【作者】 邓勇强；

【导师】 朱光喜；

【作者基本信息】 华中科技大学 ， 信息与通信工程， 2006， 博士

【摘要】 随着对宽带、高速通信业务需求的不断增加和通信技术的不断进步,作为一种提高信息传输的可靠性和有效性的重要手段的前向纠错码技术近年来获得了快速的发展,同时作为通信理论的重要组成部分,更有效可靠的纠错码技术的理论研究与应用正在越来越受到人们的关注与重视。本文正是在国家高技术研究发展计划(863计划)“数字音视频编码、传输、测试与应用示范”(No.2002AA119010)的子课题“基于无线环境的联合信源信道系统框架研究”、国家自然科学基金重大项目“未来移动通信系统基础理论与技术研究(No.60496315)”等研究项目的资助下,对近年来在纠错码领域表现抢眼的低密度校验码(Low-Density Parity-Check Codes,LDPC)的若干关键技术展开了研究。LDPC最早是在1962年由Robert G.Gallager提出的,它是一类可以用稀疏校验矩阵或因子图进行描述的线性分组码,具有接近Shannon限的良好性能和因子图等有效的分析工具,因而近年来成为纠错码领域的研究热点。因子图最早是由Tanner提出的,它是表征校验节点与变量节点关系的二部图。因子图与校验矩阵一一对应,当校验矩阵的某位置为“1”时,在因子图上分别对应校验矩阵的行和列的校验节点与变量节点之间就有一条边相连。本文正是利用因子图这个工具,对LDPC码的编码、译码和密度进化这几个方面的关键技术进行了研究。在进行后续研究前,本文首先全面的介绍了LDPC码起源、发展和当前的研究与应用情况,给出了它的因子图表示和校验约束编码结构,并基于因子图推导了译码后验概率的表达式;介绍了规则码、非规则码和基于GF(q)域的LDPC码的编码结构,对不同编码结构下LDPC的性能进行了讨论,结果表明,非规则码性能优于规则码,在GF(q)域的LDPC码性能要好于二元LDPC码,域值越高性能越好。为了获得不含短环的LDPC码的编码算法,对因子图进行了具体的分析,探讨了因子图中环对码性能影响的成因,利用图论工具和构造辅助的校验点结构图邻接矩阵的方法,分析了因子图中形成环校验节点之间的关系,获得了一些有用的定理和性质,并在这些定理和性质的基础上提出了一种新的构造算法。新的构造算法能够有效的避免短环的出现,文章给出了无4-环、6-环和8-环的LDPC码的具体构造算法,在仿真实验中显示了比随机生成算法更好的性能。本文提出的构造算法并不限定于规则码或是非规则码,可根据设定的列重序列生成符合要求的规则码或是非规则码,因而具有更好的通用性。在LDPC码的译码算法研究方面,为了获得置信传播迭代译码算法的高性能,需要能减少因子图中环对它的影响,因此,在本文译码算法的研究部分分析了因子图中存在的环对置信传播译码算法的影响,给出了一种优化的译码算法。该算法在译码中通过动态检测信息的传递路径,适时的切断通过因子图上的环传回的消息,能够在一定程度上消除因子图中环对置信传播译码算法的影响,使原始信息在不受到经环传回的重复信息的污染下传播到尽可能多的节点。在仿真实验中,我们对比了本文算法与传统算法,分析了两种算法的计算复杂度与性能,结果表明,该算法在中短码长的情况下表现出比传统算法更好的性能,在信道状况较差时,在不降低性能的情况下,本文算法具有更小的计算复杂度。在LDPC码密度进化理论分析方面,由于现有的密度进化理论是建立在基于无环因子图假设的基础上的,没有考虑因子图上存在的环以及环对迭代译码消息进化的影响。因此,本文通过讨论,获得了一般LDPC码因子图上环存在的概率表述,在这个概率表述基础上,对离散密度进化和连续密度进化在AWGN信道上的表现分别进行了分析。在离散密度进化分析中,使用了Gallager最早提出的硬判决译码算法,获得了迭代译码中误码率的进化,得到在一定初始误码率的条件下,译码误码率的收敛情况。仿真实验结果显示,有环因子图下,其离散密度进化分析获得译码阈值低于无环因子图的情况。在连续密度进化中,使用基于对数似然比量度上的概率测度进行分析,获得了消息密度进化的计算表达式。连续密度进化的计算量非常大,可采用高斯逼近进行近似计算。更多还原

