FR2829636A1 - Method for qualifying the error-correcting codes, optimization method, coder, decoder, and the corresponding application - Google Patents

Abstract

The qualification method delivering the code words each formed of at least one symbol associates with the code an information of qualification representative of the capacity of a corresponding decoder to correct the errors, which is obtained by an estimation process comprised in the determination of a pulse distance (d) in block (24), and includes two substeps: (i) the insertion of a predetermined error pulse which introduces a perturbation on a set of at least one symbol of a reference code word preliminary coded without error, and (ii) the decoding of the code word modified by the error pulse by use of a weighted-inputs decoder and analysis of the decoding result which delivers the information of qualification. The set contains one symbol, or at least two symbols belonging to a code word concurrent with the reference code word. The qualification method associates the set of at least one symbol affected by the error pulse with an intermediary datum of qualification, where the function of maximum amplitude of the error pulse does not perturb the decoding of the code word. The estimation process is repeated by incrementing the index in block (26) at least two times thus introducing a perturbation on the same set with variable amplitudes of the error pulse so to determine the pulse distance. The estimation process is repeated in a test block (28) for at least two distinct sets of symbols of the reference code word. The information of qualification is the minimum pulse distance (d) found among the determined pulse distances. The multiplicity (m) representative of the number of sets more sensitive to the error pulse is determined in block (27) as the second information of qualification, in addition to the minimum pulse distance. The sets are selected to take into account eventual periodicity of the code. The reference code word is a word whose all symbols take binary 0 value. The reference code word is subjected to a modulation in block (22) before the error pulse is inserted. The qualification method comprises a step of estimating asymptotic gain representative of the efficiency of the error-correcting code with respect to the absence of coding. The reference code word is generated and modulated in block (22), and at least one set of at least one symbol of the reference code word is selected by blocks (23,26) by setting and incrementing the index (i). The amplitude of the error pulse is varied according to a determined rule. The code belongs to a group comprising convolutional codes, convolutional turbo-codes, algebraic turbo-codes, parallel concatenated codes, serial concatenated codes, convolutional turbo-codes, algebraic method for optimizing a channel coding implements the method for qualifying an error-correcting code on at least two candidate codes and a step for selecting of the candidate codes by analyzing the information of qualification. The coder allows the correction of errors, and the decoder allows the decoding of data coded by an error-correcting code and a corresponding error correction. The application of the qualification method belongs to a group comprising the transmission of data in a noisy channel, the optimization of the coding channel with unequal protection, the estimation of the free distance of a code, and the estimation of code performance.

Description

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

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

 More specifically, the invention relates to the qualification of an error correction code, in particular to determine the most effective code (s), in terms of error correction, among a set of possible codes.

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

 The transmission of information (data, image, speech, ...) relies more and more 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 a better protection of the bits with respect to the disturbances related to the transmission. The use of strong error-correcting codes in these transmission systems was essential. It is for this purpose that the turbo-code technique has been proposed.

 The general principle of turbo-codes is in particular presented in French patent FR-91 05280, entitled Error correction coding method to at least two systematic parallel convolutional encodings, iterative decoding method, corresponding decoding module and decoder and in the article by C. Berrou, A. Glavieux and P. Thitimajshima entitled "Near Shannon Limitless Error-Correcting Coding and Decoding: Turbo-codes" published in IEEE International Conference on Communication, ICC'93, vol2 / 3, pages 1064 at 1071

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 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, No. 10, pages 1261- 1271, October 1996).

 According to this technique, it is proposed to implement a parallel concatenation coding, based on the use of at least two elementary coders. This makes it possible, during decoding, to have two redundancy symbols from two different coders. Between the two elementary coders, means of permutation are implemented, so that each of these elementary coders is fed by the same source digital data, but taken in different orders.

 A complement to this type of technique, which makes 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 product code (published in IEEE Transactions on Communications, vol 46, n 8 pages 1003 to 1010 in August 1998), in patent FR-93 13858, entitled Process for transmit 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. 121-125, London, November 1996).

 To decode the turbo-codes in blocks whether of the (involutional or algebraic) type, it has been envisaged to use means of decoding with soft inputs and outputs, that is to say that an elementary decoder of codes accepts at the 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 level of performance sought at a given noise level, it is necessary to qualify the code.

