Research On Construction Of LDPC Codes Based On Circulant Permutation Matrix

Low-density Parity-check (LDPC) codes are considered as a class of linearspace-time block codes with near Shannon limit performance, and have become a majortechnology in the channel coding field recently. As an attractive class of LDPCcodes,Quasi-cyclic LDPC are well suitable for certain practical applications since theycan easily be encoded with linear complexity and need much less storage space. Withthe intensive study, LDPC codes have potential applications in the area such as Ethernet,wireless communication, digital storage and optical network.This paper is intended to investigate the construction of QC-LDPC codes based oncirculant identity matrix. The concrete content can be divided into the following severalparts.1. The digital communication system and channel coding theory of knowledgeare decrypted briefly. And an overview of QC-LDPC codes Research is presented.2. The basic definition, construction method and decoding principle of LDPCcodes are illuminated systematically.3. A summary of characteristic on QC-LDPC codes is given. On the basis of girthjudge theorem, a random girth search algorithm is used to construct a class ofQC-LDPC codes which have performance close to random codes. An optimization isapplied to the distribution row weight and column weight for normal QC-LDPCcodes.Simulation results indicate that the codes optimized can improve finding errorand correcting error performance effectively.4. By imposing n-fold expansion on the parity-matrix of QC-LDPC code from thelattice, we obtain a kind of high code-rate QC-LDPC codes. A novel method withshortened codes from lattices is proposed to increasing the girth. Simulation resultsshow that the performance of expanded code based on shortened codes has been greatlyimproved.