Research On Construction Of LDPC Codes Based On Balanced Incomplete Block Designs

Low density parity check (LDPC) codes have been shown to achieve remarkable performance very close to the Shannon limit, and have become a hotspot of research in the channel coding field. Several classes of LDPC codes constructed using combinatorial mathematics are not only quasi-cyclic, but also perform as well as random LDPC codes. The codes constructed can be implemented using shift registers where the complexity of encoding would be linearly proportional to the code length. This encoding advantage is particularly important in practical applications.This dissertation mainly focuses on the construction of LDPC codes based on combinatorial designs, and presents some methods for constructing quasi-cyclic LDPC codes using certain special classes of balanced incomplete block designs constructed by Bose. Some results are obtained and summarized as follow:1.The basic principle of LDPC codes is illuminated. The principles of coding and decoding for low-density parity-check codes are briefly summarized.2.The principles of block designs are briefly summarized. The incidence matrixes of the balanced incomplete block designs are analyzed. Several special classes of balanced incomplete block designs constructed by Bose are investigated.3.Two kinds of regular quasi-cyclic LDPC codes are constructed by using location vector and circulation decomposition based on certain special Bose-BIBDs by researching on structural characteristics of Bose-BIBDs'incidence matrixes. The codes constructed above perform well with iterative decoding over both AWGN and binary erasure channels.4.The method for constructing irregular LDPC codes based on Bose-BIBD is presented. By analyzing some parameters'affections on the performance of this LDPC codes with simulation experiences, the parameter-selection rules are generalized.