FR2800941A1 - Digital code decoding technique uses decoding lattice based on binary tree structure for reduced error rate decoding - Google Patents

Abstract

The system is based upon the use of a Huffman binary tree and associated lattice to decode variable length coded digital words. The method provides decoding of received digital data corresponding to transmitted digital data, coded with an entropic code. Each word of an alphabet is associated with a distinct bit sequence whose length is a function of the word occurrence probability. The technique uses a decoding lattice in which each transition corresponds to a binary value 0 or 1 in the one of the bits of the sequence corresponding to one of the words. The entropic code is represented in the form of a binary tree comprising a racine node, a number of intermediate nodes, and a number of leaf nodes. A sequence of bits corresponding to one of the words is formed by considering the successive transitions of the tree from the racine node up to the leaf node associated with the word.

Description

<Desc / Clms Page number 1>

 A method of decoding data encoded by means of an entropy code, decoding device and corresponding transmission system.

 The field of the invention is that of the transmission, or broadcasting, of digital data signals. More specifically, the invention relates to the decoding of transmitted digital signals, and in particular the source decoding.

More precisely, the invention applies to the decoding of data coded using a source coding implementing variable-length code (VLC) entropic codes.

 The digital communication systems commonly used today rely on coding systems implementing on the one hand a source coding and on the other hand a channel coding. Classically, these two codings are optimized separately. The purpose of the source encoder is to minimize the redundancy of the source signal to be transmitted. Then, to protect this information from disturbances inherent to any transmission, the channel coder introduces redundancy, in a controlled manner.

 Currently, the best results are obtained in source coding (audio source, images and / or video) by discrete cosine transform (DCT) coders, or wavelets in particular, associated with VLC codes. . Channel coding advantageously employs the concept of turbo-codes [1] (the bibliographic references are collated in Appendix C, in order to facilitate the reading of the present description), and more generally iterative decoders with soft decisions. These techniques made it possible to take a decisive step towards the theoretical limit defined by Shannon [2].

 However, the optimality of the separation of source coding and channel coding is only guaranteed for length codes tending to infinity. Therefore, research is also carried out to achieve, with finite-length channel codes, coding systems and / or decoding source-channel joint.

 The invention thus relates to the decoding of entropy codes, and in particular, but not exclusively, the joint source-channel decoding of a

<Desc / Clms Page number 2>

 system implementing an entropy code.

 The joint decoding has many fields of application, for example the transmission of video images, in particular according to the MPEG 4 (Moving Picture Expert Group) standard.

 Variable length codes are well known. As an example, we quickly present, in Appendix A, the Huffman code. The particular embodiment of the invention described below applies particularly, but not exclusively, to this type of entropy code.

 Variable length codes are an important issue for limiting the band occupied by the transmitted signal, but their use makes the transmission less robust to errors. Moreover, it is difficult to use the probabilities a priori of the source at decoding, because we do not know the beginning and the end of each word, since the length of these is, by definition, variable.

Various techniques have been proposed for performing a source-channel joint decoding related to the use of these variable-length codes. Especially :
K. Sayood and N. Demir proposed in [4] a decoding at the level of the VLC codewords. We find the two major drawbacks of this type of decoding, namely a trellis complexity which increases rapidly with the number of different VLC words and a decoding which remains at the symbol (or word) level;
Ahshun H. Murad and Thomas E. Fuja [5] propose a trellis method in which the decoding trellis is that obtained by the product of the trellis of the channel decoder, the lattice of the source decoder and the lattice representing the source. This solution is clearly limited by the complexity of the decoding;
KP Subbalaskshmi and J. Vaisey [6] give a lattice structure which makes it possible to know the beginning and the end of each word and thus to use the information a priori that one has on the VLC words emitted. This decoder works at the word level and does not return extrinsic information on the decoded bits;

<Desc / Clms Page number 3>

Jiangtao Wen and John D. Villasenor [7] use a decoding block working at the word level and returning a reliability as to the decoded sequence. This decoder uses as information a priori the number of VLC words in the received sequence.

 The invention particularly aims to overcome the various disadvantages of these techniques of the state of the art.

 More specifically, an object of the invention is to provide a technique for decoding coded data using an entropy code making it possible to obtain a reduction in the symbol error rate, in particular with respect to separate decoding schemes. (tandem).

 On the implementation aspects, an object of the invention is to provide such a decoding technique with a very reduced complexity, compared to known techniques.

 In particular, an object of the invention is to provide such a decoding technique having a reasonable operational complexity, that is to say possible to implement in practice at a reasonable cost, especially when the number of words different considered by the entropy code is high.

 The invention also aims to provide such a technique delivering bit level confidence information that can be exploited by channel decoding.

 In other words, a particular object of the invention is to provide source-channel decoding methods well adapted to entropy codes, including VLC codes.

 Yet another object of the invention is to provide such a decoding technique, making it possible to improve the performances obtained with the known channel codes, and in particular the coders implementing a turbo-code.

These objectives, as well as others which will appear more clearly later, are achieved by means of a method of decoding received digital data corresponding to transmitted digital data encoded using an entropy code associating with each of the words of an alphabet a sequence of bits

<Desc / Clms Page number 4>

 distinct, the length of which depends on the probability of occurrence of that word.

