Iterative detection and decoding for non‐binary LDPC coded partial‐response channels with written‐in errors

In this study, the authors investigate the performance of iterative detection and decoding for non‐binary low‐density parity‐check (LDPC) coded partial‐response (PR) channels, where written‐in errors are present to introduce bit‐flipping to LDPC code bits prior to the transmission over PR channels. From a probabilistic perspective, the written‐in errors are modelled as the output of a binary symmetrical channel (BSC) with crossover probability equal to the write error probability. Several iterative receivers are presented for the considered system. Specifically, the authors propose a symbol‐level Bahl‐Cocke‐Jelinek‐Raviv (BCJR) channel detector based on a sectionalised representation of the joint BSC and PR trellis to produce directly the soft information of non‐binary LDPC code symbols, thus avoiding suboptimal symbol/bit log‐likelihood ratio conversions as required in bit‐level detection schemes. Simulation results show that the proposed symbol‐level iterative receiver provides much better bit‐error‐rate performance over bit‐level schemes. Moreover, the proposed receiver enables non‐binary LDPC codes to achieve a notable coding gain over their binary counterparts for channels affected with written‐in errors.