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中文摘要：
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。
英文摘要：
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.
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