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 Several techniques for qualifying error-correcting codes are already known, in particular by simulations of 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.

 Another disadvantage 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 low error rate performance when the minimum code distance is known. Nevertheless, the evaluation of the minimum distance of a code is generally not simple, unless the number of words of the code is small enough to be able to draw up an exhaustive list. In this case, it is sufficient to search for the non-zero word of 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.

calcul. In the state of the art, a document known as An algorithm to compute the free distance of turbo codes (or in French an algorithm for calculating the free distance of turbo codes) written by R. Garello, P. Pierleoni, S. Benedetto and G. Montorsi, and published in the proceedings 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 convolutional turbocodes without having to compile an exhaustive list. code words. The method described in this document is relatively effective but has the disadvantage of being expensive in terms of

calculation.

 The same problems can also arise with other types of codes than turbo codes.

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 The invention in its various aspects is intended to overcome these disadvantages of the prior art.

 More specifically, an object of the invention is to optimize the coding using error correcting codes, especially at low error rates; and therefore to provide such codes offering optimized efficiency, according to certain criteria.

 Another object of the invention is to provide such a technique for simply and efficiently qualify error correcting codes, with reasonable computing power.

 Yet another object of the invention is to provide such a technique for qualifying error correcting codes in a relatively short time.

 The invention also aims to provide such a technique, to compare efficiently and quickly a large amount of codes.

These objectives, as well as others which will appear later, are achieved by means of a process for qualifying an error correction 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 by means of an estimation process implementing the following steps: - insertion a predetermined error pulse, introducing a disturbance on a set of at least one symbol of a reference codeword previously coded without error; decoding, using a weighted input decoder, the code word modified by the error pulse, and analyzing the decoding result, delivering the first qualification information.

According to a particular characteristic, the method of qualifying an error correction code is remarkable in that the set contains a single symbol.

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 Thus, the invention allowing in particular the determination of the first code qualification information is relatively simple to put in cavern.

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

 According to one particular characteristic, the method for qualifying an error correction code is remarkable in that all the symbols of the set belong to a codeword that is concurrent with the reference code word.

 Note that, by definition, a symbol belongs to a code word competing with the reference code word if its position corresponds to that of a symbol that 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 among the symbols belonging to a code word that is concurrent with the reference codeword and which is also at a small distance from the reference code word. This allows the process to converge more quickly when the decoding of a codeword is iterative (in particular the decoding of turbo codes). In this case, it is also noted that the error pulse can be evenly distributed over all or part of the set of symbols.

In particular, it is possible to assign a large part of the error pulse to a particular symbol belonging to the set, said base symbol and the remainder of the error pulse to all or some of the other symbols of the set.

 According to one particular characteristic, the method for qualifying an error correction code is remarkable in that the set of at least one symbol affected by the error pulse is associated with an intermediate data item of qualification, a function a maximum amplitude of the error pulse affecting the assembly and not disturbing the decoding of the code word, said impulse distance.

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 According to a particular characteristic, the method for qualifying an error correction 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 impulse 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 reliably obtain the sensitivity of this symbol to an error for use of a given decoder. .

 According to a particular characteristic, the method for qualifying an error correction code is remarkable in that the pulse distance is equal to the largest integer J such that the assigned code word of the equal amplitude error pulse to the integer J be decoded correctly.

 According to a particular characteristic, the method for qualifying an error correction 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 correction code is remarkable in that the first qualification information is the minimum impulse distance, among the determined impulse distance or distances.

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

 It should be noted that the properties of the code for the symbols of which the associated pulse distance is determined in order to determine the minimum impulse distance of the code are advantageously taken into account. Indeed, it is possible to take into account the periodicity of the code. We note, in particular, that for a translation invariant code, the determination of a single distance

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 The pulse associated with any symbol of the reference code word is sufficient to determine the minimum pulse distance of the code.

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

 According to one particular characteristic, the method for qualifying an error correction code is remarkable in that the second qualification information, called multiplicity, is the ratio of: - the number of sets for which the pulse distance is equal to the distance minimal 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 into account the second qualification information.

