-code, in a dictionary of M vector-codes, the one that "resembles" it the most. In general, an exhaustive search is made among all the elements of the dictionary to select the element of the dictionary which minimizes a measurement of distance between it and the input vector.

According to the source coding theory, when the dimension becomes too large, the performance of vector quantization approaches a limit known as "source rate-distortion bound". In addition to the dimensionality of space, vector quantization can also exploit the properties of the source to be coded, for example non-linear and / or linear dependencies, or even the form of the probability distribution. In general, vector quantifier dictionaries are designed using statistical methods such as the generalized Lloyd algorithm (noted GLA for "Generalized Lloyd Algori thm"). This well-known algorithm is based on the necessary conditions of optimality of a vector quantization. From a training sequence representative of the ^• source to be coded and an initial dictionary, the dictionary is constructed iteratively. Each iteration has two stages: construction of the quantification regions by quantification of the training sequence according to the nearest neighbor rule, and - improvement of the dictionary by replacing the old code vectors with the region centroids (according to the centroid rule).

To avoid convergence towards a local minimum of this iterative deterministic algorithm, so-called "stochastic relaxation" variants (noted SKA for "Stochastic K-means algori thm") inspired by the simulated annealing technique have been proposed by introducing a part of '' random in the stage of building centroids and / or in that of building classes. The statistical vector quantifiers thus obtained have no structure, which makes their exploration costly in computation and greedy in memory. Indeed, the complexity of both coding and storage is proportional to n.2 ^nr . This exponential growth as a function of the size of the vectors and of the flow rate limits the use of unstructured vector quantizers to small dimensions and / or low flow rates in order to be able to implant them in real time.

Scalar quantization, which quantifies samples individually, is not as efficient as vector quantization because it can only exploit the form of the probability distribution of the source and the linear dependence. However, scalar quantization is less costly in computation and in memory than vector quantization. In addition, quantification scalar associated with entropy coding can achieve good performance even at moderate resolutions.

To overcome the constraints of size and dimension, several variants of basic vector quantization were studied, they try to remedy the absence of dictionary structure and thus manage to reduce complexity at the expense of quality. However, the performance / complexity compromise is improved, which makes it possible to increase the range of resolutions and / or dimensions to which vector quantization can be applied effectively in computation or memory cost.

Many schemes of structured vector quantizers have been proposed in the literature. The main ones are as follows: the tree vector quantifier which imposes a hierarchical tree structure on the dictionary: the search procedure is simplified but the quantizer requires more storage memory, the multistage vector quantizer which cascades vector quantizers lower levels: the dictionaries are reduced in size and the same applies to the computation time and the cost in memory, the vector quantizer known as "Cartesian product" of N classical vector quantizers of larger sizes and dimensions small: the input vector is broken down into N sub-vectors, each sub-vector being quantified independently of the others, - the vector quantizer "gain / orientation" constitutes a particular case of the vector quantifier "Cartesian product": two quantifiers are provided, one scalar and the other vector, which code separately, independently or not, the gain ( or norm) of the vector and its orientation (considering the normalized input vector). This type of vector quantization is also called "spherical" vector quantization or "polar" vector quantization, - the vector quantizer "code with permutation", whose vector-codes are obtained by permutations of the components of a vector-leader and its generalization to the composite (or union) of permutation codes.

The techniques described above are all based on a statistical approach.

Another radically different approach has also been proposed. This is algebraic vector quantization, which uses highly structured dictionaries, derived from regular networks of points or error correcting codes. Thanks to the algebraic properties of their dictionaries, algebraic vector quantizers are simple to implement and do not have to be stored in memory. Exploiting the regular structure of these dictionaries allows the development of optimal and fast search algorithms and mechanisms for associating in particular an index (or "index") with a corresponding vector code (for example by a formula ). Vector quantifiers algebraic are less complex to implement and require less memory. However, they are only optimal for a uniform distribution of the source (either in space or on the surface of a hyper-sphere). Being a generalization of the uniform scalar quantizer, the algebraic vector quantizer is more difficult to adjust to the distribution of the source by the technique called "companding". It is also recalled that the indexing (or numbering) of the vector codes and the reverse operation (decoding) require more calculations than in the case of statistical vector quantizers, for which these operations are performed by simple table readings.

We present below certain aspects of a quantification with variable dimension and the problems encountered.

We first indicate that vector quantization is a well-known and efficient technique for coding blocks of samples of fixed length. However, in many applications of digital signal compression, the signal to be encoded is modeled by a sequence of parameters of variable length. Efficient compression of these variable dimension vectors is crucial for the design of many multimedia encoders such as speech or audio encoders ("MBE" encoder, harmonic encoder, sinusoidal encoder, transform encoder, shape interpolation encoder). wave prototypes).

In sinusoidal encoders, the number of sinusoids extracted depends on the number of sinusoidal peaks detected in the signal, a number which varies over time depending on the nature of the audio signal.

In addition, many speech compression techniques exploit the long-term periodicity of the signal. This is the case with harmonic coders where the spectral components of a set of frequencies, which are the harmonics of the fundamental period of the speaker, are coded. The number of spectral harmonic peaks being inversely proportional to the fundamental frequency, as this fundamental period varies according to the speaker (typically, children with a frequency of vibration of the vocal cords higher than men) and over time, the number of components to be quantified also changes over time from frame to frame.

This is also the case for PWI coders (for "Prototype Waveform Interpolation") where the prototype waveforms are extracted on segments of length equal to the period of the pitch, therefore also variable in time. In PWI coders, the quantization of these variable length waveforms is carried out by coding separately the gain (or "RMS" for "Root -Mean- Square") and the normalized waveform which is itself decomposed in two waveforms of the same variable length: the REW waveform ("Rapidly Evolving Waveform") and the SEW waveform ("Slowly Evolving Waveform"). For a fixed length frame, the number of prototypes is variable, so the number of gains, REW and SEW is also variable, as well as the size of the REW and SEW waveforms. In other types of coders, such as transform audio coders, the number of transform coefficients obtained over fixed length frame lengths is imposed but it is usual to group these coefficients into frequency bands to quantify them. Conventionally, this cutting is carried out in bands of unequal widths to exploit the psychoacoustic properties of human hearing by following the critical bands of the ear. The range of variation of the dimension of these vectors of transform coefficients typically varies from 3 (for the bands of lower frequencies) to 15 (for the bands of high frequencies), in an encoder in wide band (50Hz-7000Hz), and even up to 24 in an FM band encoder (covering the audible range 20Hz - 16000Hz).

Theoretically, an optimal vector quantizer of variable dimension would use a set of dictionaries of fixed dimension, one for each possible dimension of the input vector. For example, in harmonic coders, for a pitch period of 60 to 450 Hz, the number of harmonic peaks in the telephone band varying from 7 for high voices (children) to 52 for low voices (men), it would be necessary to construct , store and implement 46 (46 = 52-7) vector quantifiers. The design of each dictionary requires a training sequence long enough to correctly represent the statistics of the input vectors. In addition, storing all the dictionaries proves to be impractical or very costly in memory. We see therefore, in the case of variable dimensions, it is difficult to take advantage of the advantages of vector quantization while respecting memory storage constraints and also training sequences.

Some aspects of a variable resolution quantization and the problems encountered are presented below.

It is first specified that the variability of the input signal is not only reflected by the variation in the number of parameters to be coded but also by the variation in the quantity of binary information to be transmitted for a given quality. For example in speech, attacks ("or-set"), voiced sounds and unvoiced sounds do not require the same bit rate for the same quality. Unpredictable attacks require a higher bit rate than more stable voices and whose stationarity can be taken advantage of by "predictors" which reduce the bit rate. Finally, unvoiced sounds do not require high coding accuracy and therefore require little bit rate.

To exploit the temporal variation of the characteristics of multimedia signals such as voice or video, it is wise to design variable rate coders. These variable rate encoders are particularly suitable for communications over networks, in packets, such as the Internet, ATM, or others.

Packet switching makes it possible to manipulate and process information bits more flexibly and therefore increase the capacity of the channel by reducing the average flow. The use of variable rate encoders is also an effective way to combat system congestion and / or adapt to the diversity of access conditions.

In multimedia communications, variable bit rate quantifiers also make it possible to optimize the bit rate distribution between: source and channel encodings: as in the concept of AMR ("Adaptive Multi Rate"), the bit rate can be switched at each 20 ms frame to be dynamically adapted to channel and traffic error conditions. The overall quality of the speech is thus improved by ensuring good protection against errors, while reducing the bit rate for coding the source if the channel degrades; the different types of media signals (such as voice and video in video conferencing applications);

- the different parameters of the same signal: in transform audio coders, for example, it is usual to dynamically distribute the bits between the spectral envelope and the different bands of coefficients. Often, entropy coding of the envelope is first performed and aims to exploit the non-uniform distribution of code words by assigning variable length codes to code words, the most likely having a length shorter than least likely, which minimizes the average length of code words. In addition, to exploit the psychoacoustic properties of the human ear, the remaining (variable) flow is dynamically allocated to the frequency bands of the coefficients according to - their perceptual importance.

New multimedia coding applications (such as audio and video) require highly flexible quantifications in both size and bitrate. The range of bit rates must in addition allow reaching a high quality, these multidimensional and multi-resolution quantifiers must aim for high resolutions. The complexity barrier posed by these vector quantifiers remains, in itself, a performance to be achieved, despite the increase in processing power and memory capacity of new technologies.

As will be seen below, most of the source coding techniques proposed aim either to solve the problems linked to a variable dimension, or the problems linked to variable resolution. Few techniques currently proposed make it possible to jointly solve these two problems.

With regard to known variable dimension vector quantization, the variability of the dimension of the parameters to be coded constitutes in itself an obstacle to the use of vector quantization. Thus, the first versions of the transform coder use Lloyd-Max scalar quantifiers. A coder of this type, called "TDAC", which the Applicant has developed, is described in particular in: - "High Quality Audio Transform Coding at 64 kbit / s", by Y. Mahieux, JP Petit, in IEEE Trans. Common, Vol. 42, No 11, pp. 3010-3019, November 1994.

Other solutions have been proposed to solve this vector quantization problem of variable dimension. The "IMBE" coder uses a complicated coding scheme with variable binary allocations and scalar / vector hybrid quantization.

An approach very commonly used to quantify vectors of variable dimension consists in preprocessing the vector of variable dimension to convert it into another vector of fixed dimension before quantification. There are several variants of this vector quantization technique associated with a dimension conversion (this type of vector quantization being noted DCVQ for "Dimension Conversion Vector

Quanti zat ion ").

Among the different dimension conversion procedures proposed, we can cite in particular: truncation, subsampling, interpolation, "length warping".

For sinusoidal speech coders or MBE, it has been proposed to approximate the spectral coefficients by an all-pole model of fixed order and then to perform a vector quantization of fixed dimension of the parameters of the model. Another vector quantization technique by non-matrix transform square solves the problem of vector quantization of variable dimension L by combining a vector quantization of fixed dimension K (K _< L) with a non-square matrix linear transform (LxK).

We also note another type of vector quantization associated with a dimension conversion which always uses a vector quantizer of fixed dimension K but the dimension conversion is applied to the vector codes to obtain vector vectors having the same dimension as the vector d 'Entrance.

