Contributions to the construction and decoding of non-binary low-density parity-check codes

Abstract

In the first part of this thesis, we propose a novel method to construct low-density parity-check (LDPC) codes over mixed alphabets. We do this by taking a sparse matrix consisting of disjoint submatrices defined over different subfields of a given field and linking their associated subgraphs. We also present a modified message passing algorithm (MPA) to reduce the number of redundant computations during decoding.In the second part, we present a multi-stage approach for decoding LDPC codes over Z_q, where q = p^m, p a prime and m > 1. We exploit the natural ring epimorphism that can be applied to Z_q, and perform decoding using a modified MPA on each homomorphic image of the code.Computer simulations showed that both mixed alphabet codes and the multi-stage approach yield improvements in bit error rate performance over the single alphabet codes and single-stage approach respectively, with some increase in decoding complexity.