WO2003023975A1

WO2003023975A1 - Method for qualifying error-correcting codes, optimization method, corresponding encoder, decoder and application

Info

Publication number: WO2003023975A1
Application number: PCT/FR2002/003057
Authority: WO
Inventors: Claude Berrou; Michel Jezequel; Catherine Douillard
Original assignee: France Telecom
Priority date: 2001-09-11
Filing date: 2002-09-09
Publication date: 2003-03-20
Also published as: FR2829636B1; FR2829636A1

Abstract

The invention concerns a method for qualifying an error-correcting code, delivering code words, each consisting at least of a symbol, the method associating with the code a first qualifying information, representing the capacity of the corresponding decoder to correct errors, obtained by using an estimation process comprising the following steps: inserting (41) a predetermined error pulse (A>error<), introducing a perturbation on a set of at least one symbol (w>i<) of a reference code word (v) previously correctly encoded; decoding (42), with a decoder with weighted inputs, the code word (w) modified by said error pulse, and analyzing the result of said decoding, delivering the first qualifying information (d>impulse, i<). The invention also concerns an optimization method, an encoder, a decoder and a corresponding application.

Description

Method for qualifying error correcting codes, optimization method, coder, decoder and corresponding application.

The field of the invention is that of the coding of digital data belonging to one or more sequences of source data intended to be transmitted, or broadcast, in particular in the presence of noises of various origins, and of the decoding of the coded data thus transmitted. .

More specifically, the invention relates to the qualification of an error correcting code, in particular in order to determine the most effective code or codes, in terms of error correction, from among a set of possible codes.

This qualification concerns in particular all the codes which can be decoded by a weighted input decoder (for example, the convolutional codes or even the concatenated codes iteratively decoded in particular the codes known under the name of “turbo-code” (registered trademark)) .

The transmission of information (data, image, speech, ...) is increasingly based on digital transmission techniques. Many efforts have been made in source coding to reduce the digital bit rate, while maintaining good quality. These techniques obviously require better protection of the binary elements from disturbances linked to transmission. The use of powerful error correcting codes in these transmission systems was essential. It is in particular for this purpose that the technique of "turbo-codes" was proposed.

The general principle of "turbo-codes" is presented in particular in French patent n ° FR-91 05280, having for title "Corrective coding method of errors with at least two parallel systematic convolutional codings, iterative decoding method, module corresponding decoding and decoder ”, and in the article by C. Berrou, A. Glavieux and P. Thitimajshima entitled“ Near Shannon limit error-correcting coding and decoding: Turbo-codes ”published in IEEE International conference on Communication, ICC'93 , vol2 / 3, pages 1064 to 1071 in May 1993. A state of the art is recalled in the article by C. Berrou and A. Glavieux "Near Optimum Error Correcting Coding and Decoding:" Turbo-Codes "(IEEE Transactions on Communications, Volume 44, n ° 10 , pages 1261-1271, October 1996). According to this technique, the implementation of a coding is proposed.

"Parallel concatenation", based on the use of at least two elementary coders. This makes it possible, during decoding, to have two redundancy symbols coming from two separate coders. Between the two elementary coders, permutation means are used, so that each of these elementary coders is supplied with the same source digital data, but taken in different orders.

A complement to this type of technique, making it possible to obtain codes called algebraic “turbo-codes”, is intended for algebraic coding (concatenated codes). This improved technique is described in the article by R. Pyndiah, A. Glavieux, A. Picart and S. Jacq "Near optimum decoding of product code" (published in IEEE Transactions on Communications, vol 46, n ° 8 pages 1003 to 1010 in August 1998), in patent FR-93 13858, having as its title "Method for transmitting bits of information by applying concatenated block codes", as well as in the article by O. Aitsab and R. Pyndiah " Performance of Reed Solomon block turbo-code ”(IEEE Globecom'96 Conference, Vol. 1/3, pages 121-125, London, November 1996).

To decode the “turbo-codes” in blocks, whether they are of the convolutional or algebraic type, it has been envisaged to use decoding means with soft inputs and outputs, that is to say an elementary decoder of codes accepts input and outputs non-binary elements, weighted according to their likelihood.

In order to optimize the choice of a code according to criteria such as, for example, the desired performance level at a given noise level, it is necessary to qualify the code. Several techniques for qualifying error correcting codes are already known, in particular by simulating performance at low error rates.

However, a disadvantage of these techniques is that they require significant computing power. Another disadvantage of these techniques is that they lead to prohibitive calculation times.

Yet another drawback of these techniques is that they do not make it possible to estimate very low error rates (for example less than 10 ^"12 ).

It is theoretically possible to estimate these performances at low error rate when the minimum distance of the code is known. Nevertheless, the evaluation of the minimum distance of a code is generally not simple, unless the number of words in the code is small enough to be able to draw up an exhaustive list. In this case, it suffices to search for the non-zero word with the lowest Hamming weight to know the minimum distance of the code. Thus, the evaluation of the minimum distance of the codes generally remains complex and no method in the state of the art makes it possible to determine the minimum distances of certain correcting codes and in particular convolutional turbo codes, quickly and / or with a power of reasonable calculation.

