LDPC码构造理论的研究进展

LDPC codes have a remarkable performance with iterative decoding that is very close to the Shannon limits. Representing the leading edge in the field of modern channel coding, LDPC codes are the preferred FEC codes in up-to-date digital communication and magnetic recording systems. The general design targets for constructing LDPC codes, and the theoretical bounds of girth and minimal distance of LDPC codes are summarized in this paper, based on which the existing well-known construction methods, constructive and random, are overviewed. For the constructive ones, various methods from BIBD,PBIBD,RS codes, finite fields, regular graph and group structure are compared, and for the random ones, Gallager’s original method, MacKay’s method, the heuristic algorithms based on girth distribution, bit filling and progressive edge growth (PEG), and the method based on the partition-and-shift technique are reviewed. Finally, some general and simple skills for constructing LDPC codes are briefly introduced and the future directions for constructing LDPC codes are suggested.