 According to the invention, this method implements a decoding trellis of which each transition corresponds to a binary value 0 or 1 of one of the bits of a sequence of bits corresponding to one of said words.

 In other words, the invention is based on a novel approach to decoding codes of varying lengths, according to which transitions are considered at the level of bits, and not classically at the level of words or symbols.

 This approach is new, and not obvious, the person skilled in the art being persuaded that the fact that the symbols are of varying lengths requires working at the level of the symbols, in order to know the beginning and the end of these.

The inventors show that this is not mandatory.

 In addition, the fact of working at the bit level makes it possible to obtain information that can be used by a channel decoder, and thus to perform a joint decoding, as will become clearer later.

 The entropy code may be represented as a binary tree comprising a root node, a plurality of intermediate nodes and a plurality of leaf nodes, a bit sequence corresponding to one of said words being formed considering successive transitions of said tree from said root node to the leaf node associated with said word. In this case, advantageously, the states of each stage of said lattice comprise a single state called extremal, corresponding to said root node and all of said leaf nodes, and a distinct state, said intermediate state for each of said intermediate nodes.

 A simple lattice with a reduced number of states is thus obtained.

 Preferably, each transition of said trellis is associated with likelihood information. Said likelihood information is then advantageously a metric taking into account, on the one hand, information representative of the transmission channel and, on the other hand, information a priori relating to the source.

 Thus, it is possible to calculate, for each of said transitions, the metric

<Desc / Clms Page number 5>

ï,[(Xk,Xt),dk,dk-l] = Pr(xk / ak = i)Pr(y[ / ak = l,dk,dk-L)Prak = i,dkldk-11, dont les informations et paramètres sont décrits par la suite. next :

ï, [(Xk, Xt), dk, dk-l] = Pr (xk / ak = i) Pr (y [/ ak = 1, dk, dk-L) Prak = i, dkldk-11, whose information and parameters are described later.

 Said entropic code may notably belong to the group comprising: # Huffman codes; # reversible variable length codes.

 The invention also relates to a sourcechannel joint decoding method of a received digital signal, based on this approach, the source coding implementing an entropy code associating with each of the words of an alphabet a distinct bit sequence, whose length is a function of the probability of occurrence of said word.

 According to the invention, this joint decoding method thus implements a source decoding using at least one decoding trellis of which each transition corresponds to a binary value 0 or 1 of one of the bits of the bit sequence corresponding to the decoding trellis. one of said words, said source decoding delivering extrinsic information to the channel decoding.

 The channel decoding can advantageously implement a turbo-code type decoding, which may be based on a parallel-type implementation or on a series-type approach.

 Advantageously, the joint decoding method of the invention is based on an iterative implementation.

 In this case, each of the iterations may comprise sequentially a channel decoding step and a source decoding step, said channel decoding step delivering channel information taken into account in said source decoding step, the latter delivering information a priori taken in said channel decoding step.

 In particular, the method may comprise: # a first channel decoding step; a first source decoding step, powered by said first channel decoding step;

<Desc / Clms Page number 6>

 a second channel decoding step, powered by said first channel decoding step and said first source decoding step, via an interleaver identical to the interleaver implemented at the coding, and feeding said first channel decoding step, via a symmetrical deinterlacer to said interleaver; a second source decoding step powered by said second channel decoding step via said de-interleaver, and feeding said first channel decoding step.

 According to another aspect of the invention, this further concerns a source-channel joint decoding method of a received digital signal, the source coding implementing an entropy code associating with each word of an alphabet a sequence of distinct bits, whose length is a function of the probability of occurrence of said word, said method implementing a channel decoding trellis, similar to the channel coding trellis, in which each state of each stage is associated with information designating the position of the considered bit in the tree representing said entropy code.

 In this case, the joint decoding method advantageously comprises, for each of said states, the following steps: # adding, to the two branches arriving in said state, the metric of the channel and the metric of the source; # comparison of the two new metrics obtained, and selection of the weakest metric; # if the said information designating the position indicates the end of a word, consider that the node is a leaf of the tree, if not, go to the next node in the tree.

 Preferably, this method implements an iterative procedure, which may for example comprise the following steps: # first channel decoding, implementing a channel decoding trellis of which each state has information indicating the position of the bit considered in the tree representing said entropy code;

<Desc / Clms Page number 7>

 second channel decoding, powered by said first channel decoding, via an interleaver identical to that implemented in coding, and feeding said first channel decoding, via a symmetrical deinterleaver of said interleaver; source decoding, powered by said second channel decoding, via said de-interleaver.

 Of course, the invention also relates to all digital data decoding devices implementing one of the decoding methods described above, as well as the digital signal transmission systems, implementing, transmission, entropy source coding and channel coding, and upon reception, decoding as described above.

Other characteristics and advantages of the invention will appear on reading the following description of preferred embodiments of the invention, given by way of a simple illustrative and nonlimiting example, and the appended drawings, among which: FIG. 1 shows an example of a Huffman code, in the form of a binary tree; FIG. 2 illustrates a so-called reduced symbol lattice, corresponding to the tree of FIG. 1; FIG. 3 shows a so-called reduced bit lattice according to the invention, corresponding to the tree of FIG. 1; FIG. 4 is a diagram illustrating a joint decoding structure of the turbo-code type, implementing a "SISO ~ huff" module according to the invention; FIG. 5 illustrates the progress of the source-channel joint decoding algorithm according to a second embodiment; FIG. 6 shows a joint decoding iterative scheme implementing the algorithm illustrated in FIG. 5; FIG. 7 shows a combination of the methods of FIGS. 4 and
6;

<Desc / Clms Page number 8>

 Figure 8, commented in Appendix A, illustrates the construction of a Huffman coding.