The disadvantage of vector quantization associated with dimension conversion is that total distortion has two components: one due to quantization, the other due to dimension conversion. To avoid this distortion due to dimension conversion, another approach to variable dimension vector quantization consists in considering each input vector of variable dimension L as formed by a subset of components of an "underlying" vector. "of dimension K (L <K) and to design and use only one" universal "dictionary of fixed dimension K which however covers the whole range of dimensions of the input vectors, the correspondence between the vector of input being effected by a selector. However, this "universal" dictionary encompassing all the other dictionaries of smaller dimensions does not seem optimal for the smaller dimensions. In particular, the maximum resolution r _max per dimension is limited by the storage constraint and by the throughput per vector of parameters. For a dictionary Ki of size 2 ^max , the amount of memory required to store this dictionary is K2 ^{Krχ aκ} values and its bit rate per vector of parameters is Kr _mwi . Thus, for the same dictionary size (and therefore the same bit rate per vector of parameters and per frame), a vector of dimension L (L <K) could have a resolution (or a bit rate per dimension) K / L times greater , and this, for a volume of information to be stored K / L times smaller.

As for known variable resolution vector quantization, a simple solution consists in, as in the case of variable dimension vector quantization, using scalar quantization, as for example in the first versions of TDAC transform coder.

However, the use of an integer resolution per sample leads to a coarse resolution granularity per band of coefficients which affects the efficiency of the dynamic binary allocation procedure. It was then proposed to use scalar quantifiers with an odd whole number of reconstruction levels, in combination with a joint binary training procedure for the coded indices. The finer granularity of the resolution provided, more conducive to the binary allocation procedure, has made it possible to improve the quality, at the cost of a complexity of the algorithm for combining indices, this algorithm being necessary for setting up bit stream efficient in terms of throughput. However, for the frequency bands Since high values have a greater number of coefficients, the constraint of an integer number of levels per sample, due to scalar quantization, still results in too coarse granularity of the resolutions per band.

Vector quantization overcomes this constraint of the number of whole levels per sample and allows fine granularity of the available resolutions. On the other hand, the complexity of vector quantization often limits the number of bit rates available. For example, the AMR-NB multi-rate speech coder, based on the well-known ACELP technique, has eight fixed bit rates ranging from 12.2 kbit / s to 4.75 kbit / s, each with a different level of protection against errors thanks to a different distribution of the bit rate between the source and channel codings. For each of the parameters of the ACELP encoder (LSP, LTP delays, excitation gains, fixed excitation), dictionaries of different resolution have been constructed. However, the number of bit rates available for each of these parameters is limited by the storage complexity of non-algebraic vector quantizers. Moreover, in the AMR-WB multi-bit coder comprising nine bit rates ranging from 6.60 to 23.85 kbit / s, the variation of bit rates is essentially ensured by the algebraic excitation dictionaries which do not require storage. There are eight dictionaries and therefore eight bit rates for fixed excitation while the other parameters which use stochastic dictionaries (LSP, gains, absolute and differential delays) have only two possible bit rates. It is indicated that the stochastic vector quantizers used in AMR multi-bit rate coders are vector quantizers with constrained structure (Cartesian product and multiple stages). A large family of variable rate quantifiers can indeed be based on constrained vector quantizers such as the already mentioned multistage quantizers, with Cartesian products, but also the tree vector quantizers. The use of these tree vector quantizers for variable rate coding has been the subject of numerous studies. The vector quantizer in binary tree was the first introduced. It naturally derives from the LBG algorithm for designing a vector quantizer by successive spli tting of the centroids from the "root" node, barycenter of the training sequence. Variants of tree vector quantifiers have been proposed by pruning ("pruning" method) or on the contrary by branching certain nodes of the tree according to their attributes such as their distortion, their population leading to vector quantizers in non binary tree and / or unbalanced.

Figures 1a and 1b represent vector quantizers structured in a tree. More particularly, FIG. 1a represents a balanced binary tree, while FIG. 1b represents a non-binary and unbalanced tree.

We easily build vector quantizers multi-resolutions from a tree vector quantizer, by selecting the number of nodes corresponding to the various desired resolutions. The hierarchical tree structure is attractive and simplifies the search procedure. On the other hand, it implies a suboptimal search and a significant increase in the memory required because all the nodes of the tree from the root node to the terminal nodes passing through all the nodes of the intermediate levels must be stored. In addition, since all the nodes of a dictionary of lower resolution are not included in the dictionaries of higher resolution, the decrease in the quantization error as a function of the increase in the throughput of the vector quantizer is not guaranteed locally.

We also know how to build variable resolution quantifiers from algebraic codes, in particular nested algebraic vector quantizers EAVQ (for "Embedded Algebraic Vector Quantizers") which use subsets of spherical codes of the regular Gosset network in dimension 8 .

In the document :

- "At 16, 24, 32 kbi t / s wideband speech coded based on

ACELP "by P. Combescure, J. Schnitzler, K. Fischer,

R. Kircherr, C. Lamblin, A. Le Guyader, D. Massaloux,

C. Quinquis, J. Stegmann, P. Vary, in IEEE Proceedings

International Conference on Acoustics, Speech, and Signal

Processing, Vol. 1, pp 5 -8, 1999, this algebraic vector quantization approach nested has been extended to variable dimension quantization using algebraic codes of different dimensions. Even if this generalization of the EAVQ quantization makes it possible to quantify vectors of variable dimension at variable resolutions, it has drawbacks.

The distribution of the input vectors must be uniform. Adapting the distribution of the source to this constraint is a very difficult task. The design of algebraic quantifiers from regular networks also poses the problem of truncating and adjusting the regions of the different regular networks to obtain the different desired resolutions and this for the different dimensions.

The present invention improves the situation.

One of the aims of the present invention is, in general, to propose an efficient and economical solution (in particular in storage memory) to the problem of variable-rate quantization of vectors of variable dimension.

Another object of the present invention is, without limitation, to propose a vector quantization advantageously adapting to the coding and decoding of digital signals using a quantification of the spectral amplitudes of the harmonic coders and / or of the transform coefficients of the frequency coders, in particular speech and / or audio signals. To this end, it proposes a dictionary comprising code vectors of variable dimension and intended to be used in a coding and / or decoding device in compression of digital signals, by vector quantization at variable bit rate defining a variable resolution, the dictionary comprising:

- on the one hand, for a given dimension, dictionaries of increasing resolution nested one inside the other,

- and, on the other hand, for a given dimension, a union:

A first set made up of vector-codes constructed by inserting, into code vectors of dictionaries of lower dimension, elements taken from a finite set of real numbers according to a finite set of predetermined insertion rules,

• and of a second set made up of code vectors which cannot be obtained by inserting into code vectors of smaller dimension elements of said finite set according to said set of rules of insertion.

Preferably, the set of insertion rules is developed from elementary rules consisting in inserting a single element from the finite set of real numbers as a component at a given position of a vector.

Each elementary rule is preferably defined by a pair of two positive integers representative: of a rank of the element in said finished set, and of an insertion position. It will be understood that the insertion rules thus characterized are read and deduced directly from the very structure of the dictionary within the meaning of the invention.

Of course, in a purely reversible manner, it is possible to define suppression rules consisting in deleting one or more elements from a finite set of given dimension N "to reach a lower dimension N (N <N ^" ).

The present invention also relates to a method for forming a dictionary according to the invention, in which, for a given dimension: a) a first set of code vectors formed is constructed by inserting / deleting into code vectors of dimension dictionaries lower / upper elements taken from a finite set of real numbers according to a finite set of predetermined insertion / deletion rules, b) a first intermediate dictionary is constructed for said given dimension, comprising at least said first set, c ) and, in order to adapt said dictionary to use with at least one given resolution, a second dictionary, final, is constructed from the intermediate dictionary, by nesting / simplifying dictionaries of increasing / decreasing resolutions, the dictionaries of increasing resolutions being nested within each other from the lowest resolution dictionary down to the d larger dictionary resolution.

Of course, the terms "nesting of a set A into a set S" mean that the set A is included in the set B. In addition, the terms "simplification of a set" A to obtain a set B ", the fact that the set A includes the set B.

As a variant or in addition, it will be understood that steps a) and b), on the one hand, and step c), on the other hand, can be substantially reversed to adapt said dictionary to use with a given dimension N code vectors.

In that case :

- in step c), we build, from an initial dictionary of resolution r _n and of dimension N ', a first dictionary, intermediate, always of dimension N "but of resolution r _N higher / lower, by nesting / simplification of dictionaries of increasing / decreasing resolutions, to substantially reach the resolution r _{N of} said first dictionary,

- in step a), to reach the given dimension N, a first set of code vectors formed is constructed by inserting / deleting, in code vectors of the first dictionary of dimension N ¹ less than / greater than said given dimension N, elements taken from a finite set of real numbers according to a finite set of predetermined insertion / deletion rules, and, in step b), following a possible step of final adaptation to the resolution r _N , we built, for said given dimension N, a second dictionary, definitive, comprising at least said first set.

Step a) can be implemented by successive increasing dimensions. In this case, for a given dimension N: aO) an initial dictionary of initial dimension n is obtained, smaller than said given dimension N, al) a first set is constructed consisting of code vectors of dimension n + i and formed by inserting in code vectors of the initial dictionary of elements taken from a finite set of real numbers according to a finite set of predetermined insertion rules, a2) a second set of code vectors of dimension n + i is provided which cannot be obtained by insertion in the code vectors of the initial dictionary of the elements of said finite set with said set of insertion rules, a3) an intermediate dictionary, of dimension n + i comprising a union of said first set and said second set, is constructed, and we repeat, at most Nn-1 times (in which case i = l), steps a1 to a3), with said intermediate dictionary as an initial dictionary, up to said given dimension N.

One can also implement step a) by successive decreasing dimensions. In this case, for a given dimension N: a'O) an initial dictionary of initial dimension n is obtained, greater than said given dimension N, a'1) a first set, of dimension ni, is constructed by selecting and extracting possible code vectors of dimension nor in the dictionary of dimension n, according to a finite set of predetermined suppression rules, a '2) a second set consisting of code vectors of dimension ni, which cannot be obtained simply by deleting, in the code vectors of the initial dictionary, elements of said finite set with said set of suppression rules, a '3) an intermediate dictionary is constructed , of dimension ni comprising a union of said first set and of said second set, and the steps a'1) to a '3) are repeated, at most nN-1 times (in which case ^' i = l), with said intermediate dictionary as an initial dictionary, up to said given dimension N.

To obtain a plurality of N dictionaries of successive dimensions 1 to N, it is possible to combine steps a1 to a3) and steps a'1) to a'3), preferably from an initial dictionary of dimension n (n <N) and by the repeated implementation of steps a1 to a3) for the dimensions n + 1 to N, and by the repeated implementation of steps a'1) to a'3) for the dimensions n-1 at 1.

We thus obtain all or part of N dictionaries whose larger dictionary has dimension N.

The finished set and the set of insert / delete rules used to build dictionaries of successive dimensions can be defined: - a priori, before building the dictionary, by analysis of a source to be quantified, - or a posteriori, after the construction of dictionaries, preferably by nesting / simplification of dictionaries of successive resolutions, this construction then being followed by a statistical analysis of these dictionaries thus constructed.

It is indicated that the source to be quantified is preferably odelized by a learning sequence and the definition "a priori" of the finite set and of the set of insertion / deletion rules is preferably carried out by a statistical analysis of the source. The aforementioned finite set is preferably chosen by estimating a one-dimensional probability density of the source to be quantified.

By combining a priori and a posteriori definitions of the finite set and insertion rules:

one can advantageously choose, a priori, a first set and a first set of insertion / deletion rules by analysis of a learning sequence, to form one or more intermediate dictionaries,

at least part of said first set and / or of said first set of insertion / deletion rules is updated, by a posteriori analysis of said one or more intermediate dictionaries,

- And, if necessary, at least part of the set of vector codes forming said one is also updated or several intermediate dictionaries.

