Performance of LDPC decoding algorithms with a statistical physics theory approach

Abstract

In 1989, N.Sourlas used the parallel that exists between the information theory and the statistical physics to bring out that low density parity check (LDPC) codes correspond to spins glass models. Such a correspondence is contributing nowadays to the similarity between the statistical physics and the error correcting codes. Hence, the statistical physics methods have been applied to study the properties of these codes. Among these methods the Thouless-Anderson-Palmer (TAP) is an approach which is proved to be similar to the Belief Propagation (BP) algorithm. Unfortunately, there are no studies made for the other decoding algorithms. The main purpose of this paper is to provide a statistical physics analysis of LDPC codes performance. First, we investigate the Log-Likelihood Ratios-Belief Propagation (LLR-BP) algorithm as well as its simplified versions the BP-Based algorithm and the λ-min algorithm with the TAP approach. Second, we evaluate the performances of these codes in terms of a statistical physics parameter called the magnetization on the Additive White Gaussian Noise (AWGN) channel. Simulation results obtained in terms of the magnetization show that the λ-min algorithm reduces the complexity of decoding and gets close to LLR-BP performance. Finally, we compare our LLR-BP results with those of the replica method.