Soutenance de thèse : Bilal Shams

Salle de soutenance

Université de Cergy-Pontoise, site des Chênes 2, salle des thèses


In this thesis we present our work in the domain of non-binary decoding algorithm  for general classes of non-binary LDPC codes.

Low-Density Parity-Check (LDPC) codes were originally presented by Gallager in 1963, and after some fundamental theoretical advancements, they were considered in standards like DVB-S2, WI-MAX, DSL, W-LAN etc. Later on, non-binary LDPC (NB-LDPC) codes were proposed in the litterature, and showed better performance for small lengths or when used on non-binary channels. However, the advantages of using NB-LDPC codes comes with the consequence of an heavily increased decoding complexity. For a code defined in GF(q), the complexity is of the order O(q^2). Similarly, the memory required for storing messages is of order O(q). Consequently, the implementation of an LDPC-decoder defined over a field order q > 64 becomes practically impossible.

The main objective of the thesis is to develop reduced complexity algorithms for non-binary LDPC codes that exhibit excellent performance and is practically implementable. For better decoding performance, not only the decoding algorithm is important, but also the structure of the code plays an important role. With this goal in mind, a new family of codes called cluster-NB-LDPC codes was developped and specific improvements of the NB decoder for cluster-NB-LDPC codes were proposed. Our principal result is that we were able to propose decoders for cluster-NB-LDPC codes with reduced complexity compared to usual decoders for NB-LDPC codes on fields, without any performance loss in error correction capability.

Composition du jury

  • Emmanuel Boutillon, professeur des Universités, Université de Bretagne Sud, Lorient, rapporteur
  • Laura Conde-Canencia, maître de conférences , Université de Bretagne Sud, Lorient, rapporteur
  • Jossy Sayir, professeur, University of Cambridge, rapporteur
  • David Declercq, professeur des Universités, ENSEA Cergy, directeur de thèse
  • Vincent Heinrich, ingénieur, ST Micro-Electonics, encadrant
  • Didier Demigny, professeur des Universités, ENSSAT, Lannion, examinateur
  • Valentin Savin, CEA - LETI, Grenoble, examinateur