Preferential embodiments
1-Introduction
The invention therefore particularly aims to present a decoding technique reducing the symbol error rate, using the prior information on the source, probabilities on the words of the VLC code or transition probabilities between the words. It has been found that this reduction is higher if the decoders use the prior information on the source at the bit level, since the extraction of information from the channel decoding can only be done at this bit level.

 Until now, most of the methods proposed for decoding VLC codes work at the level of words (or symbols, these two terms being used interchangeably later) and can not therefore provide extrinsic information at the bit level. In addition, these methods become for the most part too complex, and therefore not practical in practice, when the number of different words to be transmitted increases. The only attempt made at the bit level is presented in [5]. Very clearly, this solution has a very high operational complexity, and quickly crippling.

 The technique of the invention, on the other hand, makes it possible to determine not only the optimal sequence of words, but also the reliability associated with each of the bits of each word. To do this, the invention uses information a priori on the source, that is to say the prior probability of the VLC code words, or the Markov transition between the words of the code.

 This technique can advantageously be used in an iterative scheme of turbo-code type, and improves the performance of the transmission.

2- Rating
The following notations are used later: # a soft decision corresponds to a real non-binary decision. Thresholding on this one will give a hard decision. A sweet decision

<Desc / Clms Page number 9>

 is also called soft decision; # the ratio EB / N0 corresponds to the ratio between the energy received per useful bit divided by the monolateral spectral density of the noise; # the DC (Direct Component) band of an image is the DC component of the image after wavelet or DCT transformation; a received bit sequence is denoted by X or Y. This sequence consists of words denoted xi, these words being composed of bits denoted xij; # we use the notation p (a) = Pr {x '= a # a RVLC code (in English: Reversible VLC) [8] is a variable length code whose words are decoded in both directions; # a Soft-In Soft-Out (SISO) algorithm inputs soft values and delivers soft outputs.

3- Soft decoding source of variable length codes
It is shown in Appendix B how it is possible to extract information from the sequences of variable length words issued by a Huffman coder (see Appendix A), by modeling the source, or by a random process generating symbols. independent, either by a Markov random process.

 Figure 1 shows the example of a Huffman code, in the form of a binary tree. It consists of five words a, b, c, d, e of probabilities p (a), p (b), p (c), p (d), and p (e), and of lengths respectively 3, 3 , 2, 2 and 2.

The corresponding coding table is given below:

<Tb>
<tb> a <SEP> 111
<tb> b <SEP> 110
<tb> c <SEP> 10
<tb> d <SEP> 01
<tb> e <SEP> 00 <SEP>
<Tb>
Table 1: VLC codes of the tree of FIG. 1. By placing itself, according to the approach of the invention, at the bit level, one observes

<Desc / Clms Page number 10>

 that four states are necessary to describe in the form of trellises, the tree of FIG. 1. These states are dO for the beginning and the end of the symbols, d1, d2 and d3 for the intermediate positions. On the other hand, at the symbol level, we notice that a single state dO can suffice, as illustrated in FIG. 2. The reduced symbol lattice thus defined is then a lattice with a single state dO, from which depart and arrive as many branches that there are VLC words. In the example of FIG. 1, at each stage (t-2, t-1, t), this lattice has five branches corresponding to the words a, b, c, d and e.

 The reduced symbol lattice uses the probabilities a priori on the words of the source, working at the word level. This lattice can also be used as an auxiliary lattice during decoding using Markov probabilities.

4- Decoding according to the invention. at the bit level
It has been seen that, according to known techniques, the VLC source decoding methods use the prior probabilities of word-level VLC words, which prevents the reliability from being returned to each bit of the decoded sequence. It is shown later how the prior probabilities on words can be decomposed into a probability product a priori on the bits, then the decoding methods based on this approach are described.

4.1 Using Prior Probabilities of Bit-VLC Code Words
This part explains the decomposition of the probabilities of words into a product of binary probabilities.

p(a) = Prix, = a} = Pr{x = I,x, = 1, x\ = Il (8) Cette probabilité se décompose suivant l'équation : p(a) = Pro = 1} Prx; =1 / xô = 1} Prx = 1 x =1, x; = Il (9)
La probabilité p(a) est donc le produit de trois probabilités associées à chacun des bits du mot a. Take the example of the word a: We have from the tree of Figure 1:

p (a) = Price, = a} = Pr {x = I, x, = 1, x \ = Il (8) This probability decomposes according to the equation: p (a) = Pro = 1} Prx; = 1 / x0 = 1} Prx = 1 x = 1, x; = He (9)
The probability p (a) is therefore the product of three probabilities associated with each of the bits of the word a.

 With a lattice that indicates the position of the bit in the word that is decoded, these binary probabilities allow soft binary decoding.

