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Codes LDPC multi-binaires hybrides et méthodes de décodage itératif

Abstract : This thesis is dedicated to the analysis and the design of sparse-graph codes for channel coding. The aim is to construct coding schemes having high performance both in the waterfall and in the error-floor regions under iterative decoding. In the first part, a new class of LDPC codes, named hybrid LDPC codes, is introduced. Their asymptotic analysis for memoryless symmetric channel is performed, and leads to code parameter optimization for the binary input Gaussian channel. Additionally to a better waterfall region, the resulting codes have a very low error-floor for code rate one- half and codeword length lower than three thousands bits, thereby competing with multi- edge type LDPC. Thus, hybrid LDPC codes allow to achieve an interesting trade-off between good error-floor performance and good waterfall region with non-binary coding techniques. In the second part of the thesis, we have tried to determine which kind of machine learning methods would be useful to design better LDPC codes and better decoders in the short code length case. We have first investigated how to build the Tanner graph of a code by removing edges from the Tanner graph of a mother code, using a machine learning algorithm, in order to optimize the minimum distance. We have also investigated decoder design by machine learning methods in order to perform better than BP which is suboptimal as soon as there are cycles in the graph. In the third part of the thesis, we have moved towards quantized decoding in order to address the same problem: finding rules to decode difficult error configurations. We have proposed a class of two-bit decoders. We have derived sufficient conditions for a column-weight four code with Tanner graph of girth six to correct any three errors. These conditions show that decoding with the two-bit rule allows to ensure weight-three error correction capability for higher rate codes than the decoding with one bit.
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Lucile Sassatelli. Codes LDPC multi-binaires hybrides et méthodes de décodage itératif. Théorie de l'information [cs.IT]. Université de Cergy Pontoise, 2008. Français. ⟨tel-00819413⟩

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