大girth多进制阵列准循环LDPC码
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摘要
Tanner图中girth的大小和分布影响着码字的误码性能,通过适当地增加girth值可进一步提升多进制准循环LDPC(Low-Density Parity-Check)码性能。采用直接构造法确定短环线性约束方程,构造出满足大girth的指数矩阵,提出了基于不同域的广义二维扩展方法,进而与大girth阵列码结合构造出了大girth多进制阵列码。仿真结果表明,在高斯白噪声信道中构造出的码字具有较强的纠错性能,且在一定范围内更大的girth可取得更大的编码增益,利于有效快速的编译码,保证信息的可靠传输,满足高频带利用率。
The error performance of codewords are affected by the size and distribution of the girth in the Tanner graph,and the performance of nonbinary quasi-cyclic(QC)low-density parity-check(LDPC)can be improved by increasing girth properly.The exponential matrices with large girth are constructed by the explicit approach,which is determined by the cycle-governing linear equations. A generalized two-dimensional matrix dispersion based on two various Galois fields is proposed. The nonbinary array LDPC codes are designed by combining with the array codes of large girth and the matrix dispersion. The simulation results show that the codes considered can lead to significant gains by increasing the girth in a certain range over an additive white Gaussian noise channel. It benefits fast encoding and efficient decoding,and the error correction can ensure reliable transmission and meet high bandwidth efficiency.
The error performance of codewords are affected by the size and distribution of the girth in the Tanner graph,and the performance of nonbinary quasi-cyclic(QC)low-density parity-check(LDPC)can be improved by increasing girth properly.The exponential matrices with large girth are constructed by the explicit approach,which is determined by the cycle-governing linear equations. A generalized two-dimensional matrix dispersion based on two various Galois fields is proposed. The nonbinary array LDPC codes are designed by combining with the array codes of large girth and the matrix dispersion. The simulation results show that the codes considered can lead to significant gains by increasing the girth in a certain range over an additive white Gaussian noise channel. It benefits fast encoding and efficient decoding,and the error correction can ensure reliable transmission and meet high bandwidth efficiency.
引文
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[2]Zhou B,Kang J,Song S,et al. Construction of non-binary quasi-cyclic LDPC codes by arrays and array dispersions[J]. IEEE Trans. Commun.,2009,57(6):1652-1662.
[3]Chen C,Bai B,Wang X. Construction of nonbinary quasi-cyclic LDPC cycle codes based on singer perfect difference set[J]. IEEE Commun. Lett.,2010,14(2):181-183.
[4]Fossorier M P C. Quasi-cyclic low-density parity-check codes from circulant permutation matrices[J]. IEEE Trans. Inf. Theory,2004,50(8):1788-1793.
[5]袁建国,曾晶,郑德猛,等.斐波那契-卢卡斯序列的Type-II QC-LDPC码构造[J].华中科技大学学报(自然科学版),2018,46(5):12-16.
[7]Tasdighi A,Banihashemi A H,Sadeghi M. Symmetrical constructions for regular girth-8 QC-LDPC codes[J].IEEE Commun. Lett.,2017,65(1):14-22.
[8] Zhang G,Mathar R. Explicit construction for type-1QC-LDPC codes with girth 12[J]. IEEE Commun. Lett.,2017,21(3):460-463.
[9]杨箭.大围长准循环LDPC码的构造研究[D].重庆:重庆邮电大学,2017.
[10]Zeng L. Algebraic Constructions of nonbinary quasi-cyclic LDPC codes and efficient encoding[D]. Davis:University of California,2006.
[11] Milenkovic O,Kashyap N,Leyba D. Shortened array codes of large girth[J]. IEEE Trans. Inf. Theory,2006,52(8):3707-3722.
[12]Kang J,Huang Q,Zhang L,et al. Quasi-cyclic LDPC codes:An algebraic construction[J]. IEEE Trans. Commun.,2010,58(5):1383-1396.