Preferably, step c) of adaptation to a given resolution comprises the following operations, in order to reach increasing resolutions: cO) an initial dictionary of initial resolution r _a , less than said given resolution r _N , cl, is obtained from from the initial dictionary, an intermediate dictionary of resolution r _{a +} ι greater than the initial resolution r _n , c2) is constructed and the operation cl) is repeated until the given resolution r _{N is} reached.

Advantageously, for each iteration of the operation cl), provision is made for a construction of classes and centroids in which the centroids belonging to at least the dictionaries of resolution higher than a current resolution r _± are recalculated and updated. Furthermore, the centroids which belong to the dictionaries of resolution lower than a current resolution r _± are updated, preferably, only if the total distortions of all the dictionaries of lower resolution are decreasing from one update to the other.

In addition or as a variant, step c) comprises the following operations, now to reach decreasing resolutions: c'O) an initial dictionary of initial resolution r _n is obtained, greater than said given resolution r _N , c'I) from the initial dictionary, an intermediate dictionary of resolution r _n _ι less than the initial resolution r _n , by partitioning the initial dictionary into several subsets ordered according to a predetermined criterion, and c'2) the operation c'I) is repeated until the given resolution r _{H is} reached.

Advantageously, this partition can use the partial composition by controlled extension within the meaning of steps a) and b), using at least part of the insertion / deletion rules implemented.

To obtain a plurality of N successive dictionaries of respective resolutions ri to ru, from an initial dictionary of resolution r _n intermediate between the resolutions ri and r _N , it is advantageous to implement a repetition of step cl) to the increasing resolutions r _{n +} ι to r _H , and from step c'I) for the decreasing resolutions r _n _ι to ri.

It will be understood that the finite set and the set of insertion / deletion rules can advantageously be chosen by a study, a posteriori, of a statistics of the dictionaries of different resolutions and dimensions thus obtained, to form a dictionary in the sense of l invention, desired dimensions and resolutions.

According to one of the advantages provided by the present invention, the storage in memory necessary for the implementation of the coding / decoding can be considerably reduced. Indeed, advantageously, we store in a memory, once and for all, said set of rules of insertion / deletion, each identified by an index, and, for a given dimension: - said second set consisting of vector-codes which cannot be obtained by application of the rules of insertion / deletion to vector-codes of lower / higher dimension to the given dimension, - as well as at least one correspondence table making it possible to reconstruct any vector code of the dictionary of given dimension, using the indices of the insertion / deletion rules and indices identifying elements of said second set.

This avoids the complete storage of the dictionary for said given dimension, by simply storing the elements of said second set and links in the correspondence table to access these elements and the associated insertion / deletion rules.

Thus, it will be understood that, for a given dimension, the aforementioned second set can advantageously consist of "second" sub-sets of dimensions smaller than said given dimension.

In one embodiment, the insert / delete mechanism itself can be stored as a program routine, while the insert / delete parameters, for a given insert / delete rule, can be stored in a table general correspondence (in principle different from the aforementioned correspondence table), in combination with the index of this rule of insertion / deletion given.

Preferably, the correspondence tables are developed beforehand, for each index of a vector-code of a dictionary of given dimension which can be reconstructed from elements of current indices in the second set of current dimension, by tabulation. of three integer scalar values representing: - a current dimension of said second set, - a current element index of the second set, and - an index of insertion / deletion rule, this insertion / deletion rule at least helping to reconstruct said code vector of the dictionary of given dimension, by applying the insertion / deletion to the element corresponding to said current index and to said current dimension.

These latter characteristics can advantageously be implemented in a compression coding / decoding method, as described below.

As such, the present invention also relates to a use of the dictionary according to the invention and obtained by the implementation of the above steps, for coding or decoding in compression of digital signals, by vector quantization at variable bit rate defining a variable resolution. In particular, one searches for the nearest code vector neighboring an input vector y = (yo, ..., yk / -. Yj-i) in a dictionary of given dimension j. This use then implements the following steps: * C01) for a current index of said sought vector code, at least partial reconstruction of an index vector code corresponding to said current index, at least by prior reading of the indices appearing in the correspondence tables and, where appropriate, of an element of the second set, making it possible to develop said dictionary, the method continuing with coding / decoding steps proper, comprising: * C02) at least during coding, calculation of a distance between the input vector and the vector-code reconstituted in step COI), * C03) at least during coding, repetition of steps COI) and C02), for all the current indices in said dictionary,

C04) at least during coding, identification of the index of the at least partially reconstructed code vector whose distance from the input vector, calculated during one of the iterations of step C02), is the smallest , and

C05) at least on decoding, determination of the nearest neighbor of the input vector y as a vector-code whose index was identified in step C04).

As indicated above, it is recalled that the "second" above-mentioned assembly preferably consists of "second" sub-assemblies of dimensions smaller than a given dimension of the second assembly.

In a particular embodiment, the step COI), at least during decoding, comprises: COU) reading, in the correspondence tables, indices indicative of links to said second set and to the insertion rules and including: - the index of a current dimension of a subset of said second set, the current index of an element of said subset, - and the index of the insertion rule appropriate for the construction of the vector-code of the dictionary of given dimension, from said element,

C012) the reading, in said subset identified by its current dimension, of said element identified by its current index,

C013) the complete reconstruction of the vector-code at said given dimension by applying to said element read in step C012) the appropriate insertion rule and identified by its index read in step COU).

In a particular embodiment, with coding,

* the COI stage) includes:

COU) reading, in the correspondence tables, indices indicative of links to said second set and to the insertion rules and including: the index of a current dimension of a subset of said second set, l current index of an element, of said subset, and the index of the insertion rule appropriate for the construction of the vector-code of the dictionary of given dimension, from said element, C012) reading, in the sub -set identified by its current dimension, of said element identified by its current index, * in step C02), said distance is calculated according to a distortion criterion estimated as a function of: - of said insertion rule, - and of said element.

Thus, it is possible to provide only a partial reconstruction of the vector code with said dimension given in step COI), by reserving the complete reconstruction simply for decoding.

In an advantageous embodiment, an additional structuring property is further provided according to a union of permutation codes, and an indexing of this union of permutation codes is further exploited in the implementation of the following steps:

CP1) from an input signal, we form an input vector y = (y ₀ , ..., y, "., Yj-i) defined by its absolute vector H ⁼ (| 3'o |>'"> | 3 ^; * |»'">^; y-ι ^and P ^{ar a} sign vector ε = (ε _Q , ..., ε _k , ..., ε) with ε _k ≈ ± l,

CP2) the components of the vector | y | by decreasing values, by permutation, to obtain a leading vector | 3> | ,

CP3) we determine, among the leading vectors of the dictionary D ^j ι of dimension j, a nearest neighbor x ^j 'of the leading vector ,

CP4) an index of the rank of said nearest neighbor x ^j 'is determined in the dictionary D ^j ι,

CP5) and an effective encoding / decoding value is applied to the input vector, which is a function of said index determined in step CP4), of said permutation determined in step CP2) and of said sign vector determined in step CP1).

According to another advantageous aspect of the invention, for coding / decoding and possibly for the construction of the dictionary or dictionaries, provision is made for storing the correspondence tables and the elements of the aforementioned second set, in particular in a memory of a device for compression coding / decoding.

As such, the present invention also relates to such a coding / decoding device.

The present invention also relates to a computer program product intended to be stored in a memory of a processing unit, in particular of a computer or of a mobile terminal, or on a removable memory medium and intended to cooperate with a reader. of the processing unit, this program comprising instructions for the implementation of the above dictionary construction method.

The present invention can also target a program of this type, in particular a computer program product intended to be stored in a memory of a processing unit, in particular of a computer or of a mobile terminal integrating a coding device. / decoding, or on a removable memory medium and intended to cooperate with a reader of the processing unit, this program then comprising instructions for the implementation of the application for coding / decoding in compression above. Other characteristics and advantages of the invention will appear on examining the detailed description below, and the appended drawings in which, in addition to FIGS. 1a and 1b described above: FIG. 2a illustrates the property of nesting of a dictionary within the meaning of the invention, for a given dimension N,

FIG. 2b illustrates the property of partial composition by controlled extension of a dictionary within the meaning of the invention, FIG. 3 illustrates the nesting of the dictionaries as a function of increasing resolutions, FIG. 4 illustrates the composition of vector-codes d a dictionary from code vectors of smaller dictionaries and insertion rules, FIG. 5 illustrates the construction according to increasing resolutions of nested dictionaries without updating the dictionaries of lower resolution, FIG. 6 illustrates the diagram "TDAC" encoder block,

FIGS. 7a to 7g represent, for the wide band TDAC coder using a vector quantizer within the meaning of the invention, tables illustrating respectively:

* a cut into 32 strips (fig. 7a),

* the resolutions by dimension (fig.7b),

* the gain in memory provided by the nesting property (fig.7c),

* the memory gain provided by the two properties nesting and controlled extension (fig. 7d), * the gain in memory provided by the two structuring properties as a function of the size and the bit rate, respectively, compared to the memory size necessary for storing a dictionary without use these two properties (fig.7e), * the first leaders of the L ° set in dimensions 1, 2 and 3 (fig.7f), and * the leaders of the permutation codes of dictionaries in dimension 3 (fig.7g ), - Figures 8a and 8b show, for the TDAC coder in FM band, tables illustrating respectively: * a cut into 52 bands (fig.δa), and * the resolutions by dimension (fig.8b).

First of all, reference is made to FIGS. 2a and 2b which illustrate the two main properties of a dictionary Di ^N within the meaning of the present invention.

In FIG. 2a, for a given dimension N, dictionaries Dι ^N , D ₂ ^N , ..., D ^N of respective increasing resolutions r _l7 r ₂ , ..., r ^ are nested one inside the other. Thus, the dictionary Di ^N of maximum resolution ri can make it possible to determine a dictionary Dj ^N of resolution rj lower (j <i), as will be seen below. This first property, denoted PR, is hereinafter called "nesting property".

Referring now to FIG. 2b, any dictionary Di ^N of a given dimension N and of resolution ri is the union of two disjoint sets: o a first set D ' ^N consisting of Y ^N code vectors constructed (arrow F3) by inserting into code vectors Y ^{11 "1} dictionaries Di * ^{1" 1} of smaller dimension Nl of the elements Xj taken (arrow F2) in a finite set A of real numbers according to a finite set of insertion rules {R _m } / an insertion rule R '(j, k) determining the elements j to be inserted (arrow FI) and the way of inserting them (for example at a position k of the vector Y ^N under construction), o and a second set 'consisting of vectors Y' which cannot be obtained by inserting into vectors of lower dimension elements of this finite set according to the game of the aforementioned insertion rules.

This second property, denoted PD, is hereinafter called "partial composition property by controlled extension".

In FIGS. 2a and 2b and in the summary of the invention above, the indices in resolution and / or in dimension begin, by way of example, from the integer 1 to a given integer (i, n , or N as appropriate). Those skilled in the art of programming, in particular in C ++ language, will understand that these indices may rather start from 0 and reach i-1, n-l, or N-l, depending on the context. Thus in the example of FIG. 3 which will be described later, the greatest resolution reached is Nj-1 starting from 0.

A method of constructing a dictionary having the two structuring properties PR and PD, in particular algorithms for constructing these dictionaries thus structured. The links induced by the two structuring properties are advantageously used to develop algorithms for building such dictionaries by adapting the iterative construction algorithms commonly used and described above such as "GLA" or "SKA".

In general, it is indicated that: - dictionaries of different resolutions and of the same dimension, linked together, are constructed successively using the nesting property PR,

- as a complement or as a variant, dictionaries of different dimensions are linked, linked by the PD property of partial composition by controlled extension,

- And one thus obtains dictionaries of different dimensions and resolutions having the two structuring properties PD and PR.

Generally, to build nested dictionaries in increasing resolution for a given dimension (PR), three construction approaches are proposed.

