Search

Copyright of Annals of Telecommunications is the property of Springer Nature and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Annals of Telecommunications is the property of Springer Nature and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Annals of Telecommunications is the property of Springer Nature and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Annals of Telecommunications is the property of Springer Nature and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Annals of Telecommunications is the property of Springer Nature and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Annals of Telecommunications is the property of Springer Nature and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Annals of Telecommunications is the property of Springer Nature and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

This paper presents a block turbo decoding algorithm, from its theory to its implementation in a programmable circuit. In this study, we discuss the two prototypes realized. It will be possible to compare the complexity of the core of the process, which is the elementary decoder, thanks to the choice of essential parameters. One prototype is more dedicated to high data rates, the other one being implemented on only one FPGA which means a gain in terms of area. First, we briefly focus on the description of the siso (Soft-In Soft-out) algorithm used to implement the turbo decoder. Then, we explain the essential choices in order to adapt the algorithm for an ASIC implementation, which leads to a compromise between area and binary error rate. Finally, we present the two prototypes implemented and their experimental results. L’objectif de cet article est de présenter le turbodecodage de codes produits depuis la théorie jusqu’à la réalisation sur circuit programmable. Deux prototypes ont été réalisés, Us serviront de support à cette étude. Il sera en effet possible de comparer la complexité du décodeur élémentaire en fonction d’un certain nombre de paramètres, de mettre face à face une structure dédiée aux débits élevés et une structure optimisée en surface. Dans une première partie, on trouvera une brève description de l’algorithme srso (Soft-In Soft-Out) permettant de réaliser le turbo décodage. Vient ensuite la description de l’adaptation de cet algorithme à l’implantation sur silicium. Cette phase nécessite des choix entre complexité en terme de circuit et performance en terme de taux d’erreurs binaires. La dernière partie présente les choix d’architectures et les résultats expérimentaux des 2 prototypes. [ABSTRACT FROM AUTHOR]

Copyright of Annals of Telecommunications is the property of Springer Nature and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Annals of Telecommunications is the property of Springer Nature and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Annals of Telecommunications is the property of Springer Nature and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Annals of Telecommunications is the property of Springer Nature and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Annals of Telecommunications is the property of Springer Nature and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Annals of Telecommunications is the property of Springer Nature and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

This paper reviews the representation of binary linear block codes by multi-indeterminate “descriptive polynomials” and extends it to versions permuted with respect to the usual systematic form. The main decoding rules (word-by-word and symbol-by-symbol) can then be expressed in terms of descriptive polynomials, the computation of which is easily implemented using trellises. Particular emphasis is given to the symbol-by-symbol decoding rule where the decoder input and output are both real numbers, assuming a logarithmic measure of the likelihood ratio is employed. The same form of input and output enables successive soft decodings of concatenated codes and iterated decoding. Keeping only the largest monomial of descriptive polynomials widely simplifies decoding and, moreover, results in the same decoded word as the word-by-word decoding rule although the decisions on the symbols are still expressed as real numbers. These tools are applied to convolutional codes (for a finite message length). Decoding a non-recursive non-systematic code by means of the trellis as defined here is shown to be of same complexity as using the trellis conventionally associated with the Viterbi algorithm. On the contrary, decoding a recursive systematic code, of better potential performance, is of greater and prohibitive complexity. Keeping reasonable complexity in this case can however use iteration. Two distinct reasons for iteration of decoding are identified, which both apply to turbo coding. Cet article reprend la rep'esentation de codes en blocs linéaires par des « polynômes descripteurs » à plusieurs indéterminées et la généralise à des versions permutées par rapport à la forme systématique usuelle. Les principales règies de décodage (par mot et par symbole) peuvent être exprimées en fonction de polynômes descripteurs que l’on peut aisément calculer au moyen de treillis. On insiste surtout sur la régie de décodage symbole par symbole, où l’entrée comme la sortie du décodeur sont des nombres réels, en supposant qu’une mesure logarithmique des rapports de vraisemblance est employée. La même forme à l’entrée et à la sortie permet des décodages pondérés successifs et le décodage itéré. On simplifie largement le décodage en ne conservant que le plus grand monôme des polynômes descripteurs et, de plus, le résultat obtenu est le même que celui de la régie de décodage mot par mot bien que les décisions sur les symboles soient toujours exprimées par des nombres réels. Ces outils sont appliqués aux codes convolutifs (pour un message de longueur finie). On montre que la complexité du décodage d’un code non récursif et non systématique à l’aide du treillis déjini ici est la même qu’en employant le treillis habituellement associé à l’algorithme de Viterbi. Au contraire, le décodage d’un code récursif systématique, de meilleures performances potentielles, est d’une complexité plus grande et prohibitive. On peut cependant conserver une complexité raisonnable, dans ce cas, en faisant usage de l’itération. Deux raisons distinctes de l’itération du décodage sont identifiées, qui toutes deux s’appliquent aux turbo codes. [ABSTRACT FROM AUTHOR]

