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 filt...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.展开更多
The existing constructions of quasi-cyclic low-density parity-check （QC-LDPC） codes do not consider the problems of small stopping sets and small girth together in the Tanner graph, while their existences will lead ...The existing constructions of quasi-cyclic low-density parity-check （QC-LDPC） codes do not consider the problems of small stopping sets and small girth together in the Tanner graph, while their existences will lead to the bit error rate （BER） performance of QC-LDPC codes being much poorer than that of randomly constructed LDPC codes even decoding failure. To solve the problem, some theorems of the specific chosen parity-check matrix of QC-LDPC codes without small stopping sets and small girth are proposed. A novel construction for QC-LDPC codes with long block lengths is presented by multiplying mmin or the multiple of mmin, which is the minimum order of the identity matrix for the chosen parity-check matrix. The simulation results show that the specific chosen parity-check matrix of QC-LDPC codes can effectively avoid specified stopping sets and small girth and exhibit excellent BER performance than random LDPC codes with the same longer codes length.展开更多
提出一种基于卢卡斯数列构造围长至少为8的规则(j,k)卢卡斯QC-LDPC(L-QC-LDPC)码的方法。该方法构造的码字围长较大,能够有效地消除短环。循环置换子矩阵维数p值的下界允许连续取值,且在硬件实现方面可节省存储空间,进而降低硬件实现成...提出一种基于卢卡斯数列构造围长至少为8的规则(j,k)卢卡斯QC-LDPC(L-QC-LDPC)码的方法。该方法构造的码字围长较大,能够有效地消除短环。循环置换子矩阵维数p值的下界允许连续取值,且在硬件实现方面可节省存储空间,进而降低硬件实现成本以及复杂度。仿真结果表明,在码率为1/2、码长为1 302和误码率为10?6时,L-QC-LDPC码与OCS-LDPC码相比,净编码增益(NCG)提高了约2 d B,比确定性码的NCG提高了约0.8 d B;与二次函数相比,性能略优于二次函数LDPC(QF-LDPC)码,有约0.1 d B NCG的改善。同时,在相同码率、相近码长和误码率为10^(-6)时,L-QC-LDPC码与基于有限域的循环子集构造的QC-LDPC码相比,提高了约0.5 d B的净编码增益。展开更多
针对准循环低密度奇偶校验(QC-LDPC)码中循环置换矩阵的移位次数的确定问题,提出了一种利用组合设计中完备差集(PDF)构造QC-LDPC码的新颖方法。当循环置换矩阵的维度大于一定值时,该方法所构造的规则QC-LDPC码围长至少为6,具有灵活选择...针对准循环低密度奇偶校验(QC-LDPC)码中循环置换矩阵的移位次数的确定问题,提出了一种利用组合设计中完备差集(PDF)构造QC-LDPC码的新颖方法。当循环置换矩阵的维度大于一定值时,该方法所构造的规则QC-LDPC码围长至少为6,具有灵活选择码长和码率的优点,且所需的存储空间更少,降低了硬件实现的复杂度。仿真结果表明:在误码率为10-5时,所构造的码率为3/4的PDF-QC-LDPC(3136,2352)与基于最大公约数(GCD)构造的GCD-QC-LDPC(3136,2352)码和基于循环差集(CDF)构造的CDF-QC-LDPC(3136,2352)码相比,其净编码增益(NCG)分别有0.41 d B和0.32 d B的提升;且在码率为4/5时,所构造的PDF-QC-LDPC(4880,3584)码比GCD-QC-LDPC(4880,3584)码和CDF-QC-LDPC(4880,3584)码的NCG分别改善了0.21 d B和0.13 d B。展开更多
基金supported by the National Natural Science Foundation of China (60572093)Specialized Research Fund for the Doctoral Program of Higher Education (20050004016)
文摘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.
基金supported by the National Natural Science Foundation of China (60572093)Specialized Research Fund for the Doctoral Program of Higher Education (20050004016)
文摘The existing constructions of quasi-cyclic low-density parity-check （QC-LDPC） codes do not consider the problems of small stopping sets and small girth together in the Tanner graph, while their existences will lead to the bit error rate （BER） performance of QC-LDPC codes being much poorer than that of randomly constructed LDPC codes even decoding failure. To solve the problem, some theorems of the specific chosen parity-check matrix of QC-LDPC codes without small stopping sets and small girth are proposed. A novel construction for QC-LDPC codes with long block lengths is presented by multiplying mmin or the multiple of mmin, which is the minimum order of the identity matrix for the chosen parity-check matrix. The simulation results show that the specific chosen parity-check matrix of QC-LDPC codes can effectively avoid specified stopping sets and small girth and exhibit excellent BER performance than random LDPC codes with the same longer codes length.
文摘提出一种基于卢卡斯数列构造围长至少为8的规则(j,k)卢卡斯QC-LDPC(L-QC-LDPC)码的方法。该方法构造的码字围长较大,能够有效地消除短环。循环置换子矩阵维数p值的下界允许连续取值,且在硬件实现方面可节省存储空间,进而降低硬件实现成本以及复杂度。仿真结果表明,在码率为1/2、码长为1 302和误码率为10?6时,L-QC-LDPC码与OCS-LDPC码相比,净编码增益(NCG)提高了约2 d B,比确定性码的NCG提高了约0.8 d B;与二次函数相比,性能略优于二次函数LDPC(QF-LDPC)码,有约0.1 d B NCG的改善。同时,在相同码率、相近码长和误码率为10^(-6)时,L-QC-LDPC码与基于有限域的循环子集构造的QC-LDPC码相比,提高了约0.5 d B的净编码增益。
文摘针对准循环低密度奇偶校验(QC-LDPC)码中循环置换矩阵的移位次数的确定问题,提出了一种利用组合设计中完备差集(PDF)构造QC-LDPC码的新颖方法。当循环置换矩阵的维度大于一定值时,该方法所构造的规则QC-LDPC码围长至少为6,具有灵活选择码长和码率的优点,且所需的存储空间更少,降低了硬件实现的复杂度。仿真结果表明:在误码率为10-5时,所构造的码率为3/4的PDF-QC-LDPC(3136,2352)与基于最大公约数(GCD)构造的GCD-QC-LDPC(3136,2352)码和基于循环差集(CDF)构造的CDF-QC-LDPC(3136,2352)码相比,其净编码增益(NCG)分别有0.41 d B和0.32 d B的提升;且在码率为4/5时,所构造的PDF-QC-LDPC(4880,3584)码比GCD-QC-LDPC(4880,3584)码和CDF-QC-LDPC(4880,3584)码的NCG分别改善了0.21 d B和0.13 d B。
