The Partition Weight Enumerator of MDS Codes and its Applications

A closed form formula of the partition weight enumerator of maximum distance separable (MDS) codes is derived for an arbitrary number of partitions. Using this result, some properties of MDS codes are discussed. The results are extended for the average binary image of MDS codes in finite fields of characteristic two. As an application, we study the multiuser error probability of Reed Solomon codes.Comment: This is a five page conference version of the paper which was accepted by ISIT 2005. For more information, please contact the author

Performance of turbo coded DS-CDMA systems in correlated and uncorrelated satellite communication channels

Word processed copy.Includes bibliographical references (leaves 82-88).This thesis aims at presenting the perfonnance of turbo codes in the correlated and uncorrelated satellite fading channel. Turbo codes are known to give very good perfonnance results in A WGN channels, especially for very large input message length codes or interleaver sizes. It can be shown that good perfonnance of the turbo codes can be achieved with small interleaver sizes in a satellite channel

Conservation laws for coding

This work deals with coding systems based on sparse graph codes. The key issue we address is the relationship between iterative (in particular belief propagation) and maximum a posteriori decoding. We show that between the two there is a fundamental connection, which is reminiscent of the Maxwell construction in thermodynamics. The main objects we consider are EXIT-like functions. EXIT functions were originally introduced as handy tools for the design of iterative coding systems. It gradually became clear that EXIT functions possess several fundamental properties. Many of these properties, however, apply only to the erasure case. This motivates us to introduce GEXIT functions that coincide with EXIT functions over the erasure channel. In many aspects, GEXIT functions over general memoryless output-symmetric channels play the same role as EXIT functions do over the erasure channel. In particular, GEXIT functions are characterized by the general area theorem. As a first consequence, we demonstrate that in order for the rate of an ensemble of codes to approach the capacity under belief propagation decoding, the GEXIT functions of the component codes have to be matched perfectly. This statement was previously known as the matching condition for the erasure case. We then use these GEXIT functions to show that in the limit of large blocklengths a fundamental connection appears between belief propagation and maximum a posteriori decoding. A decoding algorithm, which we call Maxwell decoder, provides an operational interpretation of this relationship for the erasure case. Both the algorithm and the analysis of the decoder are the translation of the Maxwell construction from statistical mechanics to the context of probabilistic decoding. We take the first steps to extend this construction to general memoryless output-symmetric channels. More exactly, a general upper bound on the maximum a posteriori threshold for sparse graph codes is given. It is conjectured that the fundamental connection between belief propagation and maximum a posteriori decoding carries over to the general case

Optimisation de la transmission de phonie et vidéophonie sur les réseaux à larges bandes PMR

Cet exposé analyse les perspectives large bande des réseaux PMR, à travers l'évaluation du candidat LTE, et la proposition d'une possible évolution du codage canal, la solution brevetée des codes turbo à protection non uniforme. Une première étude dans le chapitre 2 se concentre sur l'analyse multi-couche et l'identification des problèmes clé des communications de voix et de vidéo sur un réseau LTE professionnel. Les capacités voix et vidéo sont estimées pour les liens montant et descendant de la transmission LTE, et l'efficacité spectrale de la voix en lien descendant est comparée à celle de PMR et GSM. Ce chapitre souligne certains points clé de l'évolution de LTE. S'ils étaient pas résolus par la suite, LTE se verrait perdre de sa crédibilité en tant que candidat à l'évolution de la PMR. Une telle caractéristique clé des réseaux PMR est le codage canal à protection non uniforme, qui pourrait être adapté au système LTE pour une évolution aux contraintes de la sécurité publique. Le chapitre 3 introduit cette proposition d'évolution, qui a été brevetée: les turbo codes à protection non uniforme intégrée. Nous proposons une nouvelle approche pour le codage canal à protection non uniforme à travers les codes turbo progressives hiérarchiques. Les configurations parallèles et séries sont analysées. Les mécanismes de protection non uniformes sont intégrés dans la structure de l'encodeur même à travers l'insertion progressif et hiérarchique de nouvelles données de l'utilisateur. Le turbo décodage est modifié pour exploiter de façon optimale l'insertion progressive de données dans le processus d'encodage et estimer hiérarchiquement ces données. Les propriétés des structures parallèles et séries sont analysées à l'aide d'une analogie aux codes pilotes, ainsi qu'en regardant de plus près leurs caractéristiques de poids de codage. Le taux de transmission virtuel et les représentations des graphs factor fournissent une meilleure compréhension de ces propriétés. Les gains de codage sont évalués à l'aide de simulations numériques, en supposant des canaux de transmission radio statiques et dynamiques, et en utilisant des codes de référence. Enfin, dans le chapitre 4, l'idée breveté du code turbo parallal progressif et hiérarchique (PPHTC) est évaluée sur la plateforme LTE. Une description détaillée de l'architecture des bearers de LTE est donnée, et ses conséquences sont discutées. Le nouveau codage canal est inséré et évalué sur cette plateforme, et ses performances sont comparées avec des schémas de transmission typique à LTE. L'analyse de la qualité de la voix aide à conclure sur l'efficacité de la solution proposée dans un système de transmission réel. Pourtant, même si cette dernière donne les meilleurs résultats, d'avantage d'optimisations devraient être envisagées pour obtenir des gains améliorés et mieux exploiter le potentiel du codage proposé. L'exposé se conclut dans le chapitre 5 et une courte discussion présente les futures perspectives de rechercheThis dissertation analyzes the PMR broadband perspectives, through the evaluation of the preferred candidate, LTE, and the proposal of a possible channel coding evolution, the patented solution of unequal error protection embedded turbo codes. A first study in chapter 2 focuses on the multi-layer analysis and the identification of key issues for professional-like LTE for voice and video communications. The voice and video capacities are estimated for both downlink and uplink LTE transmissions, and the downlink LTE voice system efficiency is compared with that of the PMR and Global System for Mobile Communications (GSM). This chapter helps highlighting some of the key points. If not resolved, the latter could lead to the LTE downfall as a candidate for the PMR evolution. One such key characteristic of PMR systems is the unequal error protection channel coding technique, which might be adapted to the LTE technology for its evolution to public safety requirements. Chapter 3 further introduces the proposed evolution patented ideas: the unequal error protection embedded turbo codes. We propose a new approach for the unequal error protection channel coding through the progressive hierarchical turbo codes. Both parallel and serial turbo configurations are closely studied. The unequal error protection mechanisms are embedded in the encoder s structure itself through the progressive and hierarchical insertion of new data. The turbo decoding is modified as to optimally exploit the progressive insertion of information in the encoding process and hierarchically estimate the corresponding data. Both parallel and serial configurations properties are analyzed using an analogy with a pilot code behavior, as well as a zoom on the weight error functions coefficients. The virtual code rate and factor graph interpretations also provide a better insight on the code properties. The code possible gains are highlighted through computer simulations in both static and dynamic transmission environments, by using carefully chosen benchmarks. Finally, in chapter 4, the patented idea of parallel progressive hierarchical turbo codes (PPHTC) is evaluated over the LTE platform. A detailed description is given of the voice transmission bearer architecture over LTE, and its consequences are discussed. The new channel code is inserted and evaluated over this platform and its performances compared with the existent LTE transmission schemes. The voice quality results help concluding on the efficiency of the proposed solution in a real transmission scenario. However, even though the newly presented solution gives the best results, further system optimizations should be envisaged for obtaining better gains and exploit the parallel progressive hierarchical turbo codes potential. The dissertation concludes in chapter 5 and a short discussion is given on future research perspectivesEVRY-INT (912282302) / SudocSudocFranceF