<Desc / Clms Page number 11>

 For example, if we know that we are in the second position of the word then the probability to use on the branch is Pr (x1i = 1 / x0i = 1).

Pvlx'k +1I(x = +1, j < k)} pour le mot a. Let's calculate, for the word a and for k - 0,1,2 the probabilities

Pvlx'k + 1I (x = +1, j <k)} for the word a.

Prjxj = 11 x lr Prsommet,,l 53/ sommet [0 SI} p(a) + p(b) (11) p(a) + p(b) + p(c)

Prjxj = 1 / x = 1, x; = If pr{ sommet,,2 S7/ sommet"l S3} p(a) (12) p(a) + p(b) Ce calcul peut se généraliser facilement au cas d'un code de Huffman réel.

The tree of Figure 1 gives the solution immediately. We deduce, at the different vertices of the tree, the equalities:
Pr {x0i 1} Pr {vertex, 0 = SI} p (a) + p (b) + p (c) (10)

Prjxj = 11 x lr Prsommet ,, l 53 / vertex [0 SI] p (a) + p (b) (11) p (a) + p (b) + p (c)

Prjxj = 1 / x = 1, x; = If pr {top ,, 2 S7 / vertex "l S3} p (a) (12) p (a) + p (b) This calculation can easily be generalized to the case of a real Huffman code.

Let C = (w ') be the set of Huffman code words, Sk = In ENI'v'p <k, w "px} the set of indexes of words whose first k bits are equal to the first k bits of word xi and Sks = {n # S # wkn = S} the indexes of Sk of words whose k'th bit is equal to s (s # {0, 1}), we have:

This calculation principle is illustrated here in the case of a source of independent words. For a Markov source, the principle is the same except that each calculated probability distribution depends on the previous word found.

Thus, the calculation is to be done for all the previous possible words.

 Once this decomposition is done for all the words of the VLC code, it is necessary to find the reduced binary lattice which makes it possible to use the binary probabilities. The decomposition of p (a), p (b), ... into a product of binary probabilities has imposed a certain relation between the binary probabilities and the word probabilities. These

<Desc / Clms Page number 12>

 relations are preserved only if there is a bijection between the branches of the tree and those of the lattice. It is therefore necessary the least complex mesh which gives the position of the bits in each word and which avoids identical parallel branches (same starting state, same state of arrival and same label).

4. 2 The reduced binary lattice (called SISO-huff) First, we will describe the construction algorithm of the reduced binary lattice. Then we will give the algorithm of decoding on this lattice and in particular the use of the binary probabilities a priori.

4.2.1 Algorithm for construction of reduced binary lattice
Initialization of the lattice First state of the lattice, state 0: of the tree i = construction loop
For each word in the VLC table,
For each bit of this word, build states
If the starting state of the tree branch tagged by this bit is not associated with a state of the trellis, add a state to the trellis, state i i ++
If the state of arrival of the branch is not associated with a state of the trellis,
If it corresponds to a non-terminal node of the tree,
Add a state to the trellis, state j (j == i) i ++
Otherwise associate this state with the state j (j = 0) labeling of branches
Create, if not existing, a branch between the state i and the state y labeled by the processed bit

<Desc / Clms Page number 13>

In the case of our example, the lattice of FIG. 3 is thus obtained.

 This lattice gives the position of the bit in the word. If we are in the state i, we know, from the tree, that we are in the position} of the treated word because there exists a bijective correspondence between the states i of the lattice and the positions} in the tree.

4.2.2 Algorithm for decoding from the reduced binary lattice
The decoding algorithm used on this lattice for the simulations given later is a BCJR algorithm (Bahl Cocke Jelinek Raviv) [13] modified by Benedetto in [14] to treat the parallel branches.

 The metric calculated on each branch takes into account the knowledge that one has on the channel and probabilities a priori binary calculated previously.

More precisely, the calculation formula on a branch [15] is:

At the discrete moment k, the pair (xk, xkp) is the pair of likelihoods of the received bits, dk-1 and dk are respectively the states of departure and arrival of the branch, ak is the bit of associated information to the branch.

 The first two terms on the right of equation (13) refer to the knowledge we have about the channel. The third, Pr {ak = i, dkdk-1}, corresponds to the binary probability a priori.

 This lattice can be used in a binary soft decoding of type BCJR or type SOVA (in English: "Soft Output Viterbi Algorithm"). When using the Markov a priori probabilities, using the BCJR algorithm, soft decoding requires parallel processing which indicates for each stage the most likely previous word. This treatment is that carried out by the reduced symbol lattice. This increase in complexity implies a preference for the SOVA algorithm or for the SUBMAP algorithm [11].

4. 3 Generalizations
The method presented is generalized without difficulty in cases where the Huffman table contains more bits. However, the complexity of the reduced binary lattice increases with the number of words in the Huffman table.

<Desc / Clms Page number 14>

 The application of the method of the invention to the codes RVLC [8] can of course be considered. The lattice of the SISO ~ huff block can be used by decoding in the other direction but this implies an increase in complexity. An alternative would be to use the probabilities a priori in one direction for the forward phase and in the other for the backward phase.

 On the other hand, it is interesting to search among the equivalent Huffman codes [17], which one is best adapted for the soft decoding of the SISO ~ huff block.

5- Source-channel joint decoding 5. Block diagram of use of the "SISO huff" block
The reduced binary trellis or "SISO ~ huff" allows decoding of the SISO type and can therefore be inserted in an iterative decoding scheme like that of FIG. 4.

 Each decoding block 41 to 44 of FIG. 4 extracts extrinsic information on the bits to be decoded and sends this information to the next block. The information circulating between the different blocks is, as in reference [15] extrinsic probabilities.

 Of the two DEC1 decoder DEC2,41 and channel 43, two different extrinsic information are extracted according to whether they are used by the "SISO ~ huff" block 42 or 44 or by the other channel decoder 41 or 43. 451, 452 extrinsic information used by the next channel decoder is that conventionally used in turbo-codes.The one used by the block "SISOJhuff" 42,44, shown in bold, 461, 462 corresponds to this first information which has been removed the information from the previous block "SISO ~ huff", 44,42, this in order to comply with the rule that any block of iterative decoding should not use information he has already produced.

 The overall structure of the iterative decoder is not discussed further.

It is indeed known in itself [1]. The modules E 471 and 472 are interleavers (identical to those implemented at the coding) and the E * 48 module a deinterleaver, symmetrical to the interleaver.

<Desc / Clms Page number 15>

 The information taken into account is as follows: # Xk: Likelihood information received on the information bits transmitted; # Y1k: Likelihood information on the parity bits from encoder 1; # Y2k: Likelihood information on the parity bits from encoder 2; # Proba: a priori probability; # Output ~ hard: decoded information bit.

 This diagram is an example of iterative joint decoding where the prior information and the information of the channel are used in turn on their associated lattice. It is also conceivable to use both of these information on the lattice of the channel decoder as shown in the second proposed method.

5.2 Second Source-Channel Decoding Algorithm
The joint decoding proposed in FIG. 4 iteratively and sequentially realizes the two decoding functions. The following is a technique where a single decoding block performs both operations simultaneously. This technique also applies to the decoding of a Markov source.

 The concept developed is applicable to any transmission chain composed of a channel decoder trellis (convolutional or in block) and a source that can be represented by a tree.

5.2.1 Algorithm for lattice construction
The trellis used is that of the channel coder and does not require any new construction.

5.2.2 Decoding algorithm
The decoding algorithm is of Viterbi type. It decodes the most likely sequence of words. The metric calculation involves not only the channel information (usual case) but also the binary prior probabilities.

This method is similar to the one presented by Hagenauer [15] but applied here

<Desc / Clms Page number 16>

 variable length codes.

 For this, the algorithm must know which branch of the Huffman tree corresponds to the branch currently processed on the channel decoder. This information is sufficient to give the appropriate prior binary probability (calculated as in section 4.1 and previously stored in a table).

 This information is easily accessible by keeping up to date for each stage and for each state of the trellis of the channel decoder the position of the bit in the tree.

For each stage of the channel decoder,
For each state, body of the ACS (Add Compare Select) add to the two branches arriving in the state the metric of the channel and that of the source compare the two new metrics obtained, choose the one of metric the weakest update if we reach the end of a word, n # ud = root of the tree otherwise n # ud = next node in the tree}
Let us take the example of the tree of FIG. 1. The algorithm proceeds as shown in FIG. 5. At the stage considered, there are two concurrent sequences arriving at the second state of the lattice. Each corresponds to a sequence of different VLC words. The first, in full line, corresponds to the emission of e, d, ..., the second, dotted line to b, e, ....... The probability of branch a priori for each of them , P [S2] [0] and P [S0] [1], depends on the node Si noted on the sequence and bit 0 or l which labels the branch. Once the calculation of the probability of the branch carried out, by the relation (6), one can make the classic ACS.

<Desc / Clms Page number 17>

 This solution is very interesting because, unlike the solution of the "SISO ~ huff" block, it is not limited in complexity by the size of the Huffman table and increases only very little the current complexity of the channel decoders. .

6- Application of the second algorithm to an iterative scheme of joint decoding
6.1 Using this method in an iterative scheme
A scheme for use in iterative decoding is shown in FIG.

 The first decoder 61 uses on the same trellis the information of the channel and the information a priori. On the other hand, the second decoder 62 can not use the information a priori because the interleaver 63, denoted E, breaks the relations between the VLC codewords. The latter then uses the probabilities p (0) and p (1) which are in most cases different.

6.2 Cumulation of the two approaches to joint decoding
It is possible to use the two methods proposed above in an iterative scheme, such as that given by way of example in FIG. 7. In this figure, the notations are identical to those used previously.

 The elaboration of an interleaver preserving the relations between the words makes it possible to find a compromise between optimal binary interleaving and conservation of the structure a priori on the words.

7- Performances
The possibility of soft-decision decoding of Huffman codes has been shown. Compared with previously published work, the method of the invention makes it possible to work at the bit level. It is thus possible to introduce a source decoding block with weighted inputs and outputs, called "SISO ~ huff", in a turbo-code channel decoding scheme. Another possibility is to use the information a priori on the source directly at the level of the channel decoder.

This second method is much less complex and gives results equivalent to those obtained with "SISO ~ huff".