We know in particular in the state of the art, a document "An algorithm to compute the free distance of turbo codes" (or in French "an algorithm to calculate the free distance of turbo codes") written by R. Garello, P. Pierleoni, S. Benedetto and G. Montorsi, and published in the report “Proceedings of the International Symposium on Information Theory 2000” on page 287. This document describes in particular a method for determining the minimum distance of the convolutional turbocodes without being obliged to draw up an exhaustive list of code words. The method described in this document is relatively effective but has the drawback of being costly in computation time.

The same problems can also arise with other types of codes than "turbo-codes". The invention according to its different aspects aims in particular to overcome these drawbacks of the prior art.

More specifically, an objective of the invention is to optimize the coding with the aid of error correcting codes, in particular at low error rates; and therefore to provide such codes offering optimized efficiency, according to determined criteria.

Another objective of the invention is to provide such a technique making it possible to simply and effectively qualify error correcting codes, with reasonable computing power. Yet another objective of the invention is to provide such a technique making it possible to qualify error correcting codes in a relatively short time.

The invention also aims to provide such a technique, allowing a large quantity of codes to be compared quickly and efficiently. These objectives, as well as others which will appear subsequently, are achieved using a method for qualifying an error correcting code, delivering code words, each formed of at least one symbol, remarkable in that it associates with the code a first qualification information, representative of the capacity of a decoder corresponding to correcting errors, obtained using an estimation process implementing the following steps:

- insertion of a predetermined error pulse, introducing a perturbation on a set of at least one symbol of a reference code word previously coded without error;

- decoding, using a weighted input decoder, the code word modified by the error pulse, and analysis of the result of the decoding, delivering the first qualification information. According to a particular characteristic, the method for qualifying an error correcting code is remarkable in that the set contains a single symbol. Thus, the invention allowing in particular the determination of the first qualification information of the code is relatively simple to implement.

According to a particular characteristic, the method for qualifying an error correcting code is remarkable in that the set contains at least two symbols.

According to a particular characteristic, the method for qualifying an error correcting code is remarkable in that all the symbols of the set belong to a code word competing with the reference code word. It is noted that, by definition, a symbol belongs to a code word competing with the reference code word if its position corresponds to that of ^J a symbol which has a different value in the competing code word and the reference code word .

Thus, when the set contains at least two symbols, these symbols are preferably chosen from the symbols belonging to a code word competing with the reference code word and which is also a short distance from the reference code word. This allows the process to converge more quickly when the decoding of a code word is iterative (case in particular of the decoding of turbo-codes). In this case, it is also noted that the error pulse can be distributed uniformly or not over all or part of the set of symbols. One can in particular assign a large part of the error pulse to a particular symbol belonging to the set, called the basic symbol and the remainder of the error pulse to all or part of the other symbols of the set .

According to a particular characteristic, the method for qualifying an error correcting code is remarkable in that there is associated with the set of at least one symbol affected by the error pulse an intermediate qualification data, function of a maximum amplitude of the error pulse affecting the assembly and not disturbing the decoding of the code word, called the pulse distance. According to a particular characteristic, the method of qualifying an error correcting code is remarkable in that the estimation process is repeated at least twice introducing a perturbation on the same set of at least one symbol with amplitudes of the variable error pulse, so as to determine the pulse distance.

Thus, for each symbol of the reference code word or for selected symbols, it is possible to determine the pulse distance associated with this symbol and thus, to obtain in a reliable manner the sensitivity of this symbol to an error for the use of a given decoder . According to a particular characteristic, the method for qualifying an error correcting code is remarkable in that the pulse distance is equal to the largest integer / such that the code word affected by the error pulse of equal amplitude whole / be decoded correctly.

According to a particular characteristic, the method for qualifying an error correcting code is remarkable in that the estimation process is repeated for at least two distinct sets of symbols of the reference code word.

Thus, the invention makes it possible to simply determine the pulse distance associated with several symbols of the reference code word. According to a particular characteristic, the method for qualifying an error correcting code is remarkable in that the first qualification information is the minimum impulse distance, among the determined impulse distance (s).

Thus, the minimum impulse distance is simply determined which makes it possible to qualify the code tested very reliably.

It is noted that the properties of the code are advantageously taken into account for the symbols for which the associated pulse distance is determined in order to determine the minimum pulse distance from the code. Indeed, one can in particular take account of the periodicities of the code. We note, in particular, that for a code invariant by translation, the determination of a single distance pulse associated with any symbol of the reference code word is sufficient to determine the minimum pulse distance of the code.

According to a particular characteristic, the method for qualifying an error correcting code is remarkable in that it assigns to the code a second qualification information, representative of the number of sets most sensitive to an error pulse, in the reference code word.