Copyright of Annals of Telecommunications is the property of Springer Nature and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Annals of Telecommunications is the property of Springer Nature and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Annals of Telecommunications is the property of Springer Nature and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Annals of Telecommunications is the property of Springer Nature and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Annals of Telecommunications is the property of Springer Nature and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Annals of Telecommunications is the property of Springer Nature and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Annals of Telecommunications is the property of Springer Nature and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Annals of Telecommunications is the property of Springer Nature and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Annals of Telecommunications is the property of Springer Nature and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Annals of Telecommunications is the property of Springer Nature and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Annals of Telecommunications is the property of Springer Nature and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Les auteurs se proposent d'étudier la complexité d'un algorithme de décodage pondéré des codes linéaires en blocs précédemment publié et de certaines de ses variantes simplifiées, en se restreignant au cas binaire. On présente à cet effet des calculs basés sur un modèle simplifié du fonctionnement du décodeur ainsi que des résultats de sa simulation. On commence par rappeler la description de cet algorithme en se référant au diagramme du treillis associé au code. Une description probabiliste du fonctionnement de l'algorithme sert d'introduction à un modèle dans lequel les «cotes» associées à chaque chemin du treillis, qu'il s'agit de comparer, sont scindées en deux termes additifs, l'un certain, l'autre aléatoire. Une évaluation de la complexité de l'algorithme optimal et de certaines de ses variantes simplifiées est développée à partir de ce modèle. La méthode de simulation de l'algorithme et de ses variantes, ainsi que les résultats obtenus, sont enfin présentés. This paper is devoted to study the complexity of an algorithm already published which is intended to weighted decoding of linear block codes, and of certain of its simplified variants ; the discussion is restricted to the binary case. To this end calculations based on a simplified model of the decoder operation as well as simulation results are presented. To begin with, the algorithm description is recalled, referring to the trellis associated with the code. A probabilistic description of the algorithm operation is used in order to introduce a model where each of the metrics associated with the paths, to be compared, is split into two additive parts, one of them being deterministic and the other one random. The complexity of the optimum decoding algorithm, as well as of simplified variants of it, is evaluated using this model. The method for simulating the algorithm and its variants, and the results thus obtained, are finally presented. [ABSTRACT FROM AUTHOR]

Le but essentiel de cet article est d'introduire la subjectivité, prise dans le sens de connaissance a priori de la signification des symboles, sous forme de coefficients de pondération dans les problèmes de décodage. Tout d'abord, en utilisant trois axiomes très simples et très naturels relatifs à la conservation de l'information, on aboutit à un modèle d'observation décrit par les équations de Lorentz-Poincaré, retrouvant ainsi un schéma obtenu plusieurs fois déjà par des voies différentes. Ensuite, en appliquant ce modèle à l'observation de la quantité d'information contenue dans un événement, on obtient une notion de probabilité relative ou observée d'une part, et une notion d'entropie relative généralisée. Puis, en introduisant au moyen d'axiomes judicieux un concept d'entropie totale, l'entropie relative est définie dans le cas continu comme la limite de l'entropie discrète; et on l'applique au calcul de la capacité d'un canal. Ensuite la probabilité relative est utilisée pour généraliser le critère du maximum de vraisemblance et le critère bayesien de décision, et de là on se sert des techniques de Gallager afin d'obtenir des bornes pour les probabilités d'erreur de décodage. The main purpose of this paper is to introduce subjectivity in the form of weighting coefficients in decoding problems. Subjectivity is thought of as prior knowledge of meaning. First, by using very simple informational axioms, we derive a model of observation described by the Lorentz equations. This is a new derivation of the model which we already obtained via several different ways. Then, on applying this model to observing the information involved by an event only, we get a concept of relative probability on the one hand, and of generalized relative entropy on the other hand, which we use to calculate the capacity of a channel. Finally, the relative entropy is used to derive a generalized maximum likelihood criterion and a generalized bayesian decision criterion, whereby we can obtain errors bounds for channels when semantics is taken into account, via techniques similar to those of Gallager. [ABSTRACT FROM AUTHOR]