<Desc / Clms Page number 18>

 The gains made by this type of scheme depends on the one hand on the modeling used for the source with the prior knowledge of the probabilities of the Huffman symbols or their transition probabilities, and on the other hand, on the ratio Eb / N0 on the canal.

 In the comparisons we have made, we evaluate our gains against the corresponding tandem scheme. In the range of bit error rates around 10-2 to 10-3, the two new techniques allow gains between 0.5 and 1 dB from their first iteration, this with NSC coders (in English: Non Systematic Coder) .

 Moreover, their use in an iterative scheme of the Turbo-Codes type improves the performance of 0.5 to 1.5 dB. Moreover, the joint use of the two methods makes it possible to expect an even greater cumulative gain.

 In the announced earnings ranges, the highest values are obtained at low signal-to-noise ratio, which significantly increases the operating range in transmission. It should also be noted that in a Turbo-Code type scheme, this can shift the trigger point of the Turbo-Codes effect by 0.5 to 1.5 dB.

 The first method requires the running of a decoding algorithm on the lattice "SISO ~ huff" while the second simply requires updating a table during decoding on the trellis of the channel decoder. Moreover, unlike the first method, the second one has computational complexity that does not increase with the number of words in the VLC table.

 As the use of Huffman variable length codes is very widespread, these decoding techniques may be suitable in many contexts. The applications are multiple. For example, Huffman tables are found in the MPGE4 standard for coding the coefficients of the DC band and the AC band for the intra-coded images, but also for the coding of the motion vectors.

 The invention can also be used in a more complete transmission chain by taking into account a standard image coding system,

<Desc / Clms Page number 19>

 or close to the standard, and a representative channel model of the mobile radio channel as BRAN (Broadcast Radio Network).

<Desc / Clms Page number 20>

ANNEX A
VLC Huffman
The Huffman code ([17]) is an entropy code that compresses a source by encoding the unlikely data over a bit length above the average and those highly likely over a short bit length. The Huffman code is widely used because there are no other integer codes (whose symbols are encoded on an integer number of bits) which gives a lower average number of bits per symbol. One of its essential characteristics is that a binary sequence can never be both representative of a coded element and constitute the beginning of the code of another element. This characteristic of Huffman coding allows for coding using a binary tree structure.

 There are several ways to present the construction of the Huffman code. The one that seems the simplest is based on a tree structure.

 Let the N words ai of respective probabilities p (ai). The tree is built from its N terminal vertices.

 Each terminal vertex i is assigned the probability p (ai) and will have the binary decomposition of the word a ,.

 The algorithm for constructing the tree consists in each step of summing the two lowest probabilities of the previous step to bring them together into an affected peak of the sum probability.

 In the last step, we obtain a vertex of probability 1.

 It remains to label the branches of the tree obtained by indexing by 1 the right branches of each vertex and 0 the left branches. The binary decomposition of the word ai is then obtained by descending the tree from the top of probability 1 to the vertex i.

The example explained takes the case of 4 words as shown in the figure @,

<Tb>
<tb> word <SEP> proba <SEP> encoding
<tb> a0 <SEP> p <SEP> (a0) <SEP> 111
<tb> a1 <SEP> p (a1) <SEP> 110
<tb> a2 <SEP> p <SEP> (a2) <SEP> 10
<tb> a3 <SEP> p <SEP> (a3) <SEP> 0
<Tb>

<Desc / Clms Page number 21>

critère du symbole le plus vraisemblable couramment appelé MAP 4 ax. M:n ., \0.;t..-.-r;
Algorithme de Viterbi
La recherche de la séquence la plus vraisemblable se fait avec l'algorithme de Viterbi [9] qui cherche la séquence X émise la plus probable connaissant la séquence Y reçue : max P(X/Y) (1) X
Comme la fonction logarithme est strictement croissante, il est équivalent de maximiser log P (X/Y) maxlog P(X/Y) (2)
En appliquant la loi de Bayes :
P(X/Y)P(Y) = P(Y/X)P(X) (3) le critère devient : max[log P(Y/X) + log P(X)] (4)
L'information a posteriori sur X se décompose en deux termes. Le premier log P(Y/X) concerne l'information fournie par le canal, le second log P(X) concerne l'information a priori sur la séquence émise. Decoding source of independent or Markov symbols
Two optimal structures are used for decoding an encoded sequence. Each is based on a different criterion, the criterion of the most likely sequence or the

criterion of the most likely symbol commonly called MAP 4 ax. M: n., \ 0.; t ..-.- r;
Algorithm of Viterbi
The search for the most likely sequence is done with the Viterbi algorithm [9], which looks for the most likely X sequence sent knowing the received Y sequence: max P (X / Y) (1) X
Since the logarithmic function is strictly increasing, it is equivalent to maximizing log P (X / Y) maxlog P (X / Y) (2)
By applying Bayes' law:
P (X / Y) P (Y) = P (Y / X) P (X) (3) the criterion becomes: max [log P (Y / X) + log P (X)] (4)
The posterior information on X breaks down into two terms. The first log P (Y / X) relates to the information provided by the channel, the second log P (X) relates to the information a priori on the transmitted sequence.

