【作者】 陈伟；

【导师】 周武旸；

【作者基本信息】 中国科学技术大学 ， 通信与信息系统， 2010， 硕士

【摘要】 自1996年被重新发现以来,低密度奇偶校验(Low-Density Parity-Check, LDPC)码即以其逼近Shannon极限的性能吸引了广大研究人员的注意,成为信道编码领域的研究热点。LDPC码具有低的错误平台(error floor),简单的解码器结构以及可以高速并行解码等优点,性能最好的LDPC码距离Shannon限仅0.0045dB。随着研究的深入,LDPC码的高编码复杂度的问题逐渐得到改善,出现了各种降低复杂度的编码器实现方法,使LDPC码的实际应用成为可能。本文首先介绍了信道编解码的发展历史以及LDPC码的主要研究内容,然后在对LDPC码的基本原理介绍的基础上,详细讨论了LDPC码的几个主要研究方向,包括校验矩阵的构造、编码算法和解码算法,并着重介绍了本文提出的一种基于链表的LDPC码Girth值检测算法及其应用。利用校验矩阵的参数和特性研究码字的性能是研究LDPC码的一个重要手段,影响码字性能的因素主要有校验矩阵的大小、矩阵的行重和列重、Girth值以及矩阵中的短循环数目等。Girth值与码字的最小距离是直接相关的,Girth值较大的校验矩阵的纠错性能也较强,但是追求大的Girth值将使校验矩阵构造变得更加困难。同时由于矩阵中短循环的存在,在软判决迭代解码过程中,经过几次迭代以后循环中的节点发出的信息会重新传递回来,从而造成自身信息的迭加,影响解码的准确性。为此本文提出了一种基于链表的LDPC码Girth值检测算法,将校验矩阵中的非零元素展开成具有层次结构的链表,比较链表中不同层的节点,可以找出矩阵中的所有循环。矩阵的Girth值由最短循环的长度确定,该算法可以给出矩阵中各种长度短循环的准确数目。另外,本文基于子循环块因子置换的方法得到了具有不同循环数目的矩阵,并分析了循环数目对矩阵性能的影响。仿真结果表明,特定长度的循环数目仅在一定的信噪比(SNR)条件下对码字的性能影响较明显,最短长度循环数目较少的校验矩阵纠错性能并没有提升,所以应该结合矩阵的其他参数来分析和设计校验矩阵,比如最小距离特性,目前这方面的研究还比较少,可以作为进一步研究的内容。更多还原

【Abstract】 Low-density parity-check (LDPC) codes have attracted much attention due to their Shannon-limit-approaching performance since rediscovered in 1996 and have become the hot-spot in channel coding field. LDPC codes have low error floor, simple decoder structures and fully parallel decoder implementation. The gap between the best designed LDPC code and the Shannon limit is only 0.0045dB. High encoding complexity of LDPC codes is getting reduced with further research and many low complexity encoding implementations come out and make practical use possible.The history of channel coding theