Research On LDPC Codes Check Matrix Structure And Its Decoding Algorithm

Low density parity check(LDPC) codes is a new kind of linear block codes, sinceldpc codes were found to be a class of progressive good code that very close to theShonnon limit, it has caused a great sensation. LDPC codes’ coding structure is simple, wecan use iterative algorithm for decoding, when codes’ length increased,the decodingcomplexity didn’t increase with it, Compared with Turbo codes, LDPC codes has lowererror rate, can be decoded in parallel, the decoding delay is small, with these advantages,the LDPC code has become a research focus in the field of channel coding. in this paper,we done related research on construction of check matrix and Improved decodingalgorithm, the main contents are as follows:(1) Through the research on construction algorithm of the excellent performance ofLDPC codes, this paper made two improvements on PEG algorithm: used PC (Polynomialof Cycle) labeling method combined with PEG algorithm to construct a random code,compared with the PEG algorithm, it improved the performance of LDPC codes under therequirements of girth; use the quasi-cyclic codes (Quasi-Cyclic) construction method tomake LDPC codes, the parity check matrix is composed of multiple block cyclic shiftmatrix, this special structure makes it easy to efficient coding and can realize partialparallel decoding in engineering. The experimental results show that the PC labelingmethod can reduce many short cycles of PEG algorithm, the quasi-cyclic codes(Quasi-Cyclic) construction method realize fast coding and fast encoding under thepremise of ensuring the decoding performance quite.(2) For the research of LDPC decoding algorithm, this paper implements a simplifieddecoding algorithm based on node scheduling. Finite length code would exist short cycle,It will affect the decoding performance, node scheduling algorithm is that when thenumber of iterations is half of the local girth of a variable node, we must stop updatemessage,up to the maximum girth equal the double of the iterations, we update all nodesmessages, node scheduling algorithm makes iterative times of the independent messagesas large as possible. When the check node update message,only select a finite minimumabsolute value use to calculate, compared with the MS algorithm, reduce the performanceloss caused by approximate calculation, also reduces the algorithm complexity. Theexperimental results show that the improved algorithm compared with the BP algorithm,can improve the decoding performance, reduces the number of iterations.