Probabilistic search of nonbinary LDPC codes for distributed video coding

This paper examines the applicability of the genetic algorithm (GA) to generation of nonbinary low-density parity-check (LDPC) codes over GF(q) which is suitable for distributed video coding (DVC). Error probability distribution in side-information of the DVC is approximated by Gaussian and Laplace distributions, and then a fitness of an LDPC matrix is defined under this approximation. The GA is designed to avoid LDPC matrices having small girth in the Tanner graph and to obtain column vectors with appropriate Hamming weight. This paper also outlines a parallel computation system using a cluster of personal computers to implement the proposed GA with reasonable cost. Evaluation shows that the decoded symbol error rate (SER) of the generated LDPC code is lower than that of randomly constructed LDPC code with the minimum girth of six. For example, in a 256-ary channel of Gaussian error distribution with standard deviation δ = 3.00, the decoded SER of a rate-1/2 code generated by the GA is 3.0 × 10^-4, while that of a randomly constructed code is 4.4 × 10^-1.