 According to one particular characteristic, the method for qualifying an error correction code is remarkable in that the set or sets on which the estimation process is applied is or are selected taking into account any periodic properties of the code.

 It is thus noted that the number of sets for which the pulse distance is equal to the minimum impulse distance is obtained by: a direct estimation when the determination of the pulse distance associated with each of the symbols capable of providing a distance has been made; impulse equal to the minimum impulse distance; or - by extrapolation of this number of sets in view of the determination of a limited 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).

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 According to one particular characteristic, the method for qualifying an error correction code is remarkable in that the reference code word is a word whose symbols all take the binary value 0.

 The choice of the word all O as a reference code word allows 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 correction code is remarkable in that the reference code word undergoes a 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, if necessary, the decoder but also the type of modulation used.

 According to one particular characteristic, the method for qualifying an error correction code is remarkable in that it comprises a step of estimating a gain, said asymptotic gain, representative of the effectiveness of the error correction 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 correction code is remarkable in that the asymptotic gain is approximated by: Ga = 101og (R.) where: R is the efficiency of the error correction code; dmin is the minimum impulse distance.

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

 We note that we can also define the asymptotic gain not only as a function of the minimum impulse distance but also of the multiplicity associated with this distance.

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 Thus, a good estimate of the performance of the code can be obtained in particular in a very slightly noisy channel.

According to one particular characteristic, the method for qualifying an error correction 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; assigning an error pulse of a given amplitude to the selected set (s) to form an erroneous word; decoding of the erroneous word, taking into account weighted inputs, 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 one particular characteristic, the method for qualifying an error correction 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 wherein, during the first iteration, the amplitude of the error pulse is assigned a small value and is incremented in subsequent iterations until the decoded word is different from the original code word; 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, one proceeds by dichotomy, the

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 value of the magnitude of the error being chosen according to 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 correction code is remarkable in that the code is part of the group comprising: - convolutional codes; convolutive turbo codes; algebraic turbo codes; concatenated parallel codes; - serial concatenated codes; and - combinations of the preceding codes.

 Thus, the invention is particularly well suited to the qualification of numerous codes which are used in many fields, in particular in the field of mobile communications, data transmission and / or images, etc.

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

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

 The invention also relates to a method of optimizing a channel coding, remarkable in that it implements the method of qualifying an error correction code on at least two candidate codes of a selection step

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 for the 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 into account the code / modulation association.

 According to one particular characteristic, the method for optimizing a channel coding is remarkable in that the selection step also takes into account the second qualification information and / or the asymptotic gain.

 The invention also relates to an encoder for error correction, which is remarkable in that the corresponding code is selected according to a code qualification method and / or a method for optimizing a channel coding as previously described.

 The invention further relates to a decoder for decoding encoded data using error correction code and corresponding error correction, wherein the error correction code is selected according to a method of qualification of codes and / or optimization of a 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 advantageously be implemented in copper in various applications, particularly in the field of mobile communications. , data transmission and / or images, ....

 The invention also relates to an application of the method for qualifying an error correction code and / or the method of optimizing a channel coding to the transmission of data over a noisy channel; channel coding optimization with unequal protection; - estimation of the free distance of a code; and / or - estimation of the performance of a code.

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The advantages of a method for optimizing a channel coding and applications of the qualification and / or optimization methods are the same as those of the method for qualifying an error correction code, they are not detailed further.
Other features and advantages of the invention will appear more clearly on reading the following description of a preferred embodiment, given as a simple illustrative and nonlimiting example, and the appended drawings, among which: FIG. 1 shows error rate curves known per se; FIG. 2 illustrates an algorithm for estimating the minimum distance of an error correction code, according to the invention; FIG. 3 describes a step of generating a sequence of symbols, set on the edge in the algorithm of FIG. 2; and FIG. 4 describes a pulse distance calculation step, implemented in the algorithm of FIG. 2.

 It is 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 decoding can be effective 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 dmin. The determination of this distance makes it possible to estimate the code performance for low error rates. This estimate avoids long and expensive simulations.

