Research On The Construction Of Mother Matrix Of Quasi-cyclic Low-Density Parity-Check Codes

Low density Parity code whose performance approaches to Shannon limit, is a channel code of low encoding complexity, strong error control ability, has been widely applied in all kinds of communication system. Quasi-cycle code is a kind of LDPC codes, with circulatory structure, and linear encoding complexity which reduce the hardware requirement, thus they are more practical than random ones.According to analyse the basic concepts and properties of LDPC codes, we realize that in the viewpoint of decoding algorithm, the girth is bigger the performance is better. The structure of QC-LDPC codes shows close relation to corresponding mother matrix. According previous studies, if mother matrix containing inevitable cycle, using certain search algorithm to eliminate avoided cycle in mother matrix, we can construct QC-LDPC codes that the girth equals the length of inevitable cycle. That means the inevitable cycle of mother matrix is bigger the the girth of its QC-LDPC codes is bigger, the codes performance is better.Therefore, we focus on the construction of mother matrix containing inevitable cycle. First, analyzing theorem and properties of cycle, we draw that the reason of containing inevitable cycle. Second, analyzing the structure of sub-matrix included inevitable cycle, I design a kind of algorithm to detect the length of mother matrix inevitable cycle. Using related theorems we can calculate the size of mother matrix under different length of inevitable cycle. Then, I give a kind of construction method based on block and line. To combine the method with the detection methods and Backtracking, I can construct mother matrix quickly under the larger inevitable cycle (3, k) codes. At last, I compare using the mother matrix generated QC-LDPC codes with PEG construction method generated randomly LDPC codes and Fossorier's traditional QC-LDPC codes. The performance of constructed QC-LDPC codes is far beyond the traditional QC- LDPC codes, and the same with the performance of the random LDPC codes, even better than random codes in the long codes condition, so achieve the expected effect.