According to a particular characteristic, the method for qualifying an error correcting code is remarkable in that the second qualification information, known as multiplicity, is the ratio: - of the number of sets for which the pulse distance is equal to the distance minimum impulse; on the total number of symbols in a code word. Thus, the invention makes it possible to refine the qualification of the code by taking account of the second qualification information. According to a particular characteristic, the method for qualifying an error correcting code is remarkable in that the set or sets to which the estimation process is applied is or are selected taking into account any properties of periodicity of the coded.

It is thus noted that the number of sets for which the impulse distance is equal to the minimum impulse distance is obtained by: a direct estimate when the determination of the impulse distance associated with each of the symbols capable of providing a impulse distance has been carried out equal to the minimum pulse distance; or - by extrapolation of this number of sets in view of the determination of a restricted number of minimum distances associated with a symbol, this extrapolation taking into account in particular the properties of the code (which advantageously simplifies the method). According to a particular characteristic, the method for qualifying an error correcting code is remarkable in that the reference code word is a word whose all symbols take the binary value 0.

The choice of the word “all 0” as the reference code word makes it possible in particular to have a particularly simple process to implement taking into account the linearity of the code.

According to a particular characteristic, the method for qualifying an error correcting code is remarkable in that the reference code word undergoes modulation, before the insertion of an error pulse. Thus, the invention makes it possible to obtain a qualification of the code taking into account not only the code itself and, where appropriate, the decoder but also the type of modulation used.

According to a particular characteristic, the method for qualifying an error correcting code is remarkable in that it includes a step of estimating a gain, known as asymptotic gain, representative of the effectiveness of the error correcting code relative to the absence of coding, according to at least one of the first qualification information.

According to a particular characteristic, the method for qualifying an error correcting code is remarkable in that the asymptotic gain is approached by:

Ga = 101og (Rd _min ) where: R is the efficiency of the error correcting code; d _min is the minimum impulse distance.

Thus, the invention makes it possible to assimilate the concept of minimum pulse distance from the code to the concept of free distance from the code, in particular for the concept of asymptotic gain.

We note that we can also define the asymptotic gain not only as a function of the minimum pulse distance but also of the multiplicity associated with this distance. Thus, we can get a good estimate of the performance of the code, especially in a very low noise channel.

According to a particular characteristic, the method for qualifying an error correcting code is remarkable in that it comprises the following steps: generation of the reference code word; selecting at least one set of at least one symbol of the reference code word; assignment of an error pulse of a determined amplitude to the selected set (s) to form an incorrect word;

- decoding of the wrong word, taking into account weighted entries, and delivering a decoded word; comparison of the decoded word with the initial code word. Note that the reference code word can be modulated or not. According to a particular characteristic, the method for qualifying an error correcting code is remarkable in that the amplitude of the error pulse is varied according to a determined rule, belonging to the group comprising:

a first rule according to which, during the first iteration, the amplitude of the error pulse is assigned a small value and is incremented during the following iterations until the decoded word is different from the word initial code;

a second rule according to which, during the first iteration, the amplitude of the error pulse is assigned a high value and is decremented during the following iterations until the decoded word is equal to the word of initial code;

a third rule according to which, during the first iterations, the amplitude of the error pulse is affected by two extreme values and, during the following iterations, we proceed by dichotomy, the value of the magnitude of the error being chosen as a function of the comparison sub-step; and a combination of the first and second rules with the third rule. According to a particular characteristic, the method for qualifying an error correcting code is remarkable in that the code is part of the group comprising: convolutional codes; convolutional turbo codes; - algebraic turbo codes; parallel concatenated codes; concatenated serial codes; and combinations of the preceding codes. Thus, the invention is particularly well suited to the qualification of numerous codes which are in particular used in many fields in particular in that of mobile communications, data and / or image transmission, etc.

According to a particular characteristic, the method for qualifying an error correcting code is remarkable in that it further comprises a step of determining at least one code word symbol most sensitive to errors.

According to a particular characteristic, the method of qualifying an error correcting code is remarkable in that it further comprises a step of comparing the sensitivity of the code word symbols to errors and of constructing a unevenly protected code depending on the result of the comparison step.

The invention also relates to a method for optimizing a channel coding, remarkable in that it implements the method for qualifying an error correcting code on at least two candidate codes and a selection step. for channel coding of one of the candidate codes, based on an analysis of the first qualification information assigned to each of the candidate codes.

According to a particular characteristic, the method of optimizing a channel coding is remarkable in that each of the codes is associated with a predetermined modulation, and in that the selection step takes account of the code / modulation association.

According to a particular characteristic, the method for optimizing a channel coding is remarkable in that the selection step also takes account of the second qualification information and / or of the asymptotic gain. The invention also relates to an encoder for correcting errors, remarkable in that the corresponding code is selected according to a code qualification method and / or a method for optimizing channel coding as previously described.

The invention further relates to a decoder allowing a decoding of coded data using an error correcting code and a corresponding error correction, remarkable in that the error correcting code is selected according to a method of qualification of codes and / or optimization of channel coding as previously described.

