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Quasi improvement cycle of low density parity check matrix structure and code validation

Author: ShaoMingXue
Tutor: TangYuanSheng
School: Yangzhou University
Course: Applied Mathematics
Keywords: QC-LDPC code cyclic difference set one-coincidence sequences hill-climbing algorithm
CLC: TN911.22
Type: Master's thesis
Year: 2012
Downloads: 15
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Abstract


In1962, Low-density Parity-check (LDPC) codes were proposed by Gallager, and then in1995, the rediscovery of LDPC codes by Mackay and Neal caught people’s attention again. LDPC codes have very good performance, and this makes them to be widely used in mobile communication system. LDPC codes still have quite well error performance for higher rate cases, and this make them have a broad prospect of application in optical fiber communication, deep space communication and magnetic recording channel. The advantages of LDPC codes due to their parity-check matrices, that the proportion of nonzero elements of parity-check matrix is very small.How to construct excellent and simple LDPC codes is always a hot issue. According to different construction methods, parity-check matrixes are divided into two classes:random parity-check matrix and structured parity-check matrix. The parity-check matrixes constructed by Gallager, Mackay and Richardson are randomized. Although their error performances are good, but because of the randomness of the parity-check matrixes, the simple encoding can not come true. The structured parity-check matrixes can be generated by algebraic geometry, combination way, and it can overcome the generation of short cycle and has good performance.This paper mainly construct parity-check matrices for QC-LDPC codes based on cyclic different set and one-coincidence sequences, and adjust the elements of the parity-check matrix by hill-climbing algorithm so that the desired girth can be reached, and the minimum distance can be increased.This paper mainly consists of the following three parts:In part one, we simply introduce the development of the theory and the significance of LDPC codes.In part two, we introduce some basic concept and conclusion about LDPC code, QC-LDPC codes, Tanner graphs and girth.In part three, we firstly use cyclic difference set to contrast the parity-check matrixes of QC-LDPC codes. Secondly we use one-coincidence sequences to contrast the parity-check matrixes of QC-LDPC codes, and then modify parity-check matrixes by using hill-climbing algorithm so that the desire girth can be reached. At last, we give one method to confirm the minimum distance of QC-LDPC codes, and then enlarge their minimum distance by adjusting some elements of parity-check matrixes.

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CLC: > Industrial Technology > Radio electronics, telecommunications technology > Communicate > Communication theory > Information Theory > Channel coding theory
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