The invention and development of Low-Density Parity-Check Codes (LDPC) make people achieve reliable communication approaching Shannon's capacity limit at effective power cost. LDPC codes is one of the most attractive channel codes in modern coding field.In this dissertation, some key problems of Low-Density Parity-Check (LDPC) codes are investigated with theoretical analysis and simulation. The main fruits are summarized as follows:The characters for LDPC codes are systematically summarized; The equations for updating messages of different decoding algorithms of LDPC codes are induced. Based on principles of the evolution of different message-passing algorithms, we proposed an optimization method of finding good degree distribution pairs for LDPC codes.Combining the theory analysis and simulation of the serially concatenated system of BCH codes and LDPC codes; serially concatenated system under different decoding algorithms are performaced; we also proposed the detection algorithms adapted to be implemented using hardware in serially concatenated system.