The Study Of Low Complex Structure And Decoding For LDPC Codes

LDPC codes are the focal points in the research areas of channel coding. They have been attracting much attention in current and future digitial communication systems due to their Shannon limit-approaching performance and implementary potential of high speed encoding and decoding. Although some delightful achievements on theory and application research of LDPC codes have been obtained, construction of LDPC codes and low complexity docoding algorithms are the main bottleneck in practical systems. The affection of cycles in Tanner graph on construction of LDPC codes is gradually understood by researchers, but deep and systematic studies are still required. In addition, many urgent problems need to be solved for decoding algorithms on the pursuing of good tradeoff among performance, complexity and implementation speed.Based on the structure of Quasi-Cyclic (QC) codes and Irregular Repeat Accumulate (IRA) codes, this thesis analyzed cycle structure in Tanner graph, and studied the construction of LDPC codes with low encoding complexity and the decoding algorithms with fast convergence speed and low complexity. The main work and contribution are summarized as follows:At first, this thesis analyzed the structure characters of QC-LDPC codes, and adopted the idea of constructing quasi cyclic extented LDPC (QC-E-LDPC) codes with base matrix and shift matrix. By discussing various transformations of cycles during extending base matrix, a series of theorems which could be exploited for increasing the length of cycle and decreasing number of short cycles were proposed and proved. These theorems provided the theoretical foundation for construction of QC-LDPC codes. Moreover, a novel algorithm was developed by optimizing cycle structure for constructing QC-E-LDPC codes. The upper bound of girth of QC-E-LDPC codes is three times larger than the girth of codes associated with the base matrix. Compared with existing algorithms, the proposed method can easily construct LDPC codes with large girth, excellent performance and low complexity.Secondly, since the existing of large number of codewords with low-weight for IRA codes would result in high error floor and undetected error probability, this thesis indicated that a well-constructed LDPC codes should reduce the number of low-weight codewords as more as possible while increasing the girth. From this point of view, the rules of distribution of low-weight codewords for IRA codes and IRA-like codes were summarized and proved, when variable nodes were introduced via various connection modes. All these conclusions offered the theoretical support for constructing IRA codes with optimal weight-distribution and large cycles. Furthermore, a new construction algorithm with cycle optimization-constraint was presented for IRA-like codes by introducing the ideal of cycle analysis and quasi-cyclical extension. The proposed method is flexible to code design. The analysis show that the constructed codes not only achieve almose the same performance as the computer-generated random LDPC codes, but also have much lower encoding complexity. Therefore, the constructed codes are good candidates in practical applications.Thirdly, considering that the oscillation of Extrinsic Log-Likelihood-Ratio (Ex-LLR) can deteriorate the performance of the parallel decoding algorithm based flooding message passing schedule, a modified parallel decoding algorithm was proposed for LDPC codes. The proposed algorithm eliminated the oscillation of Ex-LLR by means of the correct-erase processing. On the other hand, it exploited joint syndrome calculation and stationarity detection of means of the Ex-LLR as the stop criterion. The proposed algorithm dramatically decreases the iteration number and decoding complexity, while improving the performance of flooding decoding algorithm.Fourthly, a fast decoding algorithm was developed for QC-LDPC codes by combining the grouping serial message passing schedule and code structure, and the grouping rule of variable nodes was also established for the new decoding algorithm. The simulation and analysis results demonstrate that the proposed decoding algorithm not only has the advantage of serial message passing schedule, but also efficiently improves the speed of iterative decoding algorithm. So it is a fast and low complexity decoding algorithm.Finally, the thesis discussed the implementation of encoder and decoder for the proposed IRA-like codes in Field Programmable Gate Array (FPGA).