Combinatorial optimization for improving QC LDPC codes performance

Techniques for searching for good quasi-cyclic (QC) LDPC block codes of short and moderate lengths which are suitable for practical purposes are studied. To facilitate implementations only codes whose parity-check matrices having bidiagonal structure of their submatrices and consequently having low encoding complexity are considered. The problem of finding QC LDPC codes with the near-optimum frame or bit error rate performance is split into two independent steps: searching for the near-optimum column degree distribution of the parity-check matrix together with the best base matrix for this degree distribution and searching for the near-optimum labeling of the chosen base matrix. Sets of parameters and criteria for both steps are introduced and discussed. They allow further reduction of the search complexity without significant loss of the search optimality. New QC LDPC block codes of various code rates are obtained and their BER and FER performances are compared with those of the LDPC block codes as well as the turbo codes defined in the IEEE 802.16 WiMAX standard.