En ce qui concerne la probabilité a priori P(X), les deux hypothèses envisagées sont: - les mots émis par la source sont indépendants :

If the noise samples of the channel are independent then the noise law P (Y / X) is expressed as the product of the probability laws of the noises disturbing each of the words xi and yi and the transmitted bits x, and yji:

With regard to the prior probability P (X), the two hypotheses considered are: - the words emitted by the source are independent:

<Desc / Clms Page number 22>

Classiquement, le décodage suivant l'algorithme de Viterbi comprend une phase d'ACS (Add Compare Sélect) : à chaque étage et à chaque état, on additionne la métrique de la branche associée à chacune des deux séquences concurrentes, on compare les deux métriques obtenues et on sélectionne la séquence de métrique la plus faible. the words transmitted follow a first order Markov process, for example in the case of a subband image coder with regard to the DC component. We then

Classically, the decoding according to the Viterbi algorithm comprises a phase of ACS (Add Compare Select): at each stage and at each state, the metric of the branch associated with each of the two competing sequences is added, the two metrics are compared obtained and the lowest metric sequence is selected.

Le calcul de la probabilité p(xji = +1/Y) est complexe. Cette complexité peut-être réduite au prix d'une perte en performances. L'algorithme moins complexe est appelé algorithme SUBMAP [11]. MAP algorithm
Decoding according to MAP [10] is done according to the rule below:

The calculation of the probability p (xji = + 1 / Y) is complex. This complexity can be reduced at the cost of a loss in performance. The less complex algorithm is called the SUBMAP algorithm [11].

Weighting of the decoder decisions This weighting is information of reliability on the estimate made by the decoder. This "soft" information, sometimes called extrinsic information, can be used by an external decoder, a source decoder or any other device involved in the reception of the information [12].

. G-...tr ..,c v.C;', 4"lre;...) - l'algorithme SOYA [13] se base sur une légère modification de l'algorithme de
Viterbi; Coke Jeunch Raviv) - l'algorithme BCJR@[14] est établi sur le critère du MAP. Several algorithms provide weighted decisions on decoded values:

. G -... tr .., c vC; ', 4 "lre; ...) - the SOYA algorithm [13] is based on a slight modification of the algorithm of
Viterbi; Coke Jeunch Raviv) - the algorithm BCJR @ [14] is established on the criterion of MAP.

 A VLC coded source or from a channel coder may be represented by a trellis from which extrinsic information can be extracted. The invention proposes a new method for constructing such a trellis from the VLC code of the source.

<Desc / Clms Page number 23>

References [1] C. Berrou, A. Glavieux, and P. Thitimajshima. "Shannon limited error-correcting coding and decoding: Turbo-Codes". Proceedings of ICC, pages 1064-1070, May
1993.

[2] CE Shannon "A Machemaltical Theory of Communication", Volume 27. Bell System
Tech. J., 1948.

 [3] S. B. Zahir Azami. "Source / Channel joint coding, hierarchical protection". PhD thesis, ENST Paris, May 1999.

[4] N. Demir and K. Sayood. "Joint source / channel coding for variable length codes". in
Data Compression Conference (DCC), pp. 139-148, Snowbird, Utah, March 1998.

[5] AH Murad and TE Fuja. "Source-channel joint decoding of variable length encoded sources". In Information Theory Workshop (ITW), pp. 94-95, Killarney,
Ireland, June 1998.

 [6] K. P. Subbalakshmi and J. Vaisey. "Joint source-channel decoding of entropy coded markov sources over binary symmetric channels". In Proc. International Conference on Communications (ICC), 94-95, Vancouver, June 1999.

[7] J. Wien and JD Villasenor. "Utilizing soft information in decoding of variable length codes". In Data Compression Conference (DCC), Snowbird, Utah, March
1999.

[8] Y. Takishima, M. Wada, and H. Murakami. "Reversible variable length codes". IEEE
Transactions on Communications, 43: 158-162, 1995.

 [9] A. Viterbi. "Error bounds for convolutional codes and an asymptotically optimal decoding algorithm". IEEE Transactions on Information Theory, 13: 260-269, 1967.

[10] W. Koch and A. Baier. "Optimum and suboptimal detection of coded data distorted by time-varying intersymbol interference". GLOBECOM Proceedings, pp. 1679-1684, December 1990.

[11] P. Robertson, E. Villebrun, and P. Hoeher. "A comparison of optimal and sub-optimal map decoding algorithms operating in the log-domain". In Proc. International Conference on Communications (ICC), pages 1009-1013, Seattle, Washington,
June 1995.

 12] J. Hagenauer. "Soft-in / soft-out: the benefit of using soft values in all stages of digital receiver". Institute for communications technology, 1990.

<Desc / Clms Page number 24>

 [13] J. Hagenauer and P. Hoeher. "A Viterbi algorithm with soft-decision outputs and its applications". GLOBECOM Proceedings, pages 1680-1686, November 1989.

[14] LR Bahl, J. Cocke, F. Jelinek, and J. Raviv. "Optimal decoding of linear codes for minimizing symbol error rate". IEEE Transactions on Information theory, pages
284-287, March 1974.

[15] S. Benedetto and G. Montorsi. "Generalized concatenated codes with interleavers".

 In International Symposium on Turbocodes, pp. 32-39, Brest, September 1997.

[16] J. Hagenauer. "Source-controlled channel decoding". IEEE Transactions on Communications, 43: 2449-2457, September 1995.

