Research On LDPC Coded Modulation For High Data Rate Transmission

This thesis studies the issue of efficient encoding and decoding algorithms for LDPC codes and the analysis and design issue of Low-Density Parity-Check (LDPC) coded modulation for high data rate transmission. LDPC codes are Shannon-Capacity-Achieving linear block codes, which can even beat turbo codes at long block length. Compared with turbo codes, LDPC codes have a simple "belief propagation" decoding algorithm, which can be easily adopted for parallel implementation. Thus LDPC codes are regarded as a challenge to turbo codes and are very promising in many applications.In this thesis, first we introduce the structure of LDPC codes, including the structures of irregular LDPC codes and LDPC codes over Galois fields. We present a kind of generalized LDPC codes over set {0,1,…,2~ρ-1}.We then discuss the issue of efficient encoding and decoding algorithms for LDPC codes. With respect to the encoding issue, we introduce the linear time encoding algorithm for LDPC codes with semi-random parity check matrices, and propose the linear time encoding algorithms for generalized LDPC codes over set {0,1…,2~ρ-1} and cycle GF(2~ρ) codes. With respect to the decoding issue, we introduce thesum-product decoding algorithm and log-domain decoding algorithm for binary LDPC codes. We also introduce the Fast-Fourier-Transformation-based decoding algorithm and log-domain decoding algorithm for LDPC codes over Galois fields. We present the Fast-Fourier-Transformation-based decoding algorithm and log-domain decoding algorithm for generalized LDPC codes over set {0,1,…, 2~ρ-1}.We then give a brief discussion on the structures of LDPC coded modulation systems and analyze the receiver and the system capacities. We propose an equivalent model for the receiver of binary LDPC coded BICM. Using this model, the distribution of the outgoing Log Likelihood Ratio (LLR) messages from the receiver can be formulated by mixed symmetric Gaussian distributions. Then, we introduce the principle and application of density evolution (DE) and extrinsic information transfer (EXIT) chart technology for the analysis and design of binary LDPC coded modulation.We also discuss the principle of Gaussian approximation algorithm for the analysis and design of binary LDPC coded modulation, including the All-Gaussian Approximation (AGA) and Semi-Gaussian Approximation (SGA). We present a novel method which designs binary LDPC coded modulation using the SGA algorithm and using this method we have designed several LDPC codes with a variety of rates for LDPC coded BICM system with 8PSK modulation. Design results and simulation results show that this method is more exact than the EXIT and AGA algorithm and is simpler than the DE algorithm. This method offers a better tradeoff between the performance issue and the computation complexity issue. Finally, we discuss the principle of Monte Carlo simulations for infinite-length LDPC codes over Galois fields and present the principle of Monte Carlo simulations for infinite-length generalized LDPC codes over set {0,1,…,2~ρ-1}. Monte Carlo simulation results and performance simulation results show that generalized LDPC codes over set {0,1,…,2~ρ-1} have good performance.