Research On Construction And Application Of LDPC Codes

Low-Density Parity-Check (LDPC) codes are a class of linear block error-correcting codes based on the sparse parity-check matrix. LDPC codes have Shannon-limit approaching performance by using sum-product decoding algorithm, simple structure, low complexity of parallel iterative decoding and facilitate hardware implementation. They have been received more and more attentions. In this thesis, the construction of the check matrix and the decoding algorithm of LDPC codes are investigated. And the bit-error-ratio (BER) performance of the LDPC codes in the Pulse Code Modulation/Frequency Modulation (PCM/FM) reentry telemetry system is simulated and analysed.The main contents can be summaried as follows:Firstly, the present situation of the development about the LDPC codes is introduced. Then the concepts about the LDPC codes are presented in datail, including its definition, Tanner graphs, regular codes and irregular codes, Quasi-Cyclic LDPC codes, the common methods of coding and so on.Seceondly, the construction methods of LDPC codes, random method and structural method, are discussed emphatically. On this basis, combining the perfect cyclic difference sets with the quasi-cyclic codes, a new method for constructing QC-LDPC codes based on cyclic difference sets is proposed. There is no short girth with length of 4 and 6 in the parity-check matrix constructed by this method. Simulations show that, under the AWGN channel and the BP decoding algorithm, our QC-LDPC codes are better than the random LDPC codes in the bit error rate and they are more proper for hardware implementation.For the issue of determining cyclic shift coefficients of the quasi-cyclic sub-matrix in the quasi-cyclic low density parity check, this paper presents a method based on Z-shape and arithmetic progression sequence to compute the cyclic shift coefficients. By this method, cyclic shift coefficients can be expressed in simple analytic expressions, and cycles of length 4 in parity check matrix are eliminated.Then, the author introduces the decoding algorithms of the LDPC codes, mainly analysis the BP and Log-BP decoding algorithm. In this paper, an improved decoding algorithm is proposed. When the SNR is lower than the decoding threshold, the iterative times is decreased by the improved method.Finally, the present situation of the development about the reentry telementry technology is introduced and the model of the PCM/FM telemetry system based on LDPC codes is proposed. Meanwhile, we give the simulations of the LDPC codes under the PCM/FM telemetry system. The results show that, compared to non-encode system,the BER performance of PCM/FM reentry telemetry system based on LDPC codes has been improved greatly. By comprehensive consideration, the BER performance and complexity, normalized minimai sum-decoding algorithm is comparatively practical with BF, BP, Log-BP and minimai sum-decoding algorithm.