【Abstract】 With the increasing demand for broad-band and high-speed communication services and the developing of the communication technology, forward error correction (FEC) codes, which is an important way to improve the reliability and validity of information transmission, had developed rapidly in the past several years. At the same time, as the important part of communication theory, people paid more attention to the theoretic research and the application of more efficient and reliable error correction codes. Imbursed by the sub-item“Research on System Framework of Joint Source-Channel Coding under Wireless Circumstance”of national high-tech research and development plan(863 plan)“Digital Audio, Video Encoding, Transmission, Testing and Applying Model”(No.2002AA119010), and the great item“Research of Future Communication System Fundamental Theory and Technology (No.60496315)”, the dissertation studies several key techniques of Low-Density Parity-Check Codes(LDPC) that were considered much in error correction codes field.In 1962, Robert G. Gallager put forward Low-Density Parity-Check Codes (LDPC) firstly, which were a kind of linear block codes that can be defined by the sparse parity-check matrix or the factor graph. LDPC codes have good capability near Shannon limit and effective analysis tool such as gene graph, so they have becoming the research hotspot in error correcting codes field. Factor graph was proposed by Tanner firstly. It is a bipartite graph of check nodes and variable nodes, and corresponds to the check matrix. Using the factor graph, the paper studies some key techniques including the coding of LDPC, decoding and density evolution.First, the paper introduces the source, development, and present research and application, gives the factor graph and the coding structure, and deduces the expression of decoding posterior probability based on the factor graph. Then, the paper presents these coding structures of regular LDPC, irregular LDPC, and LDPC codes over GF(q), and discusses the capability of LDPC with different coding structure. The result shows that the capability of irregular LDPC is prior to the regular LDPC, and the capability of LDPC over GF(q) is better than the binary LDPC and the value higher the capability better.In order to get the coding algorithm without short cycles, this paper analyzes the factor graph, and discusses the cause that the cycle affects the capability of codes in factor graph. Based on the graph theory and the method of constructing assistant check point structure to connect the matrix, the paper analyzes the relation of cycle check nodes in factor graph and attains some useful theorems based on which a new constructing algorithm is proposed. The new algorithm can avoid the present of short cycles. The paper gives the detailed constructing algorithm of different LDPC, and the algorithm performances better than the randomized algorithm in simulation experiment. The proposed algorithm can form regular LDPC or irregular LDPC according to the given arrange weight and is universal.To gain the high capability of Belief Propagation(BP) iterative decoding algorithm algorithm, we propose an improved decoding algorithm through analyzing the affection of cycles. By momentarily detecting the passing path of information the proposed algorithm can cut off the information from the cycles, so the original information can be transmitted to more nodes. In the simulation we compare the new algorithm and the traditional and the result shows that the new performances better when it is middle and short codes.The present density evolution theory was under the hypothesis of factor graph without cycles. In this paper, we give the probability expression of the existence of cycles in factor graph of general LDPC codes based on which we discuss the performance of scatter and sequential density evolution in AWGN channels. In the scatter density evolution analysis, we get the evolution of the bit error probability in iterative decoding and the convergence of it under the control of a given original bit error probability. The result of the simulation shows that, in factor graph with cycles, the threshold of decoding obtained in scatter density evolution analysis is lower than that obtained in factor graph without cycles. In the sequential density evolution analysis, we obtain the calculation expression of information density evolution by analyzing the probability measure based on the log likelihood ratio measurement. The calculation of sequential density evolution can use the Gaussian approximation arithmetic.更多还原