Design of good QC-LDPC codes without small girth in the p-plane |
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Authors: | Lingjun Kong Yang Xiao |
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Affiliation: | 1. Institute of Information Science, Beijing Jiaotong University, Beijing 100044, P. R. China;Faculty of Information Engineering and Automation, Kunming University of Science and Technology, Kunming 650500, P. R. China 2. Institute of Information Science, Beijing Jiaotong University, Beijing 100044, P. R. China |
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Abstract: | A construction method based on the p-plane to design high-girth quasi-cyclic low-density parity-check (QC-LDPC) codes is proposed. Firstly the good points in every line of the p-plane can be ascertained through filtering the bad points, because the designed parity-check matrixes using these points have the short cycles in Tanner graph of codes. Then one of the best points from the residual good points of every line in the p-plane will be found, respectively. The optimal point is also singled out according to the bit error rate (BER) performance of the QC-LDPC codes at last. Explicit necessary and sufficient conditions for the QC-LDPC codes to have no short cycles are presented which are in favor of removing the bad points in the p-plane. Since preventing the short cycles also prevents the small stopping sets, the proposed construction method also leads to QC-LDPC codes with a higher stopping distance. |
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Keywords: | quasi-cyclic low-density parity-check (QC-LDPC)codes circulant matrices girth stopping set stopping distance |
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