Research On LDPC Codes With Low Error Floor Based On Graph Covers And Cyclic Liftings

LDPC (Low-Density Parity-Check) codes are currently a kind of error-correctingcodes limiting to Shannon limits. Due to the advantage of LDPC codes, such as gooddistance features, low decoding complexity, they have attracted a lot of attentation inchannel coding. With the intensive research, LDPC codes have potential applications inthe field such as wireless communication, deep space communications, optical fibercommunications and other domains.Based on the existing knowledge of error floor of LDPC codes, mainly through theanalysis of the structure of trapping sets, we study the two ways of tanner graph coversand cyclic liftings in which we can reconstruct the structure of code in order toeliminate tapping sets. Some results are obtained and summarized as follow:1. The basic principle of LDPC codes and its Tanner graphs are briefly illuminated.Introduced a simple classification of LDPC codes and given decoding algorithm ofcommonly used channel of LDPC codes.2. By making a detailed analysis of the trapping sets’s structure of error floors, amethod of tanner graph covers is given, which eliminates main tapping sets by means ofdestroying the structure of trapping sets. Emulation results show that this method caneliminates most of tapping sets and reduces the error floor of LDPC codes.3. Through an analysis of the mathematical properties of cycles in check matrix, amethod of cyclic liftings is researched, by constructing N-Lifting graph to eliminatesmall cycles in original graph and generate N-Lifting codes, which eliminatescorresponding trapping sets that is composed of the small cycles. Emulation resultsshow that this method can eliminate more trapping sets by increasing N and play a goodeffect.