 FIG. 1 illustrates three bit error rate curves, TEB, represented on the ordinate axis 11, as a function of the signal-to-noise ratio, EbVo, represented on the abscissa axis 10: a first uncoded curve, 12 , is obtained for binary data transmission using QPSK modulation without use of error code;

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pour un taux d'erreurs bit de l'ordre de 10-6) ; et une troisième courbe représente la limite théorique qui peut être obtenue en utilisant un code idéal associé à un algorithme de décodage idéal ; cette limite est fonction du rendement, R, du code (qui est le rapport du nombre de bits non codés sur le nombre de bits codés) et de la taille du bloc. a second curve 13 is obtained for a transmission of binary data using an error correction code (it is noted that this curve allows a gain, G, of several decibels, for example,

for a bit error rate of the order of 10-6); and a third curve represents the theoretical limit that can be obtained by using an ideal code associated with an ideal decoding algorithm; this limit is a function of the efficiency, R, of the code (which is the ratio of the number of uncoded bits to the number of coded bits) and 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 m 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 &num; lOlog (.M).

 Thus, 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 relies, in turn, 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, min, but a quantity, called impulse distance of the code, impulse, representative of the correction power of the code and the associated decoder.

It can be verified that for many linear codes, the pulse distance of the code, impulse is equal to the code distance, dmm.

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 According to a variant of the invention, the multiplicity, m, associated with the distance of the code, that is to say the ratio of the number of symbols with which the pulse distance of the code, dmin, is associated with the number, is also determined. total of symbols in a word Consideration of the multiplicity makes it possible in particular to estimate more finely the asymptotic gain or to provide an unequal protection of the symbols to be encoded.

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

 During a first initialization step 20, the various 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 whose free distance is to be estimated (for example, elementary codes and interleaving for turbo codes, punching pattern,. ..) 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, ...).

(des symboles +1 seraient associés aux 1 émis par le codeur). On note que cette succession de symboles égaux à -1 était transmise au décodeur correspondant au code choisi, celui-ci convergerait sans aucune difficulté vers le mot tout 0 contenant k valeurs binaires nulles. On note également que l'étape 22 est illustrée plus en détail en regard de la figure 3. Then, during a step 22, an initial codeword is generated (according to the code defined in step 21) which for a linear code contains only 0. This net of code is then modulated (according to the modulation defined in step 21) to produce a sequence (v1, V2, .... vn). For a binary modulation, a symbol of value -1 is associated with each O transmitted by the encoder

(+1 symbols would be associated with the 1 emitted by the encoder). Note that this succession of symbols equal to -1 was transmitted to the decoder corresponding to the chosen code, it would converge without any difficulty to the word all 0 containing k binary values zero. It is also noted that step 22 is illustrated in more detail with reference to FIG.

 Then, during a step 23, a variable i is initialized to 1.

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 Then, during a step 24, it determines a pulse distance, dimpulse, i associated with an error injected into the symbol symbol of the sequence (VI, V2, .... Vn). Thus, the same symbol of the sequence (VI, V2, .... Vn) is transformed into a symbol having a positive value. The amplitude of this error is increased until the decoder does not converge towards the word all 0. The encoder / decoder association is then faulted.

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

 The minimum value of the pulse that does not fault the correction system is directly related to the pulse distance, dllpulse i, associated with the binary value affected by the error. The impulse distance, d1mpulse, i, is thus determined and saved.

 It is also noted that step 24 is illustrated in more detail with reference to FIG.

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

 In the negative, during a step 26, the value of i is incremented by one unit and the step 24 is reiterated.

 It is noted that in this way, the impulse distance associated with each of the k information symbols of the sequence (va, V2, .... Vk) is determined.

 According to a variant of the test 25 and of step 26, the pulse distance associated with each symbol belonging to a subsequence of the sequence (vi, ....) is determined, this subsequence containing a lower number of symbols. strictly at k. This variant is advantageously implemented when, in particular, the error correction code has periodicity properties which are such that many information symbol positions in the sequence (VI, V2, .... Vk) correspond. at the same impulse distance and that the subset is chosen according to these properties. We note that in

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 In the case of convolutional turbo codes, these periodicities depend on the interleaving function and the possible punching pattern.

 If the result of the test 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.

 In a variant, during step 27, the multiplicity m, associated with the minimum impulse distance, is also determined. The multiplicity, m, is, by definition, the ratio of the number of symbols with which the code impulse distance, dmin, is associated with the total number of symbols in a word.