Thus, the coders and the decoders are based on a very efficient code and make it possible to obtain good performances in particular under conditions of weakly noisy transmission channel and can be implemented advantageously in varied applications in particular in the field of mobile communications. , data and / or image transmission, ....

The invention also relates to an application of the method for qualifying an error correcting code and / or the method for optimizing a channel coding to:

- data transmission over a noisy channel; l Optimized channel coding with uneven protection;

- the estimation of the free distance of a code; and / or - the estimation of the performance of a code. The advantages of a method for optimizing a channel coding and of the applications of the qualification and / or optimization methods are the same as those of the qualification method of an error correcting code, they are not described in more detail. . Other characteristics and advantages of the invention will appear more clearly on reading the following description of a preferred embodiment, given by way of simple illustrative and nonlimiting example, and of the appended drawings, among which:

- Figure 1 shows error rate curves known per se; FIG. 2 illustrates an algorithm for estimating the minimum distance of an error correcting code, according to the invention;

- Figure 3 describes a step of generating a sequence of symbols, implemented in the algorithm of Figure 2; and

FIG. 4 describes a step of calculating pulse distance, implemented in the algorithm of FIG. 2.

It will be recalled that an optimal decoding procedure would lead to choosing the code word closest to the received word. The greater the distance between code words, the more efficient the decoding can be at low error rates. The minimum Hamming distance between these words, which is the minimum number of different binary values, in these words is called the "minimum code distance". It is noted d _min . The determination of this distance makes it possible to estimate the performance of the code for low error rates. This estimation avoids long and costly simulations.

FIG. 1 illustrates three bit error rate curves, BER, represented on the ordinate axis 11, as a function of the signal to noise ratio, Eb / No, represented on the abscissa axis 10:

- a first non-coded curve, 12, is obtained for a transmission of binary data using QPSK modulation without the use of error codes; a second curve 13 is obtained for a transmission of binary data with the use of an error correcting code (it is noted that this curve allows a gain, G, of several decibels, for example, for a bit error rate of around 10 ^"6 ); and - a third curve represents the theoretical limit which can be obtained using an ideal code associated with an ideal decoding algorithm; this limit is a function of the yield, R, of the code (which is the ratio of the number of non-coded bits to the number of coded bits) and of the size of the block The lower the error rate at a given signal-to-noise ratio, the greater the difference between these curves.

It is possible to demonstrate that there is a link between the minimum distance of the code and the maximum gain obtained by it. This gain is called “asymptotic gain”, Ga, measured in decibels, and we can write as a first approximation the following relation: Ga # 101og (R. _M „) -

So, for example, a performance code, R, equal to 1/2 capable of working around the theoretical limit for a bit error rate of 10 ^"8 must have a minimum distance of about 32.

According to the state of the art, the estimation of the minimum distance of a code has always been associated with a more or less exhaustive search for code words by using certain properties to avoid unnecessary calculations as much as possible.

The general principle of the invention is based on the decoding algorithm associated with the code and not on the use of the properties of the code.

Thus, according to the invention, the limitations of the decoder are taken into account. The information extracted from it is not, in the usual sense, the minimum distance of the code, d _min , but a quantity, called "pulse distance from the code", ^ i _mpulse> representative of the correction power of the code and of the associated decoder. One can check that for many linear codes, the impulse distance of the code of _impulse is equal to the distance of the code, d ^. According to a variant of the invention, the multiplicity, m, associated with the distance from the code, that is to say the ratio of the number of symbols with which the pulse distance from the code, d _min , is associated over the distance, is also determined. total number of symbols in a word. Taking into account the multiplicity makes it possible in particular to more finely estimate the asymptotic gain or to provide for unequal protection of the symbols to be coded.

FIG. 2 illustrates an algorithm for estimating the minimum distance of an error correcting code, according to the invention.

During a first initialization step 20, the different variables used by the algorithm are initialized.

Then, during a step 21, the coding and modulation parameters are initialized by defining in particular: the code for which the free distance is to be estimated (for example, elementary codes and interleaving for turbo codes, punching pattern, etc. .) producing code words of length n (ie k binary information values and (nk) binary redundancy values); and the associated modulation (for example, BPSK, QPSK, FSK, ...).

Then, during a step 22, an initial code word is generated (as a function of the code defined during step 21) which for a linear code contains only "0". This code word is then modulated (according to the modulation defined in step 21) to produce a sequence (vj, v ₂ , .... v _n ). For binary modulation, a value symbol "-1" is associated with each "0" sent by the encoder

(symbols “+1” would be associated with “1” emitted by the coder). It is noted that this succession of symbols equal to “-1” was transmitted to the decoder corresponding to the chosen code, it would converge without any difficulty towards the word “all 0” containing k zero binary values. We also note that the step

22 is illustrated in more detail with reference to FIG. 3.

