The Research Of Decoding Algorithms Of LDPC Codes

Low-density Parity-check codes, introduced by Gallager in 1962, are linear block codes defined in terms of a sparse parity check matrix. Gallager came out two creative viewpoints:(1) to imitate the random codes by using the random permutation and the cascade of the simple sparse parity check matrix;(2) iterative decoding technique where a prior information and channel observation are both used to compute a posteriori and a priori information. However, his excellent work was neglected by the majority of the scientific community on account of external reason for a long time. Until 1993, LDPC codes have given rise to a large interest again after C.Berrou et al. first presented Turbo codes which are parallel concatenated recursive convolutional codes and exhibit good performance. In fact, the thought of encoding and decoding of Turbo codes was very similar to the former two views. In some certain, Turbo codes are just LDPC codes. After studied, LDPC and Turbo codes have similar good performance. Furthermore, the former exceed the later. Since that time, LDPC codes have attracted one's attention and become a hotspot of researching now.The goal of this paper is to study the LDPC decoding algorithm. Firstly, The present situation of the development of error-correcting code and LDPC codes, as well as some problems in this area are pointed out. Secondly, some fundamental theories and the structure of LDPC encoder and decoder are described. According to these, some analyses for the performance of LDPC codes are presented. Thirdly, in order to increase decoding rate without any effect on bit error rate, a linear calibration is put forward which can simplify calculation and make hardware convenient without negative effect on the performance of algorithm process. At the same time, the message density evolution is given in detail. The threshold of channel's parameter is also discussed. Lastly, we propose an iterative decoding stop criterion named "early detection", which can reduce the considerable complexity of decoding process of LDPC codes. It can accelerate decoding, reduce complication and improve decoding performance through the threshold decision of bit information. Although the theory and application of LDPC codes have get along well, there are many problems need to be solved, such as the conflict between simplification and reduced performance of BP decoding algorithm. It must be admitted that LDPC codes have excellent performance. They are another upsurge in error-correcting area after Turbo codes. They have wide prospect. And LDPC codes are power competitor of Turbo codes in many communications and digital memory systems which require high reliability.