LP Decoding Of LDPC Codes And Application In MIMO-OFDM Systems

With the rapid development of wireless communication technology, requirements for performance and rate of data transmission are becoming higher. Low-Density Parity-Check (LDPC) Codes is one kind of excellent linear error-correcting code with performance approaching the Shannon limit. In recent years, it has been a hot research field of channel coding because it has low decoding complexity and is suitable for hardware implementation. Using LDPC codes as forward error correction in wireless data transmission can effectively improve the transmission performance of wireless data transmission. Multiple input multiple output (MIMO) technique and Orthogonal Frequency Division Multiplexing (OFDM) are ideal for applications in wireless communications because of its excellent resistance to multipath channel fading performance.In this dissertation, some issues of coding are investigated, including the basic theory of LDPC codes, Space-Time Block Coding (STBC) in MIMO-OFDM system and application of LDPC codes. The main content involves the representations of LDPC codes, LDPC decoding methods and applications of LDPC codes in MIMO-OFDM systems.The main works are as follows:1) The development of the channel coding is summarized and the fundamentals of linear block codes (LBC) are investigated. Furthermore, the iterative decoding algorithms of LDPC codes are studied. On the basis of introducing the parity check matrix and bipartite graph representation of LDPC codes, its iterative decoding algorithms such as belief propagation (BP) algorithm and Min-Sum algorithm are mainly discussed.2) The linear programming (LP) decoding algorithm of LDPC codes is studied. The modeling process of LP decoding of LDPC codes is primarily described after convex hull and relaxed convex hull are introduced and then a more convenient form of computing is deduced.3) The performance of combined LP and BP decoding of LDPC codes is studied and simulated. Especially for short LDPC codes, it has been observed that BP decoding often performs better at low SNR ranges, whereas LP decoding performs better at high SNR levels. So a combined LP and BP decoding algorithm is studied, which significantly outperforms both a pure LP and a pure BP decoding algorithm throughout the whole SNR range. LP decoding is done with received signal of channel and the initial message of LDPC decoding is corrected according to LP decoding results and cascade factor. Then the final decoding codeword is obtained through BP decoding. Simulation results show that the cascade factors which making LP-BP cascade decoding algorithm to obtain optimal performance vary greatly when decoding performance of BP algorithm changes. If the maximum number of iterations of BP algorithm is different, bit error rate (BER) of LP-BP cascade decoding algorithm will be changed with the cascade factor. So the selection of the optimal cascade factor is determined by the decoding performance of the LP and BP algorithm together.4) The principle of STBC and MIMO-OFDM is studied and a MIMO-OFDM system based on LDPC codes is designed. LP and BP decoding algorithms of LDPC are applied to this system. Simulation results show that BER performance can be effectively reduced if LP and BP decoding method are applied to MIMO-OFDM systems. And good decoding performance can be achieved if short LDPC codes cooperate with MIMO-OFDM techniques over multipath channel environment.