 Note that the number of errors that can correct a code having a minimum distance dmm is strictly less than dmin / 2 errors. Let A be an error, the amplitude of the error pulse added to the nominal value-1 (the amplitude of the symbol applied to the input of decoder A is therefore equal to error-1). A full binary error corresponds to an amplitude error pulse 2 (change from -1 to +1). The number of binary errors equivalent to an error amplitude is therefore equal to Aerreu / 2.

 If the error pulse is corrected, then the number e is strictly less than dmin / 2. Thus, by assimilating exactly the minimum distance and the impulse distance, the error is strictly less than dmm and dimpri! is.

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

 If yes, step 21 is repeated.

 In the negative, during a step 29, a code is chosen in unction of its minimum impulse distance.

 According to a variant, during step 29, other parameters such as, for example, the multiplicity associated with the minimum impulse distance of the code and / or the complexity of the code are, furthermore, taken into account for the choice. code.

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 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 adapted to the transmission of packets, associating k bits of useful information with words of n bits after coding (the efficiency, R, of code being equal to the ratio kin).

 During a step 30, we translate the word all 0 in the code studied.

Since the code is linear, the n bits of the codeword (ul, U2, ... un) are all nil. (Here, the choice of the word all 0 answers to a simplicity concern: since the information message is all 0, the code being linear, the redundancy is all 0 too and one does not have to worry about the coding; other words, according to a variant of step 30, it is possible to choose a code word different from the word all 0).

..-un) égal à 1 ; On forme ainsi une séquence de symboles (vol, V2,... vn) correspondant au mot de code (U), U2,... un) modulé. Then, during a step 31, the symbols are defined as they would have been emitted by a modulator NRZ (or No Return to Zero). Thus, during step 31, there is associated: a -1 symbol with each binary value of the code word (ui, U2, ... un) equal to O; and - a +1 symbol to each binary value of the code word (M], M2,

..- a) equal to 1; Thus, a sequence of symbols (vol, V2, ... vn) corresponding to the modulated code word (U), U2,.

 After step 31, step 23 illustrated with reference to FIG. 2 is performed.

FIG. 4 describes the pulse distance calculation step 24, illustrated with reference to FIG. 2.

During a step 40, one initializes: a variable Y with a value equal to 2; and a sequence w of n symbols equal to the sequence v.

According to one variant, the variable J is initialized to a value greater than 2, as a function of a lower bound (a priori known) of the minimum impulse distance.

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 Then, during a step 41, an error, Aerreur, is initialized to a value equal to J-ê, where e is any real number, between 0 and 1 strictly (e is equal, for example, to 0 , 5); thus, the error, Verrez is equal to a value strictly between (J-1) and J.

affecte de la valeur Aerreur moins la valeur de Vs soit get < r 1 ( étant le paramètre initialisé lors de l'étape 23 et mise àjour lors de l'étape 26). In step 41, we select the symbol of w, wi, which we

assigns the value of error less the value of Vs is get <r 1 (being the parameter initialized in step 23 and updated in 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 is at weighted inputs). . If the code is of turbo code type, the decoding algorithm will be, for example, an iterative decoding algorithm as described in patents EP0511141 (whose title is error correction coding method to 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 needed. The number of iterations can be several hundred. The results obtained are very dependent on the quality of the decoding. The soft input / output algorithm must be able to work without knowing the variance. In particular, it is possible to 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 algorithms suitable for turbo decoding", published in European Trans. Telecommun., Vol. 8, pp. 119-125,
March-Apr. 1997, the Max-Log-MAP algorithm being derived from the MAP algorithm described in LR Bahl, J. Cocke, F.
Jelinek and J. Raviv "Optimal decoding of linear codes for minimizing

