Research On Construction And Decoding Algorithm With Low Error Floor Of LDPC Codes

Low-Density Parity-Check (LDPC) codes are a class of capacity approachingerror-correcting codes. By using low complexity sum-product algorithm, LDPC codescan get near Shannon limit decoding performance with almost all errors detectable. Dueto the advantages of LDPC codes, such as low complexity of decoding and strongerror-detection capacity, their applications in reliable communications have receivedgreat interests in recent years and have become one of most attractive field in channelcoding field.Error floor is an important issue in the theory of LDPC codes and the study ofiterative decoding algorithms. It is characterized by the error rate in high SNR regionsuddenly drops at a rate much slower than that in the region of moderate SNR. In thisdissertation, error floors of LDPC code and an iterative decoding algorithm withbacktracking are investigated. Main works are summarized as follows:1. Theory of LDPC codes and its construct methods are briefly illuminated, andintroductions to the message passing algorithm of different channels are given. Errorfloor is studied based on some properties of the application in LDPC codes, and aparticular structure in the codes’ Tanner graphs known as trapping sets is explained,which prevents decoding from converging to the correct codeword.2. A hybrid method, which combines code construction and iterative decoding tocombat the error-floor problem, is proposed. In the stage of code construction, analgorithm to improve the minimum distance of codes by eliminating distance sets isproposed. And in the stage of decoding, a modified two-stage BP (TS-BP) algorithm isproposed, the decoding performance of the method can approach the union performancebound calculated by the distribution of the low weight codewords.3. A technique to break trapping sets while decoding is thoroughly analyzed.Based on decoding results leading to a decoding failure, some bits are identified in aprevious iteration and flipped and decoding is restarted. This backtracking may enablethe decoder to get out of the trapped state. The technique is applicable to any codewithout requiring a prior knowledge of the structure of its trapping sets.