斐波那契-卢卡斯序列的Type-Ⅱ QC-LDPC码构造  

Construction of Type-Ⅱ QC-LDPC codes based on Fibonacci-Lucas sequence

作　　者：袁建国[1,2] 曾晶 郑德猛 庞宇[2] Yuan Jianguo;Zeng Jing;Zheng Demeng;Pang Yu(Key Laboratory of Optical Communication and Networks;Chongqing Key Laboratory of Photoelectronic Information Sensing and Transmitting Teehnology, Chongqing University of Posts and Telecommunications, Chongqing 400065, China)

机构地区：[1]重庆邮电大学光通信与网络重点实验室,重庆400065 [2]重庆邮电大学光电信息感测与传输技术重庆市重点实验室,重庆400065

出　　处：《华中科技大学学报（自然科学版）》2018年第5期12-16,共5页Journal of Huazhong University of Science and Technology(Natural Science Edition)

基　　金：国家自然科学基金资助项目(61671091,61471075);重庆市基础与前沿研究计划资助项目(cstc2015jcyj A40015);重庆市研究生科研创新项目(CYS17241);重庆邮电大学大学生科研训练计划资助项目(A2016-61)

摘　　要：针对Type-Ⅱ低密度奇偶校验（Type-Ⅱ QC-LDPC）码中存在着权重为2的循环矩阵而容易产生短环,从而影响译码收敛的问题,基于斐波那契-卢卡斯序列提出一种Type-Ⅱ斐波那契-卢卡斯准循环低密度奇偶校验（Type-Ⅱ F-L-QC-LDPC）码的构造方法.Type-Ⅱ F-L-QC-LDPC与Type-I QC-LDPC码相比不仅增大了码字间最小距离上限,同时还消除了环长为四的环,纠错性能优秀,译码收敛较快,所需存储元素少,计算复杂度低,硬件实现简单.仿真结果表明：当误码率（BER）为1×10-6时,利用该构造方法所构造的码率为0.6的Type-Ⅱ F-L-QC-LDPC（3 650,2 192）码与利用完备循环差集数学思想构造的Type-Ⅱ CDS-QC-LDPC（3 650,2 192）码以及利用Sidon数列数学思想构造的Type-Ⅱ S-QC-LDPC（3 650,2 192）码相比,其净编码增益（NCG）分别提高了约0.21和0.1 d B.且在同样条件下,该方法构造的码率为0.5的码型与Type-Ⅱ CDS-QC-LDPC（3 652,1 826）码相比,NCG提高了约0.2 d B.As Type-II quasi-cyclic low-density parity-check（Type-II QC-LDPC） codes are also easier to generate short cycles which can affect the convergence of decoding because of the existence of weight-2 circulant matrices. Based on the Fibonacci-Lucas sequence,a construction method of Type-II Fibonacci-Lucas quasi-cyclic low-density parity-check（Type-II F-L-QC-LDPC） code was proposed.The Type-II F-L-QC-LDPC code,compared with the Type-I QC-LDPC code,could achieve a higher minimum distance while eliminating the girth-4, with better error-correction performance and more excellent decoding convergence characteristics.Furthermore,the Type-II F-L-QC-LDPC code can also save the storage elements and reduce the computational complexity,thus,its hardware implementation was more easily realized.Simulation results show that at the bit error rate（BER） of 10-6,the net coding gain of the Type-II F-L-QC-LDPC code is respectively about 0.21 and 0.1 d B more than those of the Type-II CDS-QC-LDPC（3 650,2 192） code based on the mathematical thought of perfect cyclic difference sets and the Type-II S-QC-LDPC（3 650,2 192） code based on the mathematical thought of Sidon sequence.The net coding gain of the Type-II F-L-QC-LDPC code with the code-rate of 0.5 is about 2.0 d B more than that of the Type-II CDS-QC-LDPC（3 652,1 826） code under the same condition.

关 键 词：Type-Ⅱ QC-LDPC码 斐波那契-卢卡斯数列 最小距离 环长 净编码增益 

分 类 号：TN911.22[电子电信—通信与信息系统]