Then, during a step 23, we initialize a variable i to 1. Then, during a step 24, a pulse distance is determined, d _mptdse, ι associated with an error injected into the t ^th symbol of the sequence (v _x , v ₂ , .... v „). Thus, we transform the ^th symbol of the sequence (v _{l 5} v ₂ , .... v „) into a symbol with a positive value. The amplitude of this error is increased until the decoder does not converge on the word "all 0". The encoder / decoder association is then faulted.

By applying this method, the capacity for correcting the code is not evaluated on errors distributed over the word presented to the decoder (according to techniques known per se) but on a single symbol. Experience shows that the ability to correct remains the same.

The minimum value of the pulse which does not fault the correction system is directly linked to the pulse distance, d _impulsei , associated with the binary value affected by the error. The pulse distance, d _impulseιi , is thus determined and saved. It is also noted that step 24 is illustrated in more detail with reference to FIG. 4.

Then, during a test 25, it is determined whether the value of i is equal to k.

If not, during a step 26, the value of i is incremented by one and step 24 is repeated. We note that thus, the impulse distance associated with each of the k information symbols of the sequence is determined (vj, v ₂ , .... Vj).

According to a variant of test 25 and of step 26, the impulse distance associated with each symbol belonging to a sub-sequence of the sequence (v ₁ , v ₂ , ..-. V *) is determined, this sub-sequence containing a number of symbols strictly less than k. This variant is advantageously implemented when, in particular, the error correcting code has properties of periodicity which are such that many positions of information symbols in the sequence (v _x , v ₂ , .... v _k ) correspond to the same impulse distance and that the subset is chosen according to these properties. We note that in the in the case of convolutional turbo codes, these intervals depend on the interleaving function and the possible punching pattern.

If the test result is positive, during a step 27, the minimum pulse distance of the code is determined by retaining the smallest of the pulse distances associated with the binary values examined and determined during step 24.

Alternatively, during step 27, the multiplicity, m, also associated with the minimum pulse distance is determined. The multiplicity, m, is, by definition, the ratio of the number of symbols with which the pulse distance of the code, d _min , is associated to the total number of symbols in a word.

We note that the number of errors that can be corrected by a code with a minimum distance d _min is strictly less than d _mi J2 errors. Let A _{eneur be} the amplitude of the error pulse added to the nominal value -1 (the amplitude of the symbol applied to the input of the decoder A is therefore equal to A _error - 1). A full bit error corresponds to an error pulse of amplitude 2 (change from -1 to +1). The number of binary errors equivalent to an amplitude A _e „ _eur is therefore equal to A _emι 2.

If the error pulse is corrected, then the number e is strictly less than d _m 2. Thus, by assimilating exactly minimum distance and pulse distance, A _errmr is strictly less than d _min and d _impulse .

Then, during a step 28, it is determined whether it is necessary to determine the minimum impulse distance associated with the new code.

If so, step 21 is repeated.

If not, during a step 29, a code is chosen as a function of its minimum pulse distance.

According to a variant, during step 29, other parameters such as, for example, the multiplicity associated with the minimum pulse distance of the code and / or the complexity of the code are also taken into account for the choice code. FIG. 3 describes the step 22 of generating a sequence of symbols, illustrated with reference to FIG. 2.

It is assumed that the code whose parameters were initialized during step 21 is a linear code suitable for the transmission of packets, associating k bits of useful information with words of n bits after coding (the yield, R, of the code being equal to the ratio k / n).

During a step 30, the word “all 0” is translated into the code studied. The code being linear, the n bits of the code word (u _x , u ₂ , ... u _n ) are all zero. (Here, the choice of the word "all 0" responds to a concern for simplicity: since the information message is "all 0", the code being linear, the redundancy is "all 0" too and we do not have to worry about coding, in other words, according to a variant of step 30, you can choose a code word different from the word "all 0").

Then, during a step 31, the symbols are defined as they would have been emitted by a NRZ modulator (or “No Return to Zero”). Thus, during step 31, we associate:

- a symbol “-1” for each binary value of the code word (u _λ , u ₂ , ... u _n ) equal to 0; and

- a symbol “+1” for each binary value of the code word (uu ₂ , ... ι equal ai; We thus form a sequence of symbols (v _{l 5} v ₂ , ... v _n ) corresponding to the word of modulated code (uu ₂ , ... u _n ).

After step 31, step 23 illustrated with reference to FIG. 2 is carried out. FIG. 4 describes the step 24 for calculating pulse distance, illustrated with reference to FIG. 2. During a step 40, one initializes:

- a variable J with a value equal to 2; and a sequence w of symbols equal to the sequence v. According to a variant, the variable / is initialized to a value greater than 2, as a function of a lower bound (a priori known) of the minimum pulse distance. Then, during a step 41, an error, A _error , is initialized to a value equal to J-ε, where ε is any real number, between 0 and 1 strictly (ε is equal, for example, to 0.5); thus, the error, A _error , is equal to a value strictly between (Jl) and J. During step 41, we select the i ^th symbol of w, w, which we assign to the value A _error minus the value of v _{ or A _error -1 (i being the parameter initialized during step 23 and updated during step 26).

