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IEEE International Conference on Broadband Network and Multimedia Technology (IC-BNMT)

Circulant search algorithm for the construction of QC-LDPC codes

Xiongfei Tao, Xiaofeng Zhou, Deyu Feng, Lixin Zheng

Published Oct 1, 2011• 1 citation
Publisher

Abstract

A circulant permutation search algorithm is present in this paper, which can be employed to search appopriate circulant permutation to construct QC-LDPC codes with desired girth. The algorithm is based on a tree expansion mechanism and a select-and-discard procedure. By proposed method, a practical (3, 4) code with code length n=37368 and girth g=18 is constructed. The experiment shows that the codes construct in this paper have large girth and minimum distance, and the bit error rate performance over AWGN channels is excellent.

DOI
10.1109/icbnmt.2011.6155922

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A circulant permutation search algorithm is present in this paper, which can be employed to search appopriate circulant permutation to construct QC-LDPC codes with desired girth. The algorithm is based on a tree expansion mechanism and a select-and-discard procedure. By proposed method, a practical (3, 4) code with code length n=37368 and girth g=18 is constructed. The experiment shows that the codes construct in this paper have large girth and minimum distance, and the bit error rate performance over AWGN channels is excellent.
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The short paper proposes a method for constructing regular quasi-cyclic (QC) LDPC codes based on circulant permutation matrices via simple prime field operations. The main advantage is that regular QC LDPC codes with a variety of block lengths and rates can be easily constructed which have no cycles of length four or less. Simulation results show that within only a maximum of ten decoding iterations of sum-product algorithm(SPA) the constructed regular codes of high rates have no error floor down to the bit-error rate of 10-7.
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A compressing method for the construction of quasi-cyclic LDPC(QC-LDPC)codes was proposed,which used a QC-LDPC code with large girth as mother code.By compressing circulant permutation matrices of the mother code,shorter QC-LDPC codes would be generated.After optimization,the generated codes would have large girth and few cycles,whose lengths varied continuously in a large range.Analysis and simulation results show that these LDPC codes have good performance and can greatly reduce the size of code storage.
This paper proposes a construction method of regular(j, k) Lucas quasi-cyclic low-density parity-check(L-QC-LDPC) codes with girth at least eight based on the Lucas sequence. By this method, the girth of L-QC-LDPC codes is large, which can effectively eliminate short cycles. Besides, lower bound of circulant permutation submatrix dimension p is allowed continuous values. In addition, it can save the storage space in terms of hardware implementation which reduces the cost and complexity of hardware realization correspondingly. Simulation results show that the L-QC-LDPC codes have net coding gain(NCG) of about 2d B and 0.8d B compared with one-coincidence sequence quasi-cyclic LDPC(OCS-LDPC) codes and deterministic codes, respectively, at code rate of 1/2, code length of 1302 and bit error rate(BER) of 10?6. At the same condition, the performance of L-QC-LDPC codes is slightly better than that of the quadratic function LDPC(QF-LDPC) codes, which has an NCG improvement of around 0.1d B. Meanwhile, at code rate of 1/2, similar code length and BER of 10~(-6), the NCG of L-QC-LDPC codes outweigh about 0.5d B compared with that of QC-LDPC codes based on cyclic subgroups of finite fields.