Dans le cas binaire, l'emploi de décisions pondérées au lieu de décisions fermes apporte un bénéfice bien connu: en présence de bruit additif, gaussien et blanc, la capacité du canal et le débit critique R sont multipliés par un même facteur égal à π/ 2 (ce résultat est la limite obtenue lorsque le rapport signal à bruit tend vers 0). Cet article est consacré à évaluer le bénéfice dû à des décisions pondérées, mais pour un alphabet non binaire et un système de modulation orthogonal. On examine les deux cas de réception cohérente et non cohérente. Outre la limite pour un rapport signal à bruit qui tend vers 0, on calcule dans chacun des cas le débit critique R en fonction du rapport signal à bruit. Les résultats sont présentés graphiquement, mais certaines grandeurs sont données sous forme de tables. In the binary case, the use of soft decisions instead of hard ones is well known to provide a benefit: in the presence of additive Gaussian and white noise, the channel capacity and its cut-off rate R are both multiplied by tz/ 2 (this result obtains in the limit as the signal-to-noise ratio approaches zero). This paper is intended to evaluate the benefit due to soft decisions, but assuming a nonbinary alphabet and an orthogonal modulation system. Both coherent and noncoherent receivers are considered. Besides the limit for a vanishingly small signal-to-noise ratio, the cut-off rate R is computed in every case in terms of the signal-to-noise ratio. The results are graphically presented but certain numerical values are given in tables. [ABSTRACT FROM AUTHOR]

Un code en blocs linéaire étant donné, on définit une matrice carrée contenant à la fois ses matrices génératrice et de contrôle. En associant deux jeux d'indéterminées à ses lignes et à ses colonnes respectivement, on définit deux polynômes qui décrivent l'ensemble des combinaisons linéaires de ses lignes d'une part, de ses colonnes d'autre part. On montre que la représentation polynomiale de la liste des mots du code, celle de ses classes latérales, ainsi que leurs homologues pour le code dual, s'en déduisent en donnant des valeurs particulières à certaines indéterminées. L'article est consacré aux propriétés mathématiques de ces polynômes, notamment à des relations entre eux qui généralisent l'identité de MacWilliams. Le formalisme ainsi introduit est à la base d'une représentation des codes linéaires par le diagramme du treillis, et on en envisage quelques applications à des problèmes de décodage, thèmes éventuels d'études ultérieures. L'article proprement dit est restreint au cas binaire, mais la généralisation de ses principaux résultats à un corps fini quelconque est traitée en annexe. Given a linear block code, a square matrix is defined, which contains both its generator and paritycheck matrices. Associating two sets of indeterminates with its rows and its columns, respectively, enables defining two polynomials which describe the set of linear combinations of its rows and of its columns, respectively. It is shown that the polynomial representations of the code (as a list of words), of its cosets, and of the dual code and its cosets, result from giving certain of their indeterminates particular values. The paper is devoted to mathematical properties of these polynomials, especially to relations of each other which generalize the MacWilliams identity. The formalism thus introduced leads to trellis representations of linear block codes, and applications to decoding problems are finally suggested as possible future research topics. The paper in itself is restricted to the binary case, but the extension of its main results to any finite field is dealt with in the appendix. [ABSTRACT FROM AUTHOR]

Dans le cas de la correction d'un nombre réduit d'erreurs, les procédures de décodage algébrique peuvent être notablement simplifiées. On présente ici une réalisation d'un décodeur corrigeant deux paquets de quatre éléments binaires. Le code utilisé est un code de Reed-Solomon de paramètres (15, 11) sur le corps à 16 éléments. La structure choisie est celle du décodeur de Meggitt. La maquette, réalisée en circuits ttl (ls), comprend 49 boîtiers et peut actuellement accepter un débit de 5 Mbit/s. L'utilisation de ce type de décodeur pour d'autres codes de Reed-Solomon est aussi étudiée. Algebraic decoding procedures can be greatly simplified in case the number of errors being corrected is small. The authors present here a decoder which is capable of correcting errors occuring on four bits packets. The considered code is a (15, 11) Reed-Solomon code over GF (16). A Meggitttype decoder has been selected. The hardware implementation consists of 49 ttl (ls) packages and operates for the present at a rate of 5 Mbit/s. The utilisation of this decoding scheme is considered for other Reed-Solomon codes. [ABSTRACT FROM AUTHOR]

Copyright of Annals of Telecommunications is the property of Springer Nature and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)