On The Construction Of LDPC Codes Free Of Small Trapping Sets

Low Density Parity Check Codes(LDPC)is a linear block code for a class of sparse parity check matrices proposed by Dr.Gallager in 1963.LDPC codes is a channel coding that is close to the Shannon limit.Compared with the Turbo code,LDPC codes has many advantages and wide application prospect.among the design of structured LDPC codes,the most interesting one is called protograph LDPC codes.By lifting method,the original LDPC codes is constructed from a smaller base graph,and then the LDPC codes has a quasi cyclic structure,also known as the QC-LDPC codes.QC-LDPC codes is easy to store,and has a good advantage in the realization of the code.Due to these advantages,QC-LDPC codes have attracted the attention of many researchers and become the standard of lots of communication and storage systems.In iterative decoding,the error performance of the high SNR region will be a sudden deterioration,which is called error floor.The reason of error floor is mainly the existence of small trapping sets.Many researchers are committed to reduce the error level of LDPC codes.This paper mainly focuses on the problem of the small trapping sets of LDPC codes,and analyzes the conditions of the formation of small trap sets,and eliminate the existence of small trapping sets from the perspective of the structure,so as to improve the performance of the code and improve the reliability of information transmission.In this paper,we focus on the LDPC codes(5,3)trapping sets and(7,3)trapping sets,and present a method to construct(3,k)girth eight quasi-cyclic LDPC codes with low error floor by removing the small trapping sets from the Tanner graph.To address this issue,we analyzed the relationship between eight cycles and small trapping sets of Tanner graphs based on fully connected mother matrices without parallel edges and found that if some certain eight cycles are absent in the Tanner graphs,some certain small trapping sets like(5,3)trapping sets and(7,3)trapping sets can be avoided naturally.The above trapping sets is removed by searching algorithm indeed.The experimental simulation shows favorable error rate performance with lower error floor over AWGN channels.