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symbol error rate", paru dans la revue IEEE Trans. Inform. Theory, rr-20, pp. 248-287, Mar. 1974.) ; ou SOVA ( Algorithme de Viterbi à sorties douces de langlais Soft Output Viterbi Algorithm ) décrit notamment dans les articles : de G. Battail,"Pondération des symboles décodés par l'algorithme de Viterbi", dans la revue Ann. Télécommun., Fr.,
42, NO 1-2, pp. 31-38, en Janvier 1987 ; - de J. Hagenauer and P. Hoeher,"A Viterbi algorithm with soft- decision outputs and its applications", dans les comptes-rendus de conférence Proc. of Globecom'89, Dallas, Texas, pp. 47.11-
47-17, en Novembre 1989 et de C. Berrou, P. Adde, E. Angui and S. Faudeil,"A low complexity soft-output Viterbi decoder architecture",", dans les comptes-rendus de conférence Proc. of ICC'93, Geneva, pp. 737-740, en Mai 1993. qui ne requièrent pas la connaissance de la variance. On peut montrer que le décodeur idéal pour l'invention proposée serait un décodeur s'appuyant sur la recherche du produit scalaire minimal.

symbol error rate ", published in the journal IEEE Trans., Theory, rr-20, pp. 248-287, Mar. 1974.) or SOVA (Viterbi Algorithm with soft outputs of English langlays Soft Output Viterbi Algorithm) describes in particular in the articles: by G. Battail, "Weighting of symbols decoded by the Viterbi algorithm", in Ann. Télécommun., Fr.,
42, No. 1-2, pp. 31-38, in January 1987; - J. Hagenauer and P. Hoeher, "A Viterbi algorithm with soft-decision outputs and its applications", in conference proceedings Proc. of Globecom'89, Dallas, Texas, pp. 47.11-
47-17, in November 1989 and C. Berrou, P. Adde, E. Angui and S. Faudeil, "A low complexity soft-output Viterbi decoder architecture", "in conference proceedings Proc. '93, Geneva, pp. 737-740, in May 1993. It does 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 minimum scalar product. .

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

 If so, the limit is not exceeded and in a step 45, the variable J is incremented by one and step 41 is reiterated.

l'étape 45, on incrémente la variable J d'une valeur strictement inférieure à 1, afin de déterminer une distance impulsionnelle réelle. According to a variant of step 45, when the modulation used is such that the protection of the binary values is unequal, 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 J is incremented by a value strictly less than 1, in order to determine a real impulse distance.

 According to a variant of step 24, the variable J is assigned a value corresponding to an upper bound of the pulse distance increased by

<Desc / Clms Page number 20>

 1 in 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 codeword, and J is decremented in the step of 45.

correspondant à une borne inférieure, Jmin, de la distance impulsionnelle ; puis lors d'une deuxième itération, la variable J est initialisée avec une valeur correspondant à une borne supérieure, Jmax, de la distance impulsionnelle augmentée de 1 ; puis - lors des itérations suivantes, on affecte à J une valeur égale à la moitié de la somme de Jmin et de Jmax et, à l'issue du test 43 : si le mot décodé est égal au mot initial, on affecte à Jmax la valeur de J courante ; et - si le mot décodé n'est pas égal au mot initial, on affecte à Jmin la valeur de J courante. According to yet another variant of step 24, one proceeds by dichotomy: during the first iteration, the variable J is initialized with a value

corresponding to a lower bound, Jmin, of the impulse 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, after the test 43: if the decoded word is equal to the initial word, we assign to Jmax the current J value; and if the decoded word is not equal to the initial word, Jmin is assigned the value of current J.

 According to this last variant, the iterations are stopped when the difference between the values of Jmin and Jmax is sufficiently small.

 Note that this variant based on a priori knowledge of a framework of J and the use of the dichotomy method is particularly advantageous when the protection of the symbols of a codeword is unequal.

 If the result of the test 43 is negative, the decoding algorithm does not converge to the whole word O 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, dimp,; associated with an error injected into the symbol of the sequence (VI, V2, .... Vn) is equal to the current value of J minus 1. Indeed, the current value of Aerre <r is J- & num and since the error is strictly less than the impulse distance and since the current value of J is the minimum value which gives rise to a decoding error, it can be established:

<Desc / Clms Page number 21>

J M/.i > -i-&num; soit encore : me, ; + &num; > Y-1 > K/, t-I + &num;

(J-1) et dintpulse i étant des entiers, on en déduit leur égalité.

