Study On The Constructions And Decoding Algorithms For QC LDPC Codes

As one of the best known channel codes to generally achieve the Shannon channel capacity,Low-density parity-check code has been deeply studied since late 1990' s when it was rediscovered. Since then, LDPC codes, especially the binary Quasi-Cyclic LDPC codes have been adopted in many communication standards,involving IEEE 802.16 e, CCSDS, Wi MAX,GB20600, etc.In this thesis, we consider the finite field construction and decoding algorithm of binary LDPC codes. We firstly give the history of the development of channel coding theory, especially pay much attention to the achievements of LDPC codes. We mainly introduce two aspects,one is the construction based on finite field, and the other is the decoding algorithm.In the second part of this thesis, we present the fundamental principles of binary LDPC codes, as well as several classic encoding algorithms based on complete-triangle check matrix, partial-triangle check matrix and LFSR. In addition, the construction specifications,the encoding algorithms of binary LDPC codes in IEEE 802.16 e standard and the CCSDS standard are also mentioned.In the third part, totally 11 soft and hard decision decoding algorithms are involved and analyzed in detail, including LLR-SPA, Gallager LLR-SPA, Jacobian LLR-SPA, MSA,Normalized MSA, Offset MSA, Self-corrected MSA, Bit Flipping, Weighted Bit Flipping,Modified Weighted Bit Flipping and Improved Modified Weighted Bit Flipping. We give the complexity and simulation of each algorithm, as well as their comparison results with IEEE802.16 e standard and LDPC codes that we design in this thesis.Considering the construction method of binary QC-LDPC codes using finite field and several kinds of decoding algorithms, the innovative achievements that the author obtains are listed as follows:The first part of our work is that we generalize and improve the previous construction methods of binary QC-LDPC codes, which are designed based on the finite field. We get a class of QC-LDPC codes using the generalized RS codes and the sub-code of its sub-field. Construction methods and simulations of Rate Compatible QC-LDPC codes of a class of Rate Compatible QC-LDPC code are given. We give a sufficient and necessary condition when we consider the situations that there is without-girth-4 constraint and without-girth-6 constraint basing on the Rank Matrix. And we show this result actually can be applied to all QC-LDPC codes. After showing that the QC-LDPC codes based on generalized RS codes and sub-codes of its sub-field are satisfied with the without-girth-4 constraint, we give a simple search algorithm for QC-LDPC codes without-girth-6.The other work we do is that we improve the decoding algorithm of binary QC-LDPC codes in performance, especially the Self-corrected MSA algorithm. The feature of this algorithm lies in how the variable nodes are updated. According to the characteristic of the Selfcorrected MSA, two improved decoding algorithms, which we call Self-corrected SPA and Normalized Self-corrected MSA are proposed. Finally, the performance simulation of the above two modified decoding algorithms is carried out by binary LDPC codes, which are used in the IEEE 802.16 e standard and the CCSDS standard.