Décodage des codes LDPC définis sur des groupes abéliens

Une large classe de codes LDPC est définie et qui comprend les codes LDPC définis sur les corps finis, les anneaux et les groupes mais aussi des codes non-linéaires. Cela est rendu possible en étendant la notion de parité du code. Un algorithme rapide de type propagation de croyance est développé pour ce type de parité. Des exemples montrent des utilisations possibles de tels codes

Unsupervised Log-Likelihood Ratio Estimation for Short Packets in Impulsive Noise

International audiencelmpulsive noise, where large amplitudes arise with a relatively high probability, arises in many communication systems including interference in Low Power Wide Area Networks. A challenge in coping with impulsive noise, particularly alpha­stable models, is that tractable expressions for the log-likelihood ratio (LLR) are not available, which bas a large impact on soft­input decoding schemes, e.g., low-density parity-check (LDPC) packets. On the other band, constraints on packet length also mean that pilot signais are not available resulting in non­trivial approximation and parameter estimation problems for the LLR. In this paper, a new unsupervised parameter estimation algorithm is proposed for LLR approximation. In terms of the frame error rate (FER), this algorithm is shown to significantly outperform existing unsupervised estimation methods for short LDPC packets (on the order of 500 symbols), with nearly the same performance as when the parameters are perfectly known. The performance is also compared with an upper bound on the information-theoretic limit for the FER, which suggests that in impulsive noise further improvements require the use of an alternative code structure other than LDPC

Binary Codes for Packet Error and Packet Loss Correction in Store and Forward

Abstract-In this paper, we introduce a novel approach to correct packet errors and packet losses in store and forward by using binary error-correcting codes. Using a framework similar to what has been proposed for error control in random linear network coding, we investigate error control under two scenarios. First, we show that the Hamming metric is suitable for error control in the case of errors intrinsic to the network. Second, we investigate the case of an adversary on the network who erases and injects packets in order to corrupt the communication. Under this setting, we show that error correction is performed using a new metric, referred to as the modified Hamming metric. We then investigate using constant-weight codes and linear codes for error correction in store and forward. We thus show that the traditional approach of indexing the packets in order to recover their original order is a suboptimal restriction of our approach. I

Adaptive Discrete Vector Field in Sensor Networks

Homology groups are a prime tool for measuring the connectivity of a network, and their computation in a distributed and adaptive way is mandatory for their use in sensor networks. In this paper, we propose a solution based on the construction of an adaptive discrete vector field from where, thanks to the discrete Morse theory, the generators of the homology groups are extracted. The efficiency and the adaptability of our approach are tested against two applications: the detection and the localization of the holes in the coverage, and the selection of active sensors ensuring complete coverage

Variation on Variation on Euclid's Algorithm

International audienc

Modèle Markovien de la densité de probabilité des erreurs et application au calcul de la probabilité de propagation d'erreur de l'égaliseur à retour de décision pondérée

Une méthode de calcul de la probabilité de propagation des erreurs des égaliseurs à retour de décision (ERD) est proposée et provient d'un modèle Markovien de la densité de probabilité des erreurs. Ce nouveau modèle est une généralisation de celui proposé dans [1]. Il est obtenu par l'analyse du mélange de gaussiennes des erreurs dont les proportions suivent un processus de Markov. Cette analyse montre que l'égaliseur à retour de décision pondérée (ERDP) [2-4] est moins sensible que l'ERD classique à la propagation d'erreur

A geometrical derivation of the excess mean square error for bussgang algorithms in a noiseless environment

International audienc

On the optimal constant norm algorithm in respect to the EMSE for blind qam equalization

Publication in the conference proceedings of EUSIPCO, Viena, Austria, 200

Performance analysis of the weighted decision feedback equalizer

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