Then, during a step 42, the sequence w is decoded with a decoding algorithm adapted to the code chosen during step 21 and able to take into account the amplitudes of the symbols to be decoded (the decoder has weighted inputs) . If the code is of turbo code type, the decoding algorithm will be, for example, an iterative decoding algorithm as described in the patents

EP0511141 (whose title is “Error correcting coding method with at least two systematic convolutional codings in parallel, iterative decoding method, corresponding decoding module and decoder”) or EP735696 (whose title is

"Iterative decoding method, decoding module and corresponding decoder").

The number of iterations required depends on the distance to be determined. The greater the distance, the more iterations are required. The number of iterations can be several hundred. The results obtained are very dependent on the quality of the decoding. The soft input and output algorithm must be able to operate without knowing the variance. One can in particular use elementary decoding algorithms of the type:

- Max-Log-MAP (SUB-MAP) described in particular in the document by P. Robertson, P. Hoeher and E. Villebrun, "Optimal and suboptimal maximum a posteriori algorifhms suitable for turbo decoding", published in the journal European Trans. Telecommun., Vol. 8, pp. 119-125, March-Apr. 1997, the Max-Log-MAP algorithm being derived from the MAP algorithm described in the document by LR Bahl, J. Cocke, F. Jelinek and J. Raviv "Optimal decoding of linear codes for minimizing symbol error rate ", published in the journal IEEE Trans. Inform. Theory, IT-20, pp. 248-287, Mar. 1974.) or - SOVA (" Viterbi algorithm with soft outputs "from English" Soft Output Viterbi Algorithm ”) described in particular in the articles: by G. Battail," Weighting of symbols decoded by Viterbi's algorithm ", in the journal Ann. Télécommun., Fr., 42, N ° 1-2, pp. 31-38, in January 1987; by J. Hagenauer and P. Hoeher, "A Viterbi algorithm with soft- decision outputs and its applications", in the conference proceedings Proc. Of Globecom '89, Dallas, Texas, pp . 47.11-

47-17, in November 1989 and by C. Berrou, P. Adde, E. Angui and S. Faudeil, "A low complexity soft-output Viterbi décoder architecture", ", in the conference proceedings Proc. Of ICC '93, Geneva, pp. 737-740, in May 1993. which do not require knowledge of the variance. It can be shown that the ideal decoder for the proposed invention would be a decoder based on the search for the minimal scalar product .

Then, during a test 43, it is determined whether the decoding algorithm converges towards the word "all 0".

If so, the limit is not exceeded and during a step 45, the variable / is incremented by one and step 41 is repeated.

According to a variant of step 45, when the modulation used is such that the protection of the binary values is uneven, the minimum equivalent distance of the coding-modulation pair, particular to each binary value, is itself unequal and is generally not not an integer value. In this case, during step 45, the variable / is incremented by a value strictly less than 1, in order to determine an actual pulse distance.

According to a variant of step 24, the variable / is assigned a value corresponding to an upper limit of the pulse distance increased by 1 during step 40. Step 43 is followed by step 44 if the decoded word is equal to the initial code word, the pulse distance is then assigned the value of J. Step 43 is followed by step 45 if the decoded word is not equal to the initial code word, and j is decremented during step 45. According to yet another variant of step 24, we proceed by dichotomy:

- during the first iteration, the variable J is initialized with a value corresponding to a lower bound, Jmin, of the pulse distance; then

- during a second iteration, the variable J is initialized with a value corresponding to an upper bound, Jmax, of the pulse distance increased by 1; then

- during the following iterations, we assign to J a value equal to half the sum of Jmin and Jmax and, at the end of test 43: if the decoded word is equal to the initial word, we assign to Jmax the value of / current; and if the decoded word is not equal to the initial word, the value of / current is assigned to Jmin. According to this last variant, the iterations are stopped when the difference between the values of Jmin and Jmax is sufficiently small. It is noted that this variant based on a priori knowledge of a framework for / and the use of the dichotomy method is particularly advantageous when the protection of the symbols of a code word is uneven.

If the result of test 43 is negative, the decoding algorithm does not converge on the word "all 0" and the amplitude of the error pulse is sufficient to disturb the decoding. In this case, during a step 44, the value of the impulse distance, of _{impulse i} associated with an error injected into the i * ™ "symbol of the sequence (v _x , v ₂ , .... v _n ) is equal to the current value of J minus 1. Indeed, the current value of A _error is J-ε and as A _error is strictly less than the impulse distance and as the current value of J is the minimum value which leads to a decoding error, we can establish: J - ε>d; _{mpulse i} > J 1- ε let again: d _impulse _:, + ε> J - 1> d _{impulse: i} ~ l + ε

(Jl) and d _impulseti being integers, we deduce their equality.

After step 44, the test 25 illustrated with reference to FIG. 2 is carried out. Of course, the invention is not limited to the embodiments mentioned above.