A first approach consists in building the dictionaries according to the increasing resolutions (from the smallest resolution to the maximum resolution). A second approach conversely consists in building the dictionaries according to decreasing resolutions (from the maximum resolution to the lowest resolution).

A third approach consists in building the dictionaries from an intermediate resolution dictionary by decreasing the resolutions to the minimum resolution and by increasing them to the maximum resolution. This method is particularly advantageous when the nominal resolution of the vector quantizer of variable resolution is the aforementioned intermediate resolution.

The property PR of nesting of dictionaries, for a dimension j ultimately results in:

D ^J aD { ^• DD

Noting:

- j the number of resolutions (or possible bit rates in a variable bit rate encoder) in dimension j, all the resolutions in dimension j with r / <r <• • • <r <r _{+ l} <• • • <r ^ _

Df the dictionary of dimension j, of resolution r

T the size of the resolution dictionary

T = 2 ^jr ' ^J ie r = -log ₂ 7V Figure 3 illustrates the nesting of dictionaries based on increasing resolutions.

The flowchart of the construction algorithm according to increasing resolutions without updating the dictionaries of lower resolution is given in FIG. 5.

Referring to Figure 5, we first build the dictionary Do ^: of lower resolution, following the initialization steps 51 and 52 where we first set i≈O and the iteration index of iter≈O loop. Then the dictionary D ₀ ^j of lower resolution being fixed, the dictionary of immediately higher resolution D _ι ^j is constructed using a variant of a conventional construction algorithm, described below. The method is then iterated until the dictionary of maximum resolution D _N ^J _ is constructed.

Thus, in step 53 where, by an iterative process, we seek to construct a dictionary Dι ^j from an initial dictionary D ^ tO), formed by adding (Ti ^j - Ti_ι ^j ) vectors to the dictionary Di_ι ^j of lower resolution rι-ι.

The algorithm for constructing classes 54 is identical to a conventional algorithm, but the algorithm for constructing T centroids 55 is modified. Indeed, the (T ^ -Ti- ^) centroids not belonging to the lower resolution dictionaries are recalculated and updated, while the (Ti-ι ^j ) centroids of the lower resolution dictionaries are not updated. A variant authorizes the updating of the centroids of the dictionaries of lower resolutions in the case where the total distortions of all the dictionaries of lower resolution decrease or remain constant. In this case, the dictionaries of lower resolutions are modified accordingly.

The iter loop index is then incremented (step 56) up to a Niter number (i, j) depending on the i ^{th same} resolution and on the dimension j (test 57). Once the desired resolution Nj is reached (test 58), the dictionary is obtained at this resolution Nj (end step 59), and therefore all the dictionaries Dp of resolution r, for i ranging from 1 to j.

To build the dictionaries according to decreasing resolutions, we first build the higher resolution dictionary. Then this one being fixed, one carries out a partition of this one in several subsets which one orders according to a certain criterion. Several criteria can be used to order the partition. We can for example order the subsets according to their cardinality, their solicitation in the learning sequence (i.e. the cardinality of their quantization regions), their contribution to the total distortion or more precisely to the decay of this distortion. One can obviously combine various criteria and weigh their respective importance. Likewise, partitioning the dictionary can be performed in various ways: from the elementary partition (one element in each subset) to a more elaborate partition. This ordered partition is at the base of the construction of the nested dictionaries by progressive union of its ordered classes.

Preferably, the partition can be based on the PD property of partial composition by controlled extension by grouping elements based on the extension of the same vector-code from a subset of the set of insertion rules ( possibly equal this set itself).

It should be noted that one can do several iterations by alternating the different methods. For example, we build nested dictionaries according to the method by increasing resolutions then we apply the method by decreasing resolutions. By combining the two above methods, nested dictionaries in resolution are constructed from an intermediate resolution dictionary n- This i ^th dictionary is therefore first constructed. Then, from this dictionary, the dictionaries of lower resolution are constructed using the second method using decreasing resolutions and the dictionaries of higher resolutions using the first method using increasing resolutions.

In general, we also propose three approaches to build dictionaries of different dimensions by partial composition by controlled extension (PD property). A first approach is to increase the dimensions. Another approach is to decrease them. Finally, a last approach consists in starting by building the dictionary of an intermediate dimension and building by successive increase and decrease of the dimension the dictionaries of higher and lower dimensions. The partial composition by controlled extension has led to the development of procedures for determining the finite set of reals and the set of insertion rules that will be seen below. It is simply indicated here that, preferably, the proportion of “extended” elements (number of elements of the first set relative to the cardinal of the dictionary) increases with dimension, which makes it possible to reduce the cost of storage of the second set, increasing with dimension. This proportion can be fixed a priori by the constraints of complexity of the application (memory / computing power) or left "free". In the latter case, the construction algorithm advantageously favors the elements of the first set comprising the elements obtained by controlled extension, as will be seen below.

Thus, the second PD property of partial composition by controlled extension ultimately results in: noting:

- -D '/ the set of code vectors of £> / which can be obtained by inserting into code vectors dictionaries of the lower dimensions of the elements taken from a finite set A of R according to a set of rules

insertion {R _m } /

- Of its complement in D, set of vectors -

codes of Df which cannot be obtained by inserting into vectors of code of lower dimension elements of A according to the set of insertion rules {R _m }.

An example of insertion rules for verifying the second PD property is described below.

First, we define a set of elementary insertion rules: each elementary rule consists of inserting one and only one element from the finite set of real numbers A as a component at a given position of a vector. Each elementary rule is given by a couple of two positive integers, one giving the rank of the element in the finished set and the other the insertion position. From this set of elementary rules, we can compose any rule, more elaborate, of insertion of components.

Of course, in a purely reversible manner, it is possible to define suppression rules consisting in removing one or more elements from a finite set of given dimension N to reach a lower dimension N-n.

To define an insertion rule, we then note:

- N _has the cardinal of A and have its i ^th element: A = {a _o , ai, ..., a ..., ana-i} - R '(i _m , p _m ) the elementary insertion rule which consists in inserting ai in position p _m .

Thus, if the maximum dimension is j _ma χ, the number of possible elementary rules is N _a * j _max . For example, for N _a = 2 and jmax = 3, there are altogether six possible elementary rules: R '(0,0): insert a ₀ in position 0, R' (1,0): insert ai in position 0 , R '(0,1): insert a ₀ in position 1, R' (1,1): insert a _x in position 1, R '(0,2): insert a ₀ in position 2, R' (1 , 2): insert a _x in position 2

The composition of the rules R '(0,0) and R' (0,1) gives the rule: insert a ₀ in positions 0 and 1. It thus allows to obtain a vector-code of dimension j + 2 from d 'a code vector of dimension j.

The composition of the rules R '(1,0) and R' (0,2) gives the rule: insert a _x in position 0 and a ₀ in position 2. It also makes it possible to obtain a vector-code of dimension j + 2 from a vector code of dimension j.

More generally, we denote R (n, {(i _m , p _m )} m = 0, n = l) the composition of the n elementary rules R '(i _m , p _m ) (from m = 0 to nl), which makes it possible to obtain a code vector of dimension j + n from a code vector of dimension j. It should be noted that the i _ra are not necessarily different, on the other hand the n positions p _m are distinct. Preferably, we arranges the positions p _m in ascending order, that is: p ₀ <pι ... <p _m ... <p _n _ι.

FIG. 4 illustrates the composition of code vectors of a dictionary from code vectors of dictionaries of smaller dimensions and of insertion rules.

Several embodiments are also provided for constructing dictionaries of different dimensions, unions of two disjoint sets, a first set consisting of code vectors constructed by inserting dictionaries of smaller dimensions of the elements taken from a set into code vectors finite of real numbers according to a set of insertion rules, a second set consisting of vectors which cannot be obtained by inserting into the lower-dimensional code vectors elements of this finite set of real numbers according to this set of insertion rules .

The first set requires the determination of the finite set of reals (i.e. its cardinality and its values) as well as the set of insertion rules.

The construction of this finite set and the elaboration of the set of insertion rules are carried out: either "a priori": the finite set and the set of insertion rules are determined before building the dictionaries. This choice is preferably based on an analysis of the statistics of the source to be quantified, modeled for example by a learning sequence. For example, the choice of the finite set can be based on the one-dimensional probability density of the source (or its histogram);

- or "a posteriori": we first build the nested dictionaries in resolution for all dimensions without imposing to follow the rule of partial composition by controlled extension. The choice of the finite set and the set of insertion rules is then carried out by a study of the statistics of these "initial" dictionaries.

The two solutions "a priori" or "a posteriori" can be used successively and / or combined. For example, a first set and a first set of insertion rules can be chosen by an analysis of the learning sequence, then after a first construction of the dictionaries, an analysis of these dictionaries can lead to a total update or partial of set A and / or the set of insertion rules.

It should also be noted that the finished set and / or the set of insertion rules may or may not be dependent on the dimensions. We can then determine a specific set and / or set for each pair of dimensions (j, j '), or a specific set and / or set by size difference, or determine a global set. Again, the choice is made a priori or after statistical analysis of the learning sequence and / or dictionaries.

To build the dictionaries according to the increasing dimensions, one builds first the dictionary of weakest dimension by a classical method of design of vector quantization, as indicated above. Then, this dictionary being constructed, the dictionary of immediately superior dimension is constructed using a variant of a conventional construction algorithm. From the dictionary of lower dimension, one composes all the initial vector-codes possible by applying the rules of insertion, one possibly supplements this dictionary by vector-codes "free" (ie those which cannot not be obtained by extension). Note that the size of this initial dictionary can be larger than the desired size. From the initial dictionary, a variant of an iterative algorithm for constructing a vector quantizer is then applied. Classes are constructed by quantification of the learning sequence and centroids are updated while respecting the controlled extension constraint for the vector codes of the first set. For these vector-codes of the first set, one can either not recalculate the components obtained by insertion, or recalculate all the components and modify the vector-codes thus obtained to make reappear the components obtained by the rules of insertion. We also eliminate empty classes if the dictionary size is larger than the desired size. If at the end of the algorithm, the size of the dictionary is greater than the desired resolution, a Dictionary element classification procedure is applied to retain only the first code vectors. The iterative algorithm is possibly restarted. We then proceed to the construction of the dictionary of the higher dimension, the initial dictionary is then constructed by controlled extension from the two dictionaries of the two smallest dimensions and completed by "free" vector-codes, then we apply the variant of l iterative algorithm for constructing a vector quantizer. The process is then iterated, until building the dictionary of maximum dimension.

As a variant, in order to construct the dictionaries according to the decreasing dimensions, the dictionary of larger dimension is first constructed. Then, the latter being fixed, the possible code vectors of smaller dimension are extracted. Advantageously, the extraction procedure is facilitated by modifying the code vectors of the larger dimensions to reveal elements of A as components of these code vectors.

In a complementary variant, several iterations are advantageously carried out by alternating the two constructions according to the increasing dimensions, on the one hand, and according to the decreasing dimensions, on the other hand.

To facilitate the controlled extension procedure, the invention can in addition carry out a transformation of the components of the code vectors. An example of transformation is a high resolution scalar quantization. It is interesting to build "dictionaries" of smaller dimensions even if these dimensions are not used directly by vector quantization. For example, we can start with dimension 1 even if scalar quantization is not used. Similarly, it can also be interesting to build dictionaries of intermediate dimensions. These "dictionaries" are moreover advantageously used by the controlled extension procedure to reduce the complexity of storage and calculations.

