Chapter 4 - LDPC decoding algorithms

Abstract

Low density parity check (LDPC) decoding algorithms are very well known to be of an iterative nature based on convoluted connections between variable and check nodes. Each of these nodes perform complex mathematical operations during the decoding process. The complexity of nodes and its interconnections significantly impact the hardware architecture of the decoder and eventually its performance. Therefore, it is of paramount importance to reduce the complexity of these nodes and inter-node connections, and yet have minimal impact on performance loss. This chapter presents some of the standard LDPC algorithms along with reduced complexity decoding algorithms, namely, simplified message passing and modified min-sum algorithms. The simplified message passing algorithm provides a trade-off between implementation complexity and decoding performance using hard/soft-decision based algorithms. The modified min-sum algorithm has reduced complexity and achieves better bit error rate performance compared to the original min-sum. The operation and performance of these algorithms are presented in detail.