LDPC Decoding Based On Statistical Mechanics Of Spin-Glasses: A Study

Abstract

In this paper, the LDPC (Low Density Parity Check Codes) decoding algorithm has been investigated using statistical mechanics properties. The main advantage of LDPC codes is their performance that works in near Shannon limit, and the ability to use iterative decoding algorithms. In 1989 N. Sourlas showed that error-correcting codes can be considered as Spin-Glass systems thus making it possible to model LDPC codes as an Ising model, opening the way for information theorists to solve coding problems with the power of statistical mechanics. According to N. Sourlas, the decoding problem can be solved by finding the ground state of the corresponding spin-system Hamiltonian. The main goal of this paper is to review as simple as possible the statistical properties of LDPC codes, and how it is used especially facing the decoding problem.