It is further indicated that by judiciously combining algorithms for constructing dictionaries by resolution nesting (PR) with algorithms for construction by partial composition by controlled extension (PD), several construction methods can be developed. It should be noted that the algorithms being iterative, different techniques can be alternated. For example, we start by building the dictionary of maximum resolution for the smallest dimension, we deduce the nested dictionaries in decreasing resolutions (property PR), then we build the dictionary of maximum resolution for the immediately higher dimension thanks to the property PD , for this dimension, we build the nested dictionaries in resolution and we iterate until we get the dictionaries (nested in resolutions) of maximum dimension.

A preferred construction is used in the embodiment described below which combines the techniques dictionary building according to increasing dimensions and decreasing resolutions to build all the dictionaries M.

The coding / decoding in compression of digital signals (audio, video, etc.) using dictionaries within the meaning of the invention is described below, in particular the encoding and decoding algorithms which exploit the structure of the dictionaries ( nesting and partial composition by controlled extension). In general, it will be understood that an optimization of the memory / calculation compromise at the coder and / or at the decoder is carried out according to the constraints of the application.

By way of example, the audio coder named "TDAC coder" is used below, used to encode digital audio signals sampled at 16 kHz (in wide band). This encoder is a transform encoder which can operate at different bit rates. In particular, the bit rate can be fixed before the establishment of the call or vary from frame to frame during a call.

Figure 6 shows the block diagram of this TDAC encoder. An audio signal x (n) limited in band to 7 kHz and sampled at 16 kHz is divided into frames of 320 samples (20 ms). A modified discrete cosine transform 61 is applied to blocks of the input signal of 640 samples with an overlap of 50% (that is to say a refresh of the MDCT analysis every 20 ms). We limits the spectrum obtained y (k) to 7225 Hz by zeroing the last 31 coefficients (only the first 289 coefficients are different from 0). A masking curve is determined by the masking module 62 which then sets the masked coefficients to zero. The spectrum is divided into thirty-two bands of unequal widths. The possible masked bands are determined as a function of the transformed coefficients of the signal x (n). For each band of the spectrum, the energy of the MDCT coefficients is calculated (we speak of scale factors). The thirty-two scale factors constitute the spectral envelope of the signal which is then quantified, coded and transmitted in the frame (block 63). This quantization and this coding use a Huffman coding. The variable number of bits remaining after the quantization of the variable rate spectral envelope is then calculated. These bits are distributed for the vector quantization 65 of the spectrum MDCT coefficients. The dequantized spectral envelope is used to calculate all the masking thresholds per band, this masking curve determining the dynamic allocation of bits 64. The calculation of this masking curve band by band and from the quantized spectral envelope prevents the transmission of auxiliary information relating to binary allocation. Indeed, the decoder calculates the dynamic allocation of the bits in an identical way to the coder. The MDCT coefficients are normalized by the dequantized scale factors of their band and then they are quantified by vector quantizers of variable size and bit rate. Finally, the binary train is constructed by multiplexing 66 information on the spectral envelope and these coefficients normalized by coded band and transmitted in frame. It is indicated that the references 67 and 68 in FIG. 6 correspond to steps known per se of detection of a voiced or unvoiced signal x (n), and of tone detection (determination of tonal frequencies), respectively.

The vector quantizers with variable bit rate are described below in bands of unequal widths of the MDCT coefficients in the TDAC coder. The quantification of the MDCT coefficients normalized by band in particular uses dictionaries constructed according to the invention. Cutting into strips of unequal widths leads to vectors of different dimensions. The table in FIG. 7a which gives the strip cutting used also indicates the resulting dimension of the vector of the coefficients, that is to say the number of coefficients indicated by the third column.

The variable number of bits remaining after Huffman coding of the spectral envelope is dynamically allocated to the different bands. The table in FIG. 7b gives the numbers of resolutions Nj and the sets of flow rates per band j * Rj (therefore the values of the resolutions per band) for the dimensions j, for j ranging from 1 to 15. It will be noted that to exploit advantageously the structuring property of partial composition by controlled extension, vector quantizers have been constructed in dimensions 1, 2, 6, 11, which, however, do not correspond to any bandwidth, but whose elements are used to compose code vectors of higher dimension. We also note the fineness of the granularity of the resolutions even for large dimensions.

The zeroing of the masked coefficients in module 62 leads to choosing, when analyzing the normalized MDCT coefficients, as the starting set A = {θ} and as the set of insertion rules all possible compounds of the elementary rules d 'insertion. This is equivalent to inserting zeros at any position.

However, a more detailed analysis imposes on the dictionaries an additional structural constraint by using dictionaries formed from a union of standardized permutation codes, of type II according to which all permutations and all signs are authorized. For each type II permutation code, absolute leader is called the largest vector, in the lexicographic sense, which is obtained by ordering the absolute values of the components in descending order. The construction of dictionaries amounts to determining their standardized absolute leaders. Applying the controlled extension to these absolute leaders then consists of inserting 0s in the last components.

We also set a criterion of distortion. Preferably, the criterion of distortion chosen here is the Euclidean distance. The dictionary being normalized, the search for the vector code which minimizes the Euclidean distance with an input vector to be quantified amounts to searching for the vector code which maximizes the dot product with this input vector. In addition, the dictionary being the union of permutation codes, the search for the vector-code maximizing the scalar product with an input vector amounts to searching among the absolute leaders of the dictionary for that which maximizes the scalar product with the absolute leader of this input vector (which is also obtained by permuting the absolute values of its components to arrange them in descending order).

We define below a learning sequence for the design of vector quantizers within the meaning of the invention. As indicated above, it is preferable to determine a training sequence for the design of a quantifier. A long sequence consisting of frames of 289 MDCT coefficients normalized by the scale factor of their band is first obtained from numerous samples of audio signals in wide band. Then, for each normalized vector of coefficients, we deduce its absolute leader. From the set of absolute leaders of different dimensions, two categories of multidimensional learning sequences S ⁰ and S ^{1 are created} :

S - ≡ [1,15], S _j being the set of all the vectors formed by the first j components of the absolute leaders having j non-zero coefficients. S, - is thus constituted by the absolute leaders of dimension j having no zero coefficient, those of dimension j + 1 having a single zero coefficient, those of dimension j + 2 having two zero coefficients, ... those of dimension 15 having 15-j zero coefficients,

- and S ¹ = {s}} / e [3,4,5,7,8,9,10,12,13,14,15], S) being the set of all the absolute leaders of the bands having j coefficients.

For example, from the normalized vector of coefficients (0., 0.6.0., 0., 0.8), we deduce its absolute leader (0.8,

0.6,0. , 0., 0.) which belongs to the sequence S and an element of S ° ₂ , (0.8,0.6), formed by the first two non-zero components of its absolute leader.

The first category of sequences is preferably used to determine the initial dictionaries of

• ^The second category is preferentially used to build multidimensional and multiresolution dictionaries having the two structuring properties.

From the first category S ⁰ of sequences, we obtain a first dictionary of normalized absolute leaders for each dimension j (j ranging from 1 to 15) by application to the sequence S, - of a classical algorithm such as that called " k -means s ".. These leaders with positive real components are modified by canceling the components below a predetermined threshold, compared to the first component (that is to say the largest component). This so-called "center-" procedure clippling "advantageously makes it possible to make appear zeros and to extract absolute leaders without null components of lower dimension. To further favor the controlled extension, a transformation of the components of these extracted leaders is applied. For this purpose a normalization of each leader by its smallest nonzero component followed by a uniform scalar quantization of step 1 and with whole reconstruction levels (which amounts to rounding the components of each leader to the nearest integer). a significant reduction in memory because the absolute leaders can thus be stored in the form of integers by means of the introduction of a corrective factor of normalization in the calculation of distance. It will be noted that different real leaders obtained or not from different S, - sequences can be transformed into the same whole leader. A procedure for eliminate possible redundancies and form the set V = M L ' _j of all -, - 15] absolute leaders with non-zero integer components, -L'ant being the subset made up of these leaders of dimension j. This L '° construction technique is inspired by the dictionary construction technique by partial composition by extension controlled according to decreasing dimensions. We also note that the choice of the set A made a priori could be revised a posteriori to add the element "1" because all the leaders of L '° have at least one "1" as the last component. The set L ° serves as the basis for the composition of the initial dictionaries of leaders for the design of vector quantizers with multiple dimensions and resolutions having the two structuring properties of nesting PR and partial composition by controlled extension PD. From the sequence S ¹ , the algorithm to construct these quantifiers proceeds by increasing dimension and decreasing resolution.

For a dimension j, the initial dictionary of leaders

L _j is formed by all the leaders of L _j and by all the leaders obtained by controlled extension of the leaders of the dimensions lower j '(j'<j) by inserting (j-j ') zeros to the leaders of the sets V.,. For example in dimension 3, we compose a dictionary of leaders by extension controlled from = {(l)}, = {(ll), (21), (31), (41), (51), (91)}, completed by the leaders of E ' ₃ .

For each dimension j, the union of permutation codes characterized by LA- constitutes a high resolution dictionary, possibly greater than the maximum resolution desired. These permutation codes therefore perform a natural partition of this dictionary, each class of this partition being a permutation code represented by its leader. The construction of the nearest neighbor regions corresponding to the classes of this partition is then carried out by quantification of the sequence S ¹ . The partition is ordered according to the ascending cardinal of the permutation codes. In case of equality of the cardinals of permutation codes, the codes of the leaders obtained by controlled extension are favored compared to those of the leaders of -L'y as indicated above. In case of equality of cardinals of two classes belonging to the same set (either to D ^{, J} _N , or to D>'- L), the classes are ordered

according to a criterion combining the cardinal of their quantization region and their contribution to the decrease of the total distortion. The sum of the cardinalities of the permutation codes thus ordered is calculated for each permutation code as well as the corresponding bit rate per vector. We denote by L _j the set of leaders of L _j thus ordered. To avoid a procedure of joint binary training of the coded indices, one chooses to use only whole resolutions.

The multi-resolution dictionaries nested in resolution, with reference to the table in FIG. 7c, are therefore formed by choosing as the last permutation code for each different resolution the one whose rate of cumulation of cardinals is closest to the integer immediately higher . If the resolution of the dictionary characterized by L _j is greater than the maximum resolution desired, the last unused permutation codes are eliminated. We denote Z, - (g: Z, -j the final set

ordained leaders of D,. . At the end of the iterations on

dimensions, if certain leaders of L '° are not used to compose leaders of e {3,4,5,7,8,9,10,12,13,14,15}, the set L '° is updated in

eliminating them. We denote this set L = M. e [l, -L5]

The tables of FIGS. 7c to 7e show the gains in memory provided by the nesting property and by the property of partial composition by controlled extension. The table in FIG. 7c compares vector quantizers with multiple resolutions for different dimensions: the first quantifiers simply structured in unions of permutation codes, and the second quantifiers further possessing the property of nesting in resolutions.

In Figure 7c, we note:

- j: the dimension,

- Nj: the number of resolutions in dimension j,

- L _j : the number of leaders of the dictionary D,

- L _n j: the number of leaders of the dictionary D _. ,

- • the memory (in number of words) necessary for store the leaders of all d-dimensional dictionaries without the nesting property,

- j ^' L _j : the memory necessary to store the leaders of all dictionaries in dimension j with the property of nesting.

The table in Figure 7d compares these quantifiers, used for multiple dimensions, with quantifiers also having the structuring property of partial composition by controlled extension.

In Figure 7d, we note:

- j: the dimension

- L _D j: the number of leaders of the dictionary D _,, j

- _ _L _D k: the sum of the numbers of leaders of the dictionaries of maximum resolution of dimensions 1 to j ~ _, kL _r k • l memory necessary to store these leaders k = l without the property of partial composition by controlled extension,

- L _j : the number of leaders of the set L _j ,

-: their sum of dimensions 1 to j, j

- k _k '• ^{has the} memory necessary to store the leaders of all the dictionaries of dimensions 1 to j with the property of partial composition by controlled extension.

