Research On Decoding Algorithms And Theoretical Analysis Of LDPC Codes

In this paper, decoding algorithms of LDPC codes are investigated. An introduction of LDPC codes are given, including the basic concepts and iterative decoding algorithms of LDPC codes, especially the Log domain Belief Propagation (BP) iterative decoding algorithm and its modified algorithms, APP algorithm, Min-sum (MS) algorithm, etc. Based on iterative decoding, a modified algorithm called shuffled iterative decoding is analyzed briefly, focusing on its decoding algorithm, hardware implementation and theoretical performance analysis. The major work and innovations can be classified into the following points:(1) In order to reduce the decoding delay or the decoding complexity, employ the idea of shuffling to BP decoding, and develop two different types of shuffled BP decoding algorithms:Shuffled BP (SBP) decoding with variable node grouping and modified SBP decoding with check node grouping. The grouping strategies of SBP decoding are presented and their performances are simulated. Results show that SBP decoding algorithm has a better performance with the same decoding complexity, or a lower decoding complexity while keeping the performance unchanged. A research on shuffled iterative decoding with variable node grouping follows, while the check-node-grouping form can draw to the similar conclusions.(2) Quasi-Cyclic LDPC codes are widely used in practice, because they can greatly reduce the encoding/decoding complexity and storage space. For the Quasi-Cyclic LDPC codes using shuffled Min-sum (SMS) decoding, the decoding strategy is presented, and the hardware structure is described. The decoder includes variable node unit group, check node unit group and the memory module. A detailed explanation of decoding procedure is given, with a specific introduction on each module.(3) Gaussian Approximation (GA) algorithm is a method which gives an asymptotically analysis of LDPC codes. The dissertation uses GA algorithm to analyze the performance of LDPC codes based on SBP decoding. Under the assumption of Gaussian density, the recursive formulations of message means during the shuffled BP decoding are derived. Several LDPC code ensembles with given degree distributions is analyzed by the proposed algorithm. Numerical results show that the algorithm can verify the faster convergence property of SBP decoding effectively. In addition, it is simply described how to find the optimal degree distributions, for the purpose of constructing the parity-check matrix of LDPC codes.(4) EXIT chart is another algorithm to theoretically analyze the performance of LDPC codes in the perspective of mutual information. EXIT chart algorithm is used to analyze the performance of LDPC codes under SBP decoding. The EXIT functions of LDPC codes under BP decoding over a biAWGN channel are deduced. And with that, based on an assumption, derivations of EXIT functions are given for SBP decoding. Furthermore, we extend the assumption range, and deduced another representation of EXIT chart. The EXIT chart algorithms are simulated, and the results give a strong support of the superiority of SBP decoding.