In particular, the person skilled in the art can make any variant in the parameters to be considered for the choice of a code. A person skilled in the art will in particular be able to take into account the frame error rate, FER, (or “Frame Error Rate” in English) estimated according to the following relationship:

FER = - Erfci \ R.d „

'N „or:

- m represents the multiplicity associated with the pulse distance of the code; - k, the number of information bits of a code word;

- E _b / N ₀ , the signal to noise ratio;

- R, the yield of the code;

- d _min , the pulse distance of the code; and

Erfc, the complementary error function, well known according to the relation:

2 ^∞ Erfc (x) = -r = f exp (-t ² ) dt

By difference with the uncoded curve, we can deduce an approximate formula of the asymptotic gain, following, for example, the relation:

Gα # 101og (R,. Note that the invention is not limited to the estimation of a minimum distance, but also makes it possible to determine the most sensitive symbols and therefore to propose coding schemes with multi-level protections. uneven levels or coding performance. In addition, according to the invention, when the pulse distance of the code is determined, the error can be distributed over several symbols, provided that it is certain that these symbols will all belong to a selected competing code word (which means that these symbols are chosen at positions where the symbols of the reference code word and the positions of the competing code word differ), in the event of a decoder failure. Preferably, the error pulse will be carried on competing code words which are a short distance from the reference code word. This is the case, for example, if the error pulse is distributed over an information symbol and the corresponding redundancy symbol, which is written as the sum (modulo 2) of the information symbol and other information (the state of the coder for a convolutional code, for example). Thus, if the information bit changes, so does the redundancy bit and these two bits are part of the concurrent code word.

Generally, the distribution of the error pulse is preferably done by considering a "base" which is the symbol to be tested. This symbol receives a fraction of the error pulse and other symbols, possibly the remainder. It will thus be possible to determine the impulse distance associated with each basic symbol tested. We note that thus, when we distribute the error over several symbols, the multiplicity, m, is then, the ratio of the number of basic symbols with which is associated the pulse distance of the code, d _min , over the total number of symbols in a word.

It is also noted that the invention also makes it possible to determine the processing of codes with an infinite message. In this case, we consider a message long enough to avoid edge problems (start and end of message) and we only look for the distances on the symbols far enough away from the start and end of the message.

We also note that the invention is applicable not only to convolutional turbocodes (parallel concatenation) but is also applicable to simple convolutional codes or to codes constructed from a serial concatenation, and more generally to all the codes from which the decoder can draw. profit samples weighted input (in English "soft input"), especially those using the Viterbi algorithm or the MAP algorithm (from English "Maximum a Posteriori") or its simplified versions.

It should be noted that the invention is not limited to a purely material implantation but that it can also be implemented in the form of a sequence of instructions of a computer program or any form mixing a material part and a part. software. In the case where the invention is implemented partially or completely in software form, the corresponding sequence of instructions may be stored in a removable storage means (such as for example a floppy disk, a CD-ROM or a DVD-ROM) or no, this storage means being partially or totally readable by a computer or a microprocessor.

It should also be noted that the invention is not limited to the methods for qualifying or optimizing code described above but extends to the codes obtained by at least one of these methods, to the coder (respectively to the decoder) allowing to code (respectively decode) data according to this code.

Claims

1. Method for qualifying an error correcting code, delivering code words, each formed of at least one symbol,

5 characterized in that it associates with said code a first qualification item of information, representative of the capacity of a decoder corresponding to correcting errors, obtained using an estimation process implementing the following steps:

- insertion (41) of a predetermined error pulse (A _eιτeuτ ), 10 introducing a disturbance on a set of at least one symbol

(w,) a reference code word (v) previously coded without error;

- decoding (42), using a weighted input decoder, of the code word modified (w) by said error pulse, and analysis of the result of said decoding, delivering said first qualification information

^ \ "impulse, i / *

2. Method for qualifying an error correcting code according to claim 1, characterized in that said set contains a single symbol.

3. Method for qualifying an error correcting code according to claim 1, characterized in that said set contains at least two 0 symbols.

4. Method for qualifying an error correcting code according to claim 3, characterized in that all the symbols of said set belong to a code word competing with said reference code word.

5. Method for qualifying an error correcting code according to any one of claims 1 to 5, characterized in that an intermediate datum associated with said set of at least one symbol affected by said error pulse qualification, function of a maximum amplitude of said error pulse affecting said set and not disturbing the decoding of the code word, called pulse distance.

6. Method for qualifying an error correcting code according to claim 5, characterized in that said estimation process is repeated (26) at least twice introducing a disturbance on the same set of at least one symbol with amplitudes of said variable error pulse, so as to determine said pulse distance.

7. Method for qualifying an error correcting code according to any one of claims 5 and 6, characterized in that said pulse distance is equal to the largest integer J such that said code word containing said affected set of said error pulse of amplitude equal to said integer J is decoded correctly.

