On Design of Optimized Low-Density Parity-Check Codes Starting From Random Constructions

In this paper we present a novel two step design technique for Low Density Parity Check (LDPC) codes, which, among the others, have been exploited for performance enhancement of the second generation of Digital Video Broadcasting- Satellite (DVB-S2). In the first step we develop an efficient algorithm for construction of quasi-random LDPC codes via minimization of a cost function related to the distribution of the length of cycles in the Tanner graph of the code. The cost function aims at constructing high girth bipartite graphs with reduced number of cycles of low length. In the second optimization step we aim at improving the asymptotic performance of the code via edge perturbation. The design philosophy is to avoid asymptotically weak LDPCs that have low minimum distance values and could potentially perform badly under iterative soft decoding at moderate to high Signal to Noise Ratio (SNR) values. Subsequently, we present sample results of our LDPC design strategy, present their simulated performance over an AWGN channel and make comparisons to some of the construction methods presented in the literature.