[17] AE Escott and S. Perkins. "Binary Huffman equivalent codes with a short synchro-nizing codeword". IEEE Transactions on Information Theory, 44: 346-351, January
1998.

[18] D. A. Huffman. "Method for the reconstruction of minimum redundancy codes".

 Key Papers in The Development of Information Theory, pp. 47-50, 1952.

[19] K. Sayood and J. C. Borkenhagen. "Utilization of correlation in low rate dpcm systems for channel error protection". In Proc. International Conference on Communications (ICC), pp 1888-1892, June 1986.

Claims (19)

 1. A method of decoding received digital data corresponding to transmitted digital data encoded with the aid of an entropy code associating with each word (50 to 58) of an alphabet a distinct bit sequence, the length of which is function of the probability of occurrence of said word (50 to 58), characterized in that it implements a decoding trellis of which each transition corresponds to a binary value 0 or 1 of one of the bits of a sequence of bits corresponding to one of said words. The decoding method according to claim 1, said entropy code being represented as a binary tree comprising a root node (50), a plurality of intermediate nodes (51 to 53) and a plurality of nodes. sheets (54 to 58), a sequence of bits corresponding to one of said words being formed by considering the successive transitions of said tree from said root node to the leaf node associated with said word, characterized in that the states each stage of said lattice comprises a single state called extremal (dO), corresponding to said root node and all of said leaf nodes, and a distinct state, said intermediate state (dl to d3) for each of said n # intermediary uds. 3. decoding method according to any one of claims 1 and 2, characterized in that is associated with each transition of said trellis information likelihood. 4. decoding method according to claim 3. characterized in that said likelihood information is a metric taking into account on the one hand information representative of the transmission channel and on the other hand a binary probability a priori. 5. Decoding method according to claim 4, characterized in that for each of said transitions, the following metric is calculated:

 6. Decoding method according to any one of claims 1 to 5, <Desc / Clms Page number 26>  characterized in that said entropy code belongs to the group comprising: # Huffman codes; # reversible variable length codes. A source-channel joint decoding method of a received digital signal, the source encoding implementing an entropy code associating with each of the words (50 to 58) of an alphabet a distinct bit sequence, the length of which is function of the probability of occurrence of said word, characterized in that it implements a source decoding (42,44) using at least one decoding trellis of which each transition corresponds to a binary value 0 or 1 of one of the bits of the bit sequence corresponding to one of said words (50 to 58), said source decoding delivering extrinsic information to the channel decoding (41, 43). 8. Joint decoding method according to claim 7, characterized in that the channel decoding (42,44) implements a turbo-code type decoding. 9. Joint decoding method according to claim 8, characterized in that said turbo-code type decoding is based on a parallel-type implementation. 10. Joint decoding method according to claim 8, characterized in that said turbo-code type decoding is based on a serial type of implementation. 11. Joint decoding method according to any one of claims 7 to 10, characterized in that it is based on an iterative implementation. The method of joint decoding according to claim 11, characterized in that each of the iterations comprises sequentially a channel decoding step (41, 43) and a source decoding step (42, 44), said channel decoding step delivering information channel taken into account in said source decoding step, the latter delivering a priori information taken into account in said channel decoding step. 13. Joint decoding method according to claim 12, characterized in that it comprises: a first channel decoding step (41); <Desc / Clms Page number 27>  a first source decoding step (42), powered by said first channel decoding step; a second channel decoding step '43), fed by said first channel decoding step and said first source decoding step, via an interleaver (47) identical to the interleaver implemented at the coding, and feeding said first step channel decoding means, via a deinterleaver (48) symmetrical to said interleaver; a second source decoding step (44) fed by said second channel decoding step via said de-interleaver (48), and feeding said first channel decoding step (41). 14. A source-channel joint decoding method of a received digital signal, the source encoding implementing an entropy code associating with each of the words of an alphabet a distinct bit sequence, whose length is a function of the probability of occurrence of said word, characterized in that it implements a channel decoding trellis, similar to the channel coding trellis, in which is associated with each state of each stage information indicating the position of the bit considered in the tree representing said entropy code. 15. A method of joint decoding according to claim 14, characterized in that it comprises, for each of said states, the following steps: adding, to the two branches arriving in said state, the metric of the channel and the metric of the source; # comparison of the two new metrics obtained, and selection of the weakest metric; # if the said information designating the position indicates the end of a word, consider that the node is a leaf of the tree, if not, go to the next node in the tree. 16. Joint decoding method according to any one of claims 14 and 15, characterized in that it implements an iterative procedure. <Desc / Clms Page number 28>  17. Joint decoding method according to claim 16, characterized in that it comprises the following steps: # first channel decoding, implementing a channel decoding trellis of which each state has information indicating the position of the bit considered. in the tree representing said entropy code; second channel decoding, powered by said first channel decoding, via an interleaver identical to that implemented in coding, and feeding said first channel decoding, via a symmetrical deinterleaver of said interleaver; source decoding, powered by said second channel decoding, via said de-interleaver. 18. A digital data decoding device implementing the decoding method according to any one of claims 1 to 17. 19. System for transmitting a digital signal, characterized in that it implements, on transmission, an entropy source coding and a channel coding, and on reception, a decoding according to the method of the one any of claims 1 to 17.