8. Method for qualifying an error correcting code according to any one of claims 5 to 7, characterized in that said estimation process is repeated (28) for at least two distinct sets of symbols of said code word reference.

9. Method for qualifying an error correcting code according to any one of claims 5 to 8, characterized in that said first qualification information is the minimum impulse distance (d ^^), among the impulse distance (s) determined.

10. Method for qualifying an error correcting code according to any one of claims 5 to 9, characterized in that it assigns (27) to said code a second qualification information (m), representative of the number of said sets the most sensitive to an error pulse, in said reference code word.

11. Method for qualifying an error correcting code according to claims 9 and 10, characterized in that said second qualification information, known as multiplicity, is the ratio:

- the number of said sets for which said pulse distance is equal to said minimum pulse distance;

- on the total number (n) of symbols in a code word.

12. Method for qualifying an error correcting code according to any one of claims 1 to 11, characterized in that said assembly or said assemblies according to claim 8 on which or which is applied said estimation process is or are selected taking into account any periodicity properties of said code.

13. Method for qualifying an error correcting code according to any one of claims 1 to 12, characterized in that said reference code word is a word in which all of said symbols take the binary value 0.

14. Method for qualifying an error correcting code according to any one of claims 1 to 13, characterized in that said reference code word undergoes modulation (31), before said insertion of a pulse of fault.

15. Method for qualifying an error correcting code according to any one of claims 1 to 14, characterized in that it comprises a step of estimating a gain, called asymptotic gain (Ga), representative of the effectiveness of said error correcting code with respect to the absence of coding, as a function of said first qualification information.

16. Method for qualifying an error correcting code according to claim 15, characterized in that said asymptotic gain is approximated by: Ga = 101og (Rd _min ) where: R is the yield of said error correcting code; d _min is the minimum pulse distance, as defined in claim 9.

17. Method for qualifying an error correcting code according to any one of claims 1 to 16, characterized in that it comprises the following steps: generation and modulation (22) of said reference code word; - selection (23,26) of at least one set of at least one symbol of said reference code word; assignment (41) of an error pulse of a determined amplitude to said set (s) selected to form an incorrect word; decoding (42) said erroneous word, taking into account weighted entries, and delivering a decoded word; comparing said decoded word with said initial code word.

18. Method for qualifying an error correcting code according to any one of claims 1 to 17, characterized in that the amplitude of said error pulse is varied according to a determined rule, belonging to the group comprising :

a first rule according to which, during the first iteration, the amplitude of said error pulse is assigned a small value and is incremented during the following iterations until said decoded word is different from said code word initial; a second rule according to which, during the first iteration, the amplitude of said error pulse is assigned a high value and is decremented during the following iterations until said decoded word is equal to said code word initial;

a third rule according to which, during the first iterations, the amplitude of said error pulse is affected by two extreme values and, during the following iterations, one proceeds by dichotomy, the value of the amplitude of said error being chosen according to said comparison sub-step; and a combination of said first and second rules with said third rule.

19. Method for qualifying an error correcting code according to any one of claims 1 to 18, characterized in that said code is part of the group comprising: convolutional codes; - convolutional turbo codes; algebraic turbo codes; parallel concatenated codes; concatenated serial codes; and combinations of the preceding codes.

20. Method for qualifying an error correcting code according to any one of claims 1 to 19, characterized in that it further comprises a step of determining at least one code word symbol the more susceptible to errors.

21. Method for qualifying an error correcting code according to any one of claims 1 to 20, characterized in that it further comprises a step of comparing the sensitivity of the code word symbols to errors and constructing an unevenly protected code as a function of the result of said comparison step.

22. Method for optimizing a channel coding, characterized in that it implements the method for qualifying an error correcting code according to any one of claims 1 to 21 on at least two candidate codes and a step of selecting for said channel coding one of said candidate codes, as a function of an analysis of said first qualification information assigned to each of said candidate codes.

23. A method of optimizing a channel coding according to claim 22, characterized in that each of said codes is associated with a predetermined modulation, and in that said selection step takes account of the code / modulation association.

24. Method for optimizing a channel coding according to any one of claims 22 and 23, characterized in that said selection step also takes account of said second qualification information according to any one of claims 10 and 11 and / or said asymptotic gain according to any one of claims 15 and 16.

25. Encoder for correcting errors, characterized in that the corresponding code is selected according to a qualification process according to one any of claims 1 to 21 and / or according to a method of optimizing channel coding according to any of claims 22 to 24.

26. Decoder allowing a decoding of coded data using an error correcting code and a corresponding error correction, characterized in that said error correcting code is selected according to any one of claims 1 to 21 and / or according to a method for optimizing a channel coding according to any one of claims 22 to 24.

27. Application of the method for qualifying an error correcting code according to any one of claims 1 to 21 and / or the method for optimizing a channel coding according to any one of claims 22 to 24, characterized in that said application belongs to the group comprising:

- data transmission over a noisy channel;

- optimization of channel coding with uneven protection;

- the estimation of the free distance of a code; and - the estimation of the performance of a code.