JM / .i> -i- &num; again, me; + &num;>Y-1> K /, tI + &num;

(J-1) and dintpulse i being integers, we deduce their equality.

After step 44, the test 25 illustrated with reference to FIG. 2 is performed.

 Of course, the invention is not limited to the embodiments mentioned above.

Rate en anglais) estimé selon la relation suivante :

FER = mk Erf-Eb N.) R. d.,,,) = f. j

où : - m représente la multiplicité associée à la distance impulsionnelle du code ; - k, le nombre de bits d'information d'un mot de code ; - / ? Vo, le rapport signal à bruit ; - R, le rendement du code ; - dmm J la distance impulsionnelle du code ; et

- Erfc, la fonction d'erreur complémentaire, bien connue suivant la relation :

r/e () =-y=-F exp (-) - V7r'"="

Par différence avec la courbe non codée, on peut en déduire une formule approchée du gain asymptotique, suivant, par exemple, la relation :
Ga&num;10log(R.dmin). In particular, the skilled person can make any variant in the parameters to be considered for the choice of a code. The person skilled in the art may notably take into account the frame error rate, FER, (or Frame Error

Rate in English) estimated according to the following relation:

FER = mk Erf-Eb N.) R. d. ,,,) = f. j

where: - m represents the multiplicity associated with the pulse distance of the code; k, the number of information bits of a code word; - /? Vo, the signal to noise ratio; - R, the code yield; - dmm J the pulse distance of the code; and

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

r / e () = -y = -F exp (-) - V7r '"="

By difference with the uncoded curve, we can deduce an approximate formula of the asymptotic gain, following, for example, the relation:
Ga &num; 10 log (R.dmin).

 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 thus to propose coding schemes with multilevel protections or unequal coding efficiency .

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 Furthermore, according to the invention, when determining the pulse distance of the code, the error can be spread over several symbols, provided that it is certain that these symbols will all belong to a competing code word retained (which means that these symbols are chosen at positions where the symbols of the reference code word and the positions of the competing codeword differ), in the event of decoder failure. The error pulse will preferably be carried on competing code words which are at 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 encoder for a convolutional code, for example). Thus, if the information bit changes, the redundancy bit also and these two bits are part of the competing code word.

 In general, the distribution of the error pulse is preferentially 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 pulse distance associated with each basic symbol tested. We note that, when the error is distributed over several symbols, the multiplicity, m, is then the ratio of the number of basic symbols with which the pulse distance d1, dmin, is associated with the total number of symbols. in a word.

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

 Note also that the invention is applicable not only to convolutional turbocodes (parallel concatenation) but is also applicable to simple convolutional codes or codes built from a serial concatenation, and more generally to all codes whose decoder knows how to draw profit of samples

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 soft input, especially those using the Viterbi algorithm or the MAP algorithm (Maximum A Posteriori) or its simplified versions.

 Note that the invention is not limited to a purely hardware implementation but it can also be implemented in the form of a sequence of instructions of a computer program or any form mixing a hardware part and a part software. In the case where the invention is partially or totally implemented in software form, the corresponding instruction sequence can 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 completely readable by a computer or a microprocessor.

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

Claims (27)

 (Impulse,)). 2. A method of qualifying an error correcting code according to claim 1, characterized in that said set contains a single symbol.

