Usage of LDPC Codes in a Gilbert Channel

Abstract

Although low-density parity-check (LDPC) codes in modern communication standards have been extensively studied over a memoryless channel, their burst error correction capacity in channels with memory has yet to be thoroughly analyzed. The conventional approach to transmission in channels with memory uses interleaving within a buffer of several codewords. However, such an approach reduces the efficiency of the redundancy embedded by the error-correcting code. It is known from information theory that considering channel memory during decoding allows the transmission rate to be increased. An evaluation of the decoding error probability of different types of low-density parity-check codes in channels with memory is presented along with estimates of minimum distance and burst error correction capability for the considered codes. The decoding error probability is estimated for conventional decoding with deinterleaving and decoding taking channel memory into account. The decoding error probability is estimated for several parameters of a channel with memory and different buffer lengths. The obtained results reveal the absence of the unique decoding approach for all parameters of the channel with memory. The best decoding error probability is determined by the degree of channel memory correlation.