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Research on the Construction of Mother Matrix of Quasi-cyclic Low-Density Parity-Check Codes

Author: WangLin
Tutor: LiuWeiZhong
School: Huazhong University of Science and Technology
Course: Software Engineering
Keywords: Low-density parity check code Quasi-cyclic Mother matrix Cycle Length Inevitable ring
CLC: TN911.2
Type: Master's thesis
Year: 2010
Downloads: 7
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Abstract


Low Density Parity Check (Low-density Parity-check, LDPC) code is a performance approaching the Shannon limit , low complexity , anti-interference ability of error correction channel coding has become widely used in various communication systems being . Wherein the code is of a quasi-cyclic (Quasi-cyclic, QC) LDPC codes , due to its linear encoding low complexity , and can reduce the storage space requirements , thereby having a higher practicability . Through the study of the basic concepts as well as the nature of the LDPC code can be known from the perspective of the decoding algorithm , the minimum loop length bigger LDPC code performance better . The structure of the QC-LDPC code is closely related to it corresponds to the mother matrix . Already know through previous studies , the mother matrix can be avoided in the short ring when the the mother matrix inevitable ring , can be eliminated by a specific search algorithm to construct the smallest ring long for the inevitable ring long QC-LDPC codes . This means the mother matrix inevitable loop length of the greater , it generates QC-LDPC code , the minimum loop length is larger , thus the better the performance of QC-LDPC code . According to the findings , mainly from the point of view of the inevitable ring to study the structure of the parent matrix method . First, through the analysis of the ring long Theorem and nature , draw the inevitable cause of the ring . Secondly, the analysis of the structural characteristics of the sub-matrix contains the inevitable ring detection algorithm devised a mother matrix inevitable ring long . Then, through the relevant theorem to calculate the size of the mother matrix under different inevitable ring long . Then a block progressive structuring method , this method is combined with the detection algorithm and backtracking larger inevitable loop length ( 3 , k ) code mother matrix can be quickly constructed . Finally, the mother matrix of QC-LDPC code extended PEG construct method generated random LDPC code and Fossorier traditional QC-LDPC code comparison found that the performance of QC-LDPC code structure is far more than the traditional QC-LDPC code , and LDPC random code performance is almost the same , even in the case of the larger of the code length exceeds the random code, so as to achieve the expected results .

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