Quasi-cyclic Ldpc Codes, Theoretical Research And Constructed

Low-density parity-check codes have been one of the major research topics in the information and communication field. It is a class of channel codes based on graphs and can achieve good performance close to the Shannon-limit when iteratively decoded, which perform better than the Turbo codes. In this dissertation, the theory, design of QC-LDPC codes is studied and a new method of constructing quasi-cyclic LDPC codes based on circulant permutation matrices from the difference family is proposed. The constructed codes are with no short cycle of length4 or in other word, their girth is at least 6; with large flexibility in choose of code rate. Because of the special quasi-cyclic structure, this allows simple encoding and small size of required memory, while maintaining good performance. Simulations show that the constructed QC-LDPC codes with sum-product iterative decoding perform well under BPSK modulation over an additive white Gaussian noise (AWGN) channel. The main works are as follows:1. Introducing the definition and unique advantages of LDPC codes,Tanner graph representation and girth of the parity-check matrix,the present research situation of QC-LDPC codes.2. Introducing the definitions as well as the structure method of the perfect cyclic difference sets, cyclic difference sets and disjoint difference sets.3. The structure of QC-LDPC codes and the structure constructions of parity-check matrix based on circluant permutation matrices are researched.4. The bit-error rate performance of the constructed QC-LDPC codes is demonstrated by computer simulations.