The table in Figure 7e compares vector quantizers with multiple resolutions and dimensions: the first quantifiers simply structured in union of permutation codes and the latter having in addition the structuring properties of nesting in resolutions and partial composition by controlled extension.

In Figure 7e, we note:

- j: the dimension

- Nj: the number of resolutions in dimension j

- I ^th number of leaders in dimension j to store for Nj resolutions without the nesting property or the controlled partial extension property

-: the memory (in number of words) necessary for store these leaders of all d-dimensional dictionaries without these two properties: the memory (in number of words) necessary for store leaders of all dictionaries from dimensions 1 to j without these two properties

L _j : the number of leaders of the set L ° _j : their sum of dimensions 1 to j j

- _ _j ^ k • 'l ^{has the} memory necessary to store the leaders Jt≈l of all the dictionaries of dimensions 1 to j with the two properties of nesting and partial composition by controlled extension. In the three tables, the last column shows the importance of the memory reduction factor. The only nesting property makes it possible to reduce the memory by a factor greater than 3 in dimension 3, 5 in dimension 7, 7 in dimension 15. Thanks to the nesting property, instead of storing all the Df Leaders for all resolutions in dimension j, stores only the leaders of A _{N ^J} _ι ^are leaders of Lj). The addition of the partial composition by controlled extension makes it possible to further reduce the memory as shown in the last column of the table in FIG. 7d. The additional gain provided by this property is by a factor greater than:

- 1.5 in dimension 4,

- 3 in dimension 8,

- and 7 in dimension 15.

As shown in FIG. 7e, compared to quantifiers simply structured in union of permutation codes, the use of quantifiers having moreover the two structuring properties of nesting in resolutions and of partial composition by controlled extension makes it possible to reduce the memory. by a factor 4 in dimension 3, 13 in dimension 7 and by a factor greater than 35 for dimensions greater than 11.

With the partial composition property by controlled extension, only the leaders of L ° must be stored, the leaders of the {Lj} being found from a correspondence table from the indexes of the leaders of Lj to the indexes of the leaders of L ° . We now describe how to effectively implement vector quantizers.

To implement a vector quantizer of dimension j and resolution r _± , the following three problems must be solved:

- search for the nearest neighbor of an input vector

- search for the index of a vector code of D, and conversely, search for a vector code of Df from its index.

With regard to indexing, it is indicated that there are several known ways of indexing the code vectors of a dictionary, a union of type II permutation codes. The numbering used in the embodiment is inspired by that used to index the spherical codes of the Gosset network.

For any dimension j (j e {3,, 5, 7, 8, 9, 10, 12, 13, 14, 15}), each code vector of D _. is indexed by an offset

characteristic of its permutation code, of a binary index giving its combination of signs and of its rank in its permutation code. The offset of a permutation code is the sum of the cardinalities of the permutation codes preceding it in D _N ^J. . Among the formulas

numbering of permutations, we chose the formula known as Schalk ijk.

In addition to this classic numbering of the code vectors of Dt _f . _ι ' ^we use a correspondence table of

Lj leaders index to L ° leaders index. The leaders of L ° being stored, there is thus a great freedom of indexing of L °. For example, we can classify these leaders with non-zero integer components by increasing dimension. Each index m ^j of a leader X ⁷ of Lj is associated with an index l _m of a leader x ^j 'of L °. From this index l _m , we find the dimension _ 'of the leader x ⁷ ' and the leader himself. The leader x ^j is then found by inserting (j-j ') zeros as the last components of x ³ '.

The table in Figure 7f gives the first 23 leaders of L °. The table of figure 7g gives the leaders of the permutation codes of the dictionaries in dimension 3 by indicating for each leader x ³ which leader x? 'de L -, of dimension j'(j'≤j), has been extended to obtain it. Incidentally, we notice that if j = j ', then x ^J ' ≈ x ³ .

In Figure 7f, we note:

-1: the leader's index in L ° (among the 516),

- j: its dimension,

- 1 ^J : its index in the leaders of L _j .

In Figure 7g, we note: the leader index x ³ among the 23 leaders of D _N , the dictionary index of lower resolution to which the leader belongs (ie x ³ ^ -? _ι and x ³ e Df), jr ±: the bit rate per vector of this dictionary D? , j ': the dimension of the leader x ³ ' of L ° (number of non-zero components), l _m : the index of x ^J 'among the 516 leaders of L °.

The coding and decoding algorithms, properly so called in the general case, are described below and we will see below the particularly advantageous case where an additional structural constraint (union of permutation codes) has been added.

It is first indicated that they preferentially use the structure of the dictionaries induced in particular by the property of controlled extension which makes it possible to reduce the complexity of the algorithm for finding the nearest neighbor. In particular, one can group the vector-codes having the same insertion rule. For example, in the case of a Euclidean distance distortion criterion which will be treated in detail below, if L code vectors jx, / = 0, l; --- E - lj of dimension j of a dictionary Dj are obtained by the same insertion rule R (n, {(i _m , p _m )} m = 0, n - l) to

starting from L code vectors xj ^{~ n} of dimension jn of

dictionary Dj, ^{~ n} , the calculation of L distances of

vectors— xj codes to an input vector _^ Can be accelerated by calculating nl, first the term ∑ψ _p 'm ~ ^a i " _m m) then by calculating the L m = 0 distances of the vector-codes xj ⁿ to the vector y' of dimension (jn) obtained by removing from y the n components

As indicated above, for each dimension, only part of the dictionary of maximum resolution must be stored, the other vector-codes are deduced from elements taken from the dictionaries of maximum resolution of lower dimension and insertion rules .

A detailed example of coding / decoding in compression is given below in the use of the dictionary creation method according to the invention.

First of all, we indicate that instead of storing, for all the dimensions j to be considered, the set of all the dictionaries , we therefore only store {D ' ^J _N } as well as correspondence tables. These tables make it possible to reconstruct a code vector of D _N ^J from its index. As described above, there are several ways to build these tables and therefore store them. For example, we can, for all dimensions j to be considered, tabulate for each index m -, - (of a vector code x? Of D _N ^J ) three integer scalar values: j ', m' and l _r , where l _r is the number of the insertion rule which allows to reconstruct x ^j by partial composition by controlled extension applied to the element of index m 'of the set of D' ^J _{N i} . Correspondence tables do not require more than the storage of 3 ^ 2 ^ ^' words (we

remember that Ti ^j is the size of the dictionary Di ^j ). As for the storage proper of the dictionaries of a vector quantizer with resolutions and dimensions

multiple, it requires ∑J∑T words in the case of a 7 = 1 i = \ vector quantizer not having the two structuring properties of nesting in resolutions and partial composition by extension, while storing the dictionaries of a vector quantizer having these two structuring properties requires N him only _ jT ^J _N. words, by noting T ' _N ^J the size of = 1 the set D ^{, J} _N ( ^J _N <T). However, in general,

T ^υ _N is much smaller than T ^, because we naturally try to favor the set D ' ^j _N with respect to

1 set D ^υ _N. Some digital examples of gain in storage will be given in an embodiment described below.

The coding algorithm which consists in finding the nearest neighbor x ³ in -D / of an input vector = (yo>---> y _k >---> y _j -ύ preferably includes the following steps:

The COO step) consists of an initialization step where one poses: d _m in = VALMAX; m _mirι = -1; m ^J = 0 For any index m ⁷ e [0,? V [:

The following step COI) consists in the reconstruction of the code vector x ^J of index m ³ and is preferably carried out as follows: a) reading of the three indices j ', m' and l _r in the correspondence tables associated with D _N ^J , b) reading in the set -D '^ of the vector x ^3' 'of dimension j' and of index m ', c) reconstruction of the code vector x ³ by applying to x ³ ' of the property of partial composition by extension controlled according to the rule of insertion of index l _r .

Step C02) consists in calculating the distance d (y, x ³ ) between y and x according to the chosen distortion criterion. The following steps C03) and C04) consist in repeating the operations COI) and C02) to identify the vector index whose distance to the input vector is minimum. So :

* if d (y, x ³ ) <d _min then d _min = d (y, x ^J ) and m _min = m ³

* then, we increment m ³ : m ³ = m ³ + l

* an end test is planned: if m ^{3 '} <T go to step COI), otherwise: stop. At the end step C05), the nearest code vector close to the input vector y is determined as a vector code whose index m _m i _n has been identified in correspondence of the smallest distance d _m i _n with the input vector y-

Thus, the algorithm continues with step C05): * End nearest neighbor x of y in D {is the vector-code of index m _m i _n

The decoding algorithm which consists in searching for a code vector of Dj from its index is given by step COI) of the coding algorithm. It is indicated, in particular, that the decoding implies the complete reconstruction of the code vector x (operation c) of step COI)), whatever the index to be decoded.

On the other hand, during coding, this reconstruction can be partial. Indeed, it can sometimes be omitted if the distortion criterion in the distance calculation of step C02) can be broken down into two terms: one dependent only on the index of the insertion rule, and another on the vector -code x ³ '. For example, in the case of a Euclidean distance distortion criterion, it is possible, at the initialization stage

COO), pre-calculate, for each insertion rule of index 7 - / - 1, l _r used in D (, the distance d _t = 2__ _P ~ ^a if (if l ^a m = 0 insertion rule index l _r consists in inserting jj ¹ components a _t in positions p _m , m going from 0 to j-j'-l).

The calculation of the distance between y and the vector x ^: (j ', m', l _r ) of step C02) then amounts to calculating the

αi _s tan e: ≈ù: x ³ 'is the vector obtained in operation b) of step COI), and y' the vector of dimension j ', obtained by removing from y the jj' components y _D , the distance d (y, x ³ ) then being obtained by simple summation d (y, x) = d _l + d (y ', x ³ ' j.

This is the reason for defining, above, "partial" the reconstruction of a code vector x ³ 'of dimension j' smaller than dimension j (which would be the dimension of a code vector x ³ completely rebuilt), during the coding process.

On the other hand, if a vector x ³ 'intervenes several times in the composition of vector-codes of D {(with different insertion rules), we can also precompute in the initialization step, the terms d (y ', x ⁱ '). So we see that the storage compromise (temporary) / complexity of coding can be adjusted according to the need of the application.

Similarly, the storage / indexing complexity compromise can also be adjusted as required by the application.

For coding, in the case of the additional constraint of a union of codes with permutations aforementioned, the algorithm of search of nearest neighbor, for the spherical codes of the regular network of Gosset in dimension 8, is easily generalized by simplifying to these dictionaries, by union of type II permutation codes.

Such a search algorithm is described in particular in: "Algorithm of Spherical Algebraic Vector Quantization by the Gosset Network E ₈ ", C. Lamblin, JPAdoul, Annales Des Télécommunications, n ° 3-4, 1988.

A first simplification is brought about by the "freedom" of the signs of type II permutation codes which the permutation codes of the Gosset network with odd components do not have. A second simplification is provided by taking into account the number of non-zero components of each leader for the calculation of the scalar product. This illustrates the exploitation of the structure induced by the property of partial composition by extension controlled by the coding algorithm. A final modification takes into account the storage of the leaders of L ° in whole form, which leads to the introduction in the scalar product calculation a corrective factor equal to the inverse of the Euclidean norm of these leaders with strictly positive integer components.

An embodiment is described below in which the search for the nearest neighbor of an input vector y of dimension j in the dictionary Dj uses, in addition to the two structuring properties of the invention, the union structure of codes with aforementioned permutation.

Overall, three additional steps are planned: two preliminary steps (before the COI reconstruction step) above) to determine the absolute leader and the sign vector ε of the vector to be coded (steps CP1) and CP2)), and a last step to calculate the rank of its closest neighbor in the dictionary (step CP5)).

