Research On Two-bit Bit Flipping Decoding Algorithms Based On Collective Error Correction

With the rapid development of modern information technology, the requirement of digital communication system is becoming more and more high. And low density parity check codes have been proposed in the communication field. LDPC codes have the characteristics of low complexity, strong error correction ability and so on. The channel capacity can approach Shannon limit by belief propagation iterative decoding. In the modern digital communication system, the error correction code decoding performance have a great impact on the communication system. The frame error rate of LDPC codes is less than1210-and even much lower. And the improvement of LDPC codes decoding performance become the focus of people’s attention. In general, it is mainly related to two factors on the improvement of decoding performance, on the one hand the speed of decoding is enhanced, on the other hand, the frame error rate of decoding is reduced. The paper mainly studies the bit flipping decoding algorithm of LDPC codes and error configurations of Tanner graphs of LDPC codes. The two-bit bit flipping decoding algorithm, the definition of trapping set profile and the construction process of trapping set profile are given. The selective scheme of TBF decoding algorithms are studied for different trapping set profiles. In this paper, the main contents are summarized as follows:1. The development of the digital communication system and the current state on research of LDPC code are introduced systematically. Tanner graph representation of LDPC codes and related concepts of trapping set are described in detail. It is analyzed summarily about two typical decoding algorithms of LDPC codes.2. On the basis of bit flipping decoding algorithm, the two-bit bit flipping decoding algorithm one is given by one additional bit at a variable node about problems that the algorithms cannot be successful convergence for some error configurations. They validate the successful convergence of the algorithm with examples after several iterations.3. On the basis of bit two-bit bit flipping algorithm one, the problems are found about decoding failure by analyzing other error configurations. The two-bit bit flippingalgorithm two is given by one additional bit at a check node. Meanwhile, They validate the successful convergence of the algorithm with examples after several iterations. The successful convergence conditions of decoding are given by analyzing algorithms. The simulation of two-bit bit flipping decoding algorithm is realized in BSC channel, and the simulation results show that the performance of the TBF decoding algorithm is supeirior to the BP.4. For the different error configurations, the definition and construction of trapping set and trapping set profile are presented in combination with collective error correction. The construction are expanded processes by additional a variable node in the subgraph. And the graph set sequence of excluding trapping set is presented. In the end, the trapping set profiles of a Tanner code graph are presented by recursion.5. The method of selective TBF algorithms are given about eliminating trapping set profiles in Tanner code on the basis of different error configurations. The effective methods of selective TBF algorithms are presented by analyzing difference of selective single TBF algorithm and selective multiple TBF algorithms. In the end, The selective multiple TBF decoding algorithms are realized based on different trapping set profiles, and the simulation results prove the validity of the algorithms.