Research On Decoding Algorithmes And Construction Of Check Matrix Of Structurd LDPC Codes Constructed Algebraically

In this paper，we mainly research on LDPC codes’ construction of check matrix、decoding algorithm、performance analysis and eliminating error floor. It is illustratedthat the structured LDPC codes constructed algebraically have much lower encodingcomplexity for their cycle or quasi-cycle constructions compared with the LPDC codesconstructed randomly, while their large row weight and more redundancy checks keepthe same or better performance. In this paper, we further verify, using many ofsimulation data, that various modified decoding algorithm can reduce the decodingcomplexity effectively with small performance loss, and we could get that thebit-flipping decoding algorithm based on hard decision in structured LDPC codes’decoding have much lower decoding complexity and nearly same performance, which issuitable for high speed decoding and hardware implementation. Besides, the DensityEvolution and Gaussian Approximation are introduced into analysing the decodingperformance. The simulation data are identical with the before-mentioned results, and italso demonstrates that the Density Evolution is a accurate and efficient method forperformance evaluation.The LDPC codes’ error floor restricts their further progress in high speedcommunication system、deep space communication system、magnetic storage andoptical communication system etc. In this paper, we study and research the constructionof cycles and trapping sets which are the principal criminal for error floor. When wefind the cycles and trapping sets in Tanner graph, two methods are used for eliminatingerror floor, one is eliminating the cycles in check matrix; the other is making use oftrapping sets for auxiliary decoding. Through the simulating, when the length of codesis not long, and the constructions of the check matrix are not complex, both of the twomethods can eliminate the error floor from10^-5to10^-8or much lower.