The research described above is carried out, no longer among the T code vectors of Dj (ie no longer for m 'e [0, T, ^J [), but only on the set Lj (i) of L _DJ

DJ leaders (for me [0, Zy [, noting L _DJ the number

leaders or DJ permutation codes).

In this embodiment, the search for the nearest neighbor of y in Dj amounts to first searching for the most close neighbor of in the set L _j (i) (among the L _βl

first leaders of Lj). As described above, it is not necessary to completely reconstruct these leaders (operation c) of the COI step)), the distortion criterion (here the modified scalar product) being calculated only on the non-zero components of each leader. It suffices therefore to determine for each leader, the corresponding leader in L ° using the correspondence table of the indexes of the leaders of Lj to the indexes of the leaders of L ° associating with each index πP of a leader x ³ of L _j an index l _m from a leader x ³ 'from L °.

The algorithm then preferably takes place according to the following example:

* Step CP1):

Passing the input vector; = (y ₀ , ..., y _k , ..., y _j _ _l ) to its absolute vector and to its sign vector ε = (ε ₀ , ..., ε _k , ..., ε _j _ _l ) with ε _k = l if .y ^ ≥O and ε _k = - \ otherwise.

* Step CP2):

Leader search by permuting its components to arrange them in descending order

* Step CP3):

* Stage CoO '): Initialization: ps _m ax = - 1 -; m _max = - 1; m ^D = 0

for any index m ^{3 '} e [0, L _βS [ * COI step '): reconstruction of the leader of index m ^j : a) Reading of the index l _m of the leader x ³ ' associated with the leader of index m ³ of Lj, in the correspondence table associating the leaders of L _j to those of L °, then determination of the dimension j 'of the leader x ³ ' and reading of the corrective factor α (with b) Reading in the set L ° of the leader x ³ 'of dimension j' and of index l _m .

* Step C02 ') Calculation of the scalar product modified between

and x ³ ': ps (\ y \ x ^J' ) - x _k ^J )

The following steps consist in repeating the operations COI ') and C02') to identify the index of the leader-code whose scalar product modified with the absolute leader of the input vector is maximum. So: if ps (\ y \ x ^{J '} )> ps _max then ps _max m ³

* then, we increment m ³ : m = m + l

* End test if m <L _Dj go to step COI '), otherwise stop,

At this end step, the index of the nearest neighbor of y in Dj is calculated by the procedure of indexing a union of permutation codes from the number of the permutation code m _max found in step CP3) , the rank of the permutation carried out in step CP2) and the vector of signs determined in step CP1). It should be noted that step CP2) can be accelerated. Indeed, if nf is the maximum number of non-zero components of the leaders of Lj (i), it suffices to search for the nf largest components of \ y \. There are several variants of step CP3) depending on the desired storage / complexity compromise. If one wants to minimize the number of computations, one can tabulate for all the leaders of L ° simply their dimension j 'and their corrective factor. The determination of the dimension j 'mentioned in step CP3) consists in this case of a reading of the correspondence table. Conversely, if we rather want to reduce memory, this determination is calculated from the index l _m . Likewise, the corrective factor can be calculated after reading the leader x ³ '.

Thus, the algorithm for finding the nearest neighbor to an input vector y of dimension j in the dictionary Dj, using a union structure of permutation codes, can preferably be summarized as follows:

CP1) we pass from the input vector y = (yo, "., Yk,.", Yj-ι) to its absolute vector l-] ^{= and has its} sign vector ε = (ε ₀ , ..., εk, ..., εj-ι) with if yk≥O and -1 otherwise,

CP2) we are looking for the leader | 5> | of | _y | by permuting its components to arrange them in descending order, CP3) we are looking for the closest neighbor of | j7 | in

the set Lj (i) of DJ leaders (in fact among the Mj

first leaders of Lj by noting Mj the number of codes to

permutations of Dj). As indicated above, this step amounts to finding the leader of L ° which maximizes the scalar product modified from the list of Mj leaders of

L ° indicated by the correspondence table of the Lj leader indexes to the L ° leader indexes. If the dimension of a leader x ³ 'of L ° is j'(j'≤j), the computation of its scalar product with is only performed on the j 'first components of , then multiplied by the inverse of the Euclidean norm of x ³ '.

CP4) and the index of the rank of this nearest neighbor of y in Dj is calculated by the procedure of indexing a union of permutation codes from the number of the permutation code found in the previous step, of the rank of the permutation carried out in step CP2) and of the vector of signs determined in step CP1).

In short, step CP2) can be accelerated. Indeed, if nj is the maximum number of non-zero components of the leaders of L _j (i), it suffices to search for the nj largest components of M. We will now describe a decoding algorithm, in the general sense, without necessarily using the indexing of union of permutation codes described above as an advantageous embodiment. The decoding algorithm is preferably presented as follows.

From an index mj received, it is determined whether this index corresponds to a vector-code belonging to D _N _ _x or to π ³

In the first case, mj is associated with a unique index in

D'- __. , and the vector-code is obtained by a simple

correspondence table reading.

In the second case, mj points to an element E * '^, - _. (j '<j) and on an insertion rule.

The determination of the ap ^ p ^ artenance of xm ^J. _j to D '{N _τj -, 1 or to

its complement can be carried out in different ways. For example, you can use a binary indication for each index. We can also for each resolution i index the elements of the complementary Dj_,

in Dj starting with the elements obtained by controlled extension belonging to £> ', followed by the elements

"free" belonging to D'f. Belonging to D ' ^J _N _- or to

D ^{, J} N _M j_, i is then made by simple tests. Likewise, the

insertion rule can be explicitly indexed or not. For example, in the embodiments described below, the insertion rule is implicitly found from the index. It will also be understood that the compromise storage / indexing complexity can be adjusted according to the needs of the application.

We return here to the particular case of the additional constraint defined by the union of permutation codes.

Preferably, the decoding algorithm is inspired by the document: "Algorithm of Spherical Algebraic Vector Quantization by the Gosset Network E ₈ ", C. Lamblin, JP Adoul, Annales Des Télécommunications, n ° 3-4, 1988, in additionally using the correspondence table of Lj leader indices to those of L °.

From the index of a vector code in Dj, we determine the index of its leader in L _j (i), its rank in its permutation code and the sign of its non-zero components. The correspondence table then gives the leader's index in L ° which is then obtained by a simple reading of the table stored in memory as well as its normalization factor which makes it possible to normalize the decoded vector-code.

Another example of implementation of the present invention is given below. This example is still based on the TDAC transform coder, but for use in coding digital audio signals sampled at 32 kHz and 15 kHz bandwidth (FM band), in contrast to the example given above of the use of the TDAC encoder in wide band to encode digital audio signals sampled at 16 kHz.

The principle of this coder is similar to that of the TDAC coder in wide band at 16 kHz. The audio signal, band limited to 16 kHz and now sampled at 32 kHz, is also split into 20 ms frames. This leads after MDCT transformation to obtain 640 coefficients. The spectrum is cut into 52 bands of unequal widths, the cutting of the widened band being identical to the cutting carried out by the TDAC encoder in wide band.

The table in FIG. 8a gives the strip cutting used and the resulting dimension of the vector of the coefficients (corresponding to the number of coefficients indicated in the third column).

The quantification of the spectral envelope also uses Huffman coding and the remaining variable bit rate is dynamically allocated to the coefficients from the dequantified version of this spectral envelope.

The quantification of the MDCT coefficients uses dictionaries constructed according to the invention. As in the case described above, the dictionaries are also structured in union of permutation codes. For dimensions less than 15, the vector quantizers are the same as those for the widened band. We build dictionaries for dimensions 16, 17, 18, 19, 20 and 24. For dimension 24, this structure has also been combined with the structure in Cartesian product. The last high band of 24 coefficients is cut into two vectors of dimension 12: one is formed by the even coefficients, the other by the odd coefficients. Here, the vector quantizers constructed for dimension 12 have been used.

The table in Figure 8b gives the number of different resolutions and their values for dimensions 1 to 24.

The present invention thus provides an effective solution to the problem of vector quantization at variable speed and dimension. The invention jointly solves the two problems of variable resolution and dimension by providing a vector quantizer whose dictionaries, for the different dimensions and resolutions, have the structuring properties PR and PD above.

For a given dimension, the nesting of the dictionaries guarantees, on the one hand, the local decrease in distortion depending on the resolution and, on the other hand, significantly reduces the amount of memory required for storage because the dictionaries of the resolutions do not have to be stored, since all the elements of these dictionaries are in the dictionary of maximum resolution. Compared to the vector quantizer structured in a tree of figures la and lb, the choice to nest the dictionaries therefore already brings two advantages: the assurance of a decrease in local distortion according to increasing resolutions and reduced storage. It also allows a great finesse of resolution with, if necessary, a granularity lower than the bit, facilitating the choice of dictionaries of sizes not necessarily equal to powers of 2. This fine granularity of the resolutions is particularly interesting if several vectors of dimension and / or of variable resolution are to be quantified by frame, by associating with these rate quantifiers by non-integer vector an algorithm for binary training of the indices.

The PR nesting property of dictionaries means that you only have to store dictionaries of maximum resolution. Thanks to the second PD property, the amount of storage memory is even reduced. Indeed, a part of the elements of the dictionaries of maximum resolution does not have to be stored because it is deduced from elements taken in the dictionaries of maximum resolution but of smaller dimension, by taking account of insertion rules {R _m } predefined. The proportion of elements thus structured is easily adaptable and allows fine adjustment of the amount of storage memory.

The structure induced by these two properties PR and PD therefore makes it possible to advantageously reduce the memory required for storage. It can obviously be even more so by imposing on dictionaries additional structural constraints such as those already mentioned in the introductory part with reference to the state of the art above. In preferred embodiments, for example, provision is made for the use of spherical vector quantizers, union of permutation codes, combined where appropriate with the Cartesian product structure described above.

Compared to the algebraic vector quantizers, this structure of dictionaries induced by the two properties offers a great flexibility of design as well for the choice of the dimensions as for that of the resolutions. In addition, these vector quantifiers adapt to the statistics of the source to be coded and thus avoid the problem of the delicate design of a mandatory "vector companding" in algebraic vector quantization to make the distribution of the source to be coded uniform.

Claims

1. Dictionary comprising vector vectors of variable dimensions and intended for use in a coding and / or decoding device in compression of digital signals, by vector quantization at variable bit rate defining a variable resolution, characterized in that it comprises: - on the one hand, for a given dimension, dictionaries of increasing resolution nested one inside the other,

- and, on the other hand, for a given dimension, a union:

A first set made up of vector-codes constructed by inserting, into code vectors of dictionaries of lower dimension, elements taken from a finite set of real numbers according to a finite set of predetermined insertion rules,

• and of a second set made up of code vectors which cannot be obtained by inserting into code vectors of smaller dimension elements of said finite set according to said set of rules of insertion.

2. Dictionary according to claim 1, characterized in that said set of insertion rules is elaborated from elementary rules consisting in inserting a single element of the finite set of real numbers as a component at a given position of a vector.

3. Dictionary according to claim 2, characterized in that each elementary rule is defined by a pair of two positive integers representative: of a rank of the element in said finished set, and of an insertion position.

4. Method for forming a dictionary according to one of claims 1 to 3, the dictionary comprising code vectors of variable dimension and intended for use in a coding and / or decoding device in compression of digital signals, by vector quantization with variable bit rate defining a variable resolution, in which, for a given dimension: a) a first set is constructed consisting of vector-codes formed by inserting / deleting into vector-codes of dictionaries of lower / upper dimension elements taken from a finite set of real numbers according to a finite set of predetermined insertion / deletion rules, b) a first, intermediate dictionary is constructed for said given dimension, comprising at least said first set, c) and, to adapt said dictionary to a use with at least a given resolution, we build, from the intermediate dictionary, a second di ctionnaire, final, by nesting / simplification of dictionaries of increasing / decreasing resolutions, the dictionaries of increasing resolutions being nested one in the other of the dictionary of lower resolution until the dictionary of higher resolution.

