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基于Fibonacci-Lucas序列构造大围长QC-LDPC码的方法

袁建国, Yuan Jian-guo, 曾晶, Jing Zeng, 袁梦, Yuan Meng, 范福卓, Fan Fuzhuo, 刘家齐, 郑德猛, Zheng Demeng

Published Aug 25, 2018• 0 citations

Abstract

基于斐波那契-卢卡斯序列并结合三角旋转法提出一种围长至少为8的斐波那契-卢卡斯准循环低密度奇偶校验(fibonacci-lucas quasi-cyclic low-density parity-check, F-L-QC-LDPC)码的构造方法。该方法所构造的F-L-QC-LDPC码不存在四环和六环，计算复杂度低，硬件实现简单且节省硬件存储空间，具有优秀的纠错性能。仿真结果表明，当误码率(bit error rate, BER)为10-6时，该方法所构造的码长为2 700且码率为0.5的码型，相较于基于Fibonacci数列并结合三角旋转法构造的同码长码率的QC-LDPC(2 700, 1 352)码，净编码增益(net coding gain, NCG)提高了约1.0 dB，相较于基于卢卡斯数列大围长构造方法构造的QC-LDPC(2 700, 1 353)码，NCG提高了约1.6 dB。且同样条件下，该方法构造的码长为2 580且码率为0.5的码型与基于等差数列构造的QC-LDPC(2 580, 1 292)码相比，NCG提高了约1.0 dB。

DOI: 10.3979/j.issn.1673-825x.2018.04.011

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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.

Powerful forward error correction codes such as quasi-cyclic low density parity check (QC-LDPC) are required in next-generation coherent optical communication systems [1]. This work describes the design and experimental verification of a high net coding gain (NCG), low complexity QC-LDPC code. Towards this end, we develop a field programmable gate array (FPGA) based platform specially designed for optimization and performance evaluation of LDPC codes. The proposed FPGA framework includes several features such as the capability of changing the internal resolution of the decoder algorithm or capturing error patterns for error-floor analysis. Experimental results derived from the FPGA platform show that the designed QC-LDPC code is able to achieve an NCG of 11.6 dB at a bit-error-rate (BER) of 10-15with an overhead of 25% and a codeword length of only 16K bits.

设计的一条改进欧几里德几何学的几何学途径伪周期(质量管理) 有高率、低的错误地板的低密度的同等值检查(LDPC ) 代码被论述。构造 QC-LDPC 代码与高率比原来的代码有更低的错误地板。最小的重量 codeword 的分发被分析，并且最小的重量 codeword 的一个足够的存在条件被发现。很多 QC-LDPC 与更低的错误地板编码的模拟表演能被减少最小的重量 codewords 的数字设计令人满意这个足够的条件。

To meet the increasing requirement on the transmission characteristics of optical communication systems,based on the structure of parity-check matrix of Richardson-Urbanke algorithm,a lowercomplexity constructing method is proposed for the quasi-cyclic low-density parity-check(QC-LDPC) codes in the optical communication systems,and a QC-LDPC(4288,4020) code with 93.7% higher code-rate is also constructed.Simulation shows that the constructed QC-LDPC(4288,4020) code has net coding gain of about 1.7 dB over the classic RS(255,239) code which has been widely used for optical communication systems and 0.3 dB more than that of SCG-LDPC(3969,3720) code with the same 93.7% higher code-rate,and the NCG of the QC-LDPC(4288,4020) code is about 1.3 dB away from the Shannon limit at bit error rate BER of 10-7;furthermore,the error floor of QC-LDPC(4288,4020) code is lower than that of the randomly constructed LDPC(4288,4020) with the column weight of 3.