Low-density parity -check codes and iterative decoding algorithms for input -constrained channels and channels with memory.

Abstract

The quest to construct good error-correcting codes that are amendable to low complexity decoding has been vigorously pursued since 1948 when Shannon introduced the channel coding theory. A class of codes, known as Low-Density Parity Check (LDPC) Codes, have received a lot of attention of late, due to their near capacity-achieving performance while employing low-complexity iterative decoding algorithms. We have applied Gallager's method and typical set decoding method to evaluate lower bounds on the maximum achievable rate and error exponents of LDPC codes when used over the binary erasure channel and the binary-input AWGN channel. The results indicate that LDPC codes can achieve performance nearly as good as the best codes when used on these channels. In this dissertation, we also investigate some applications of LDPC codes and their iterative decoding algorithms. First, we study the performance of LDPC codes when used over the block interference channel with a receiver that performs joint channel state estimation and information bit decoding. The theoretical performance of the algorithm is evaluated using the density evolution technique which reveals the dependency of the system performance on the code degree sequence. In the second part of the dissertation, the concatenation of an outer LDPC code with an inner runlength-limited (RLL) code is investigated. A message-passing algorithm is employed to exchange soft information between the two decoders. The algorithm efficiently exploits the redundancy inherent in the RLL code resulting in additional coding gain over the unconcatenated LDPC codes. The density evolution technique is extended to analyze the performance of such a system.