Optimization of Bilayer Lengthened QC-LDPC Code for Relay Channel Based on Differential Evolution

A novel optimization algorithm to design a bilayer lengthened QC-LDPC code for relay channel is proposed in this paper, which combine differential evolution algorithm and bilayer graph for LDPC codes. We aim to construct QC-LDPC codes with best girth(maximum girth and minimum numbers of shortest cycles)both at relay node and destination node. Proposed algorithm is composed of two steps, first the exponent matrix of QC-LDPC code for lower graph is searched by differential evolution algorithm, then the exponent matrix of QC-LDPC code for overall graph is also found by differential evolution algorithm based on the obtained exponent matrix for lower graph. Simulation results verify the validity of proposed algorithm. Constructed QC-LDPC codes may perform well both at relay node and destination node.