Study Of LDPC Decoding And Its Combined Equalization Techniques For Wireless Communication

The linear block code is called a binary low-density parity-check code if its parity-check matrix is sparse. This sort of code was originally proposed by Dr. Gallager in 1962, which is now rediscovered and attracts a large amount of interest partly due to the extreme success of turbo codes both in theory and practice. LDPC codes and turbo codes are similar in many aspects, both can extremely approach to the Shannon limits by their unique ways. Moreover, LDPC codes are relatively easy to be characterized, and can outperform turbo codes with sufficiently long block lengths. This thesis presents a comprehensive study on the performance of LDPC codes and combined equalization with LDPC codes. First, we briefly introduce the encoding structure of LDPC codes and related complexity issues, then for its decoding using so-called stand belief propagation (BP) algorithm together with the theoretical fundamentals and the practical steps achieving this goal. The performance simulations are also carried out over an additive white Gaussian noise (AWGN) and fading channels to find out the crucial factors that can seriously affect the decoding performance. In order to further improve the performance, we propose a new approach that can effectively eliminate the short cycles of the bipartite graph for the LDPC encoding. Meanwhile, we also investigate the convergence properties of iterative LDPC decoding characterized by both source and estimated symbol sets from theory and numerical simulations. Finally, we focus on the performance of combined equalization and LDPC codes, and BER results and corresponding convergence properties are thus obtained over the ISI channel by the simulations.