 1. A method for qualifying an error correction code, delivering code words, each formed of at least one symbol, characterized in that it associates with said code a first qualification information, representative of the capacity of a decoder corresponding to correcting errors, obtained by means of an estimation process implementing the following steps: insertion (41) of a predetermined error pulse (terror), introducing a disturbance on a set of at least one symbol (w,) of a reference code word (v) previously coded without error; decoding (42), using a weighted input decoder, of the modified code word (w) by said error pulse, and analyzing the result of said decoding, delivering said first qualification information; 3. A method of qualifying an error correcting code according to claim 1, characterized in that said set contains at least two symbols. 4. A method of qualifying an error correcting code according to claim 3, characterized in that all the symbols of said set belong to a codeword concurrent with said reference code word. 5. A method of qualifying an error correcting code according to any one of claims 1 to 5, characterized in that associating said set of at least one symbol affected by said error pulse an intermediate data of qualification, a function of a maximum amplitude of said error pulse affecting said set and not disturbing the decoding of the code word, said impulse distance. <Desc / Clms Page number 25> A method of qualifying an error correcting code according to claim 5, characterized in that said estimation process is repeated (26) at least twice introducing a perturbation on the same set of at least one symbol with amplitudes of said variable error pulse, so as to determine said pulse distance. 7. A method of qualifying an error correcting code according to any one of claims 5 and 6, characterized in that said impulse distance is equal to the largest integer J such that said code word containing said affected set of said amplitude error pulse equal to said integer J is decoded correctly. A 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 codeword reference. 9. A method of 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 (impulse) among the determined impulse distance or distances. 10. A method of qualifying an error correcting code according to any one of claims 5 to 9, characterized in that it assigns (27) said code a second qualification information (m), representative of the number of said sets most sensitive to an error pulse, in said reference code word. 11. A method of qualifying an error correcting code according to claims 9 and 10, characterized in that said second qualification information, called multiplicity, is the ratio:

 the number of said sets for which said pulse distance is equal to said minimum pulse distance over the total number of symbols in a code word. <Desc / Clms Page number 26> A method of qualifying an error correcting code according to any one of claims 1 to 11, characterized in that said set or sets according to claim 8 on which said estimation process is applied is are selected taking into account any periodicity properties of said code. 13. A method of qualifying an error correcting code according to any one of claims 1 to 12, characterized in that said reference code word is a word of which all said symbols take the binary value 0. 14. The method of qualifying an error correcting code according to any one of claims 1 to 13, characterized in that said reference code word undergoes a modulation (31), before said insertion of a pulse of fault. 15. A method of qualifying an error correction code according to any one of claims 1 to 14, characterized in that it comprises a step of estimating a gain, said asymptotic gain (Ga), representative of the effectiveness of said error correction code compared to no coding, according to said first qualification information. 16. Method for qualifying an error correcting code according to the

 claim 15, characterized in that said asymptotic gain is approximated by:

 Ga = 101og (R.)

 where: R is the yield of said error correcting code; dmin is the minimum impulse distance as defined in claim 9. 17. A method of qualifying an error correcting code according to any one of claims 1 to 16, characterized in that it comprises the following steps:

 - generating and modulating (22) said reference code word; selecting (23, 26) at least one set of at least one symbol of said reference code word; <Desc / Clms Page number 27>  assigning (41) an error pulse of a determined magnitude to said selected audit (or audits) to form an erroneous word; decoding (42) said erroneous word, taking into account weighted inputs, and delivering a decoded word; comparing said decoded word with said initial code word. 18. A method of 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 given 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 word of initial code; 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 equals 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, a dichotomy is performed, the value of the amplitude of said error being chosen according to said substep of comparison; and a combination of said first and second rules with said third rule. 19. A method of 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; <Desc / Clms Page number 28>  algebraic turbo codes; concatenated parallel codes; series concatenated codes; and combinations of the preceding codes. 20. A method of 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 on more sensitive to errors. 21. A 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 unequal protection code according to the result of said comparing step. 22. A method for optimizing a channel coding, characterized in that it implements the method for qualifying an error correction code according to any one of claims 1 to 21 over at least two candidate codes. and a selection step for said channel coding of one of said candidate codes, based on an analysis of said first qualification information assigned to each of said candidate codes. 23. A method for 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 into account the code / modulation association. 24. The method of optimizing a channel coding according to claim 22, wherein said selection step also takes into account said second qualification information according to claim 10 and 11 and / or asymptotic gain according to any one of claims 15 and 16. 25. Encoder for error correction, characterized in that the corresponding code is selected according to a qualification method according to one of <Desc / Clms Page number 29>  any of claims 1 to 21 and / or according to a channel coding optimization method according to any one of claims 22 to 24. 26. Decoder for decoding coded data using error correction code and corresponding error correction, characterized in that said error correction code is selected according to any one of claims 1 to 21 and / or according to a channel coding optimization method 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 of optimizing a channel coding according to any one of claims 22 to 24, characterized in that said application belongs to the group comprising: - the transmission of data over a noisy channel; - channel coding optimization with unequal protection; - estimation of the free distance of a code; and estimating the performance of a code.