5. Method according to claim 4, in which, for a given dimension N: aO) an initial dictionary of initial dimension n is obtained, less than said given dimension N, a1) a first set is constructed consisting of code vectors of dimension n + i formed by inserting into vector codes of the initial dictionary elements taken from a finite set of real numbers according to a finite set of predetermined insertion rules, a2) a second set of code vectors of dimension n is provided + i which cannot be obtained by insertion into the code vectors of the initial dictionary of the elements of said finite set with said set of insertion rules, a3) an intermediate dictionary is constructed, of dimension n + i comprising a union of said first set and of said second set, and steps a1 to a3) are repeated, at most Nn-1 times, with said intermediate dictionary as an initial dictionary, up to said dimen given sion N.

6. Method according to claim 4, in which, for a given dimension N: a'O) an initial dictionary of initial dimension n is obtained, greater than said given dimension N, a'1) a first set is constructed, of dimension neither, by selection and extraction of possible code vectors of dimension nor in the dictionary of dimension n, according to a finite set of predetermined suppression rules, a '2) a second set is made up consisting of code vectors of dimension ni, ne obtainable by deletion, in the code vectors of the initial dictionary, of the elements of said finite set with said set of suppression rules, a'3) an intermediate dictionary, of dimension ni comprising a union of said first set and said second set, is constructed, and we repeat, . at most nN-1 times, steps a'1) to a'3), with said intermediate dictionary as initial dictionary, up to said given dimension N.

7. Method according to claims 5 and 6, in which N successive dictionaries of respective dimensions 1 to N are obtained, from an initial dictionary of dimension n, by the repeated implementation of steps a1 to a3) for the dimensions n + 1 to N, and by the repeated implementation of steps a'1) to a'3) for dimensions nl to 1.

8. Method according to one of claims 4 to 7, in which said set of insertion / deletion rules is elaborated from elementary rules consisting in inserting / deleting a single element from the finite set of reals as a component at a given position of a vector.

9. Method according to claim 8, in which each elementary rule is defined by a pair of two representative positive integers:

-a row of the element in said finished set, -and an insertion / removal position.

10. Method according to one of claims 4 to 9, in which one defines a priori said finite set and said set of rules of insertion / deletion, before constructing the dictionary by analysis of a source to be quantified.

11. The method of claim 10, wherein said source is modeled by a training sequence and the definition of said finite set and of said set of insertion / deletion rules is carried out by statistical analysis of said source.

12. Method according to one of claims 10 and 11, wherein said finite set is chosen by estimation of a one-dimensional probability density of said source.

13. Method according to one of claims 4 to 9, in which said finite set and said set of insertion / deletion rules are defined a posteriori, after construction of dictionaries by nesting / simplification of dictionaries of successive resolutions, followed by a statistical analysis of these dictionaries thus constructed.

14. Method according to claims 10 and 13, in which:

- a priori, a first set and a first set of insertion / deletion rules are chosen by analysis of a learning sequence, to form one or more intermediate dictionaries,

- at least part of said first set is updated and / or of said first set of insertion / deletion rules, by a posteriori analysis of said one or more intermediate dictionaries,

- And, if necessary, at least part of the set of vector codes forming said one or more intermediate dictionaries is also updated.

15. Method according to one of claims 4 to 14, in which step c) comprises the following operations: cO) an initial dictionary of initial resolution r _n , less than said given resolution r _N , cl) is obtained from from the initial dictionary, an intermediate dictionary of resolution r _{n +} ι greater than the initial resolution r _n , c2 is constructed. operation cl) is repeated until the given resolution r _{N is} reached.

16. The method as claimed in claim 15, in which, for each iteration of operation cl), provision is made for the construction of classes and centroids in which the centroids belonging to at least the dictionaries of resolution higher than a current resolution τ_ are recalculated and update.

17. The method as claimed in claim 16, in which the centroids which belong to the dictionaries of resolution lower than a current resolution ri are only updated if the total distortions of all the dictionaries of lower resolution are decreasing from update to the other.

18. Method according to one of claims 4 to 14, in which step c) comprises the following operations: c'O) an initial dictionary of initial resolution r _{n /} greater than said given resolution r _N , c 'is obtained I) from the initial dictionary, an intermediate dictionary of resolution r _n -i lower than the initial resolution r _{n is constructed} , by partitioning the initial dictionary into several subsets ordered according to a predetermined criterion, and c'2) we repeat operation c'I) until reaching the resolution given r _N.

19. The method of claim 18, wherein said predetermined criterion is chosen from the cardinality of the subsets, a solicitation of the subsets in a learning sequence, a contribution of the subsets to a total distortion or preferably to a decrease of this distortion.

20. Method according to one of claims 18 and 19, wherein said partition uses at least part of said insertion / deletion rules.

21. The method of claims 15 and 18, in which N successive dictionaries of respective resolutions ri to r _N are obtained, from an initial dictionary of intermediate resolution r _n , by the repeated implementation of step cl) for increasing resolutions r _{n +} ι to r _N , and by the repeated implementation of step c'I) for decreasing resolutions r _n _ι to r _x .

22. Method according to one of claims 4 to 21, in which, to adapt said dictionary to use with a given dimension N of vector-codes, steps a) and b) are substantially reversed, on the one hand, and step c), on the other hand, so that: - in step c), we build, from an initial dictionary of resolution r _n and of dimension N ', a first dictionary, intermediate, always of dimension N ¹ but of higher / lower resolution r, by nesting / simplification of dictionaries of increasing / decreasing resolutions, in order to substantially reach the resolution r _{N of} said first dictionary,

- in step a), to reach the given dimension N, a first set of code vectors formed is constructed by inserting / deleting, in code vectors of the first dictionary of dimension N ′ lower / greater than said given dimension N, elements taken from a finite set of real numbers according to a finite set of predetermined insertion / deletion rules, and, in step b), following a possible step of final adaptation to the resolution r _N , we constructs, for said given dimension N, a second dictionary, definitive, comprising at least said first set.

23. Method according to one of claims 4 to 22, in which said set of insertion / deletion rules, each identified by an index (l _r ), is stored in a memory, once and for all, and, for a given dimension:

- Said second set consisting of code vectors which cannot be obtained by application of 1 insertion / deletion to code vectors of dimension lower / greater than the dimension given according to said set of rules of insertion / deletion, - as well as at least one correspondence table making it possible to reconstruct any vector code from the dictionary of given dimension, using the indices of the insertion / deletion rules and indices identifying elements of said second set, which makes it possible to avoid the complete storage of the dictionary for said given dimension, by simply storing the elements of said second set and links in the correspondence table to access these elements and the associated insertion / deletion rules.

24. The method of claim 23, wherein the correspondence tables are prepared beforehand, for each index (m ³ ) of a vector code (x ³ ) of the dictionary (D ^J N _j ) of given dimension (j) can be reconstructed from elements of current indices (m ') in the second set of current dimension (j'), by a tabulation of three integer scalar values representing:

- a current dimension (j ') of said second set,

- a current index (m ') of an element of the second set, and

- an index (l _r ) of insertion / deletion rule, this insertion / deletion rule at least contributing to reconstruct said vector-code (XJ) of the dictionary (D ³ _N j) of given dimension (j), applying the insertion / deletion to the element of said current index (m ') and said current dimension (j').

25. Use of the dictionary obtained by the implementation of the method according to one of claims 23 and 24, in coding / decoding in compression of digital signals, by vector quantization at variable bit rate defining a variable resolution, in which the vector is sought. -code (x ³ ) closest to an input vector y = (yo .—. yk / - # yj-ι) in a dictionary (D ^x _j ) of given dimension (j), and including the following steps :

COI) for a current index (m ³ ) of said sought vector code (x ³ ), at least partial reconstruction of an index code vector (m ') corresponding to said current index (m ³ ), at least by reading preliminary indices (j ', m', l _r ) appearing in the correspondence tables making it possible to develop said dictionary,

C02) at least during coding, calculation of a distance between the input vector and the vector-code reconstructed in step COI),

C03) at least during coding, repetition of steps COI) and C02), for all the current indices in said dictionary,

C04) at least during coding, identification of the index (m _m i _n ) of the at least partially reconstructed code vector, the distance (d _m i _n ) of which with the input vector, calculated during one of the iterations of step C02), is the smallest, and

C05) at least on decoding, determination of the nearest neighbor of the input vector (y) as a code vector (x ³ ) whose index (m _m i _n ) was identified in step C04).

26. Use according to claim 25, in which step COI), at least during decoding, comprises:

COU) reading, in the correspondence tables, indices indicative of links to said second set and to the insertion / deletion rules and including: the index of a current dimension of a subset of said second set , the current index of an element of said subset, and the index of the insertion / deletion rule appropriate for the construction of the vector-code of the dictionary of given dimension, from said element, C012) reading, in the subset identified by its current dimension, of said element identified by its current index,

C013) the complete reconstruction of the vector-code at said given dimension by applying to said element read in step C012) the appropriate insertion / deletion rule and identified by its index read in step COU).

27. Use according to claim 25, in which, on coding,

* the COI stage) includes:

COU) reading, in the correspondence tables, indices indicative of links to said second set and to the insertion / deletion rules and including: the index of a current dimension of a subset of said second set , the current index of an element of said subset, - and the index of the appropriate insertion / deletion rule for the construction of the vector code of the dictionary of given dimension, C012) the reading, in the subset identified by its current dimension, of said element identified by its current index ,

* in step C02), said distance is calculated according to a distortion criterion estimated as a function of: the index of the insertion / deletion rule, and of the element of the subset identified by its index current, which makes it possible to only partially construct the vector-code at said dimension given in step COI), by reserving the complete reconstruction simply for decoding.

28. Use according to one of claims 25 to 27, in which an additional structuring property is further provided according to a union of permutation codes and exploiting an indexing of said union of permutation codes, and in which:

CP1) from an input signal, an input vector y = (y _o , -, yk, -.-, Yj-i) defined by its absolute vector | J | = (| JO | '" ^, » | Λ |'" ^, J yj-ι) ^and P ^{ar a} sign vector ε = {ε _ϋ , ..., ε _k , ..., ε _j _ _λ ) with ε _k = ± l,

CP2) the components of the vector | y | by decreasing values, by permutation, to obtain a leading vector | j | ,

CP3) we determine, among the leaders of the dictionary Di of dimension j, a nearest neighbor x ³ 'of the vector leader | j | , CP4) an index of the rank of said nearest neighbor x ³ ′ is determined in the dictionary D,

CP5) and an effective encoding / decoding value is applied to the input vector, which is a function of said index determined in step CP4), of said permutation determined in step CP2) and of said sign vector determined in step CP1).

29. Use according to one of claims 25 to 28, in which at least said correspondence tables are stored in a memory of an encoding / decoding device.

30. Computer program product intended to be stored in a memory of a processing unit, in particular of a computer or of a mobile terminal, or on a removable memory medium and intended to cooperate with a reader of the unit treatment, characterized in that it includes instructions for implementing the method according to one of claims 4 to 24.

31. Computer program product intended to be stored in a memory of a processing unit, in particular of a computer or of a mobile terminal incorporating an encoding / decoding device, or on a removable memory medium and intended to cooperate with a reader of the processing unit, characterized in that it includes instructions for implementing the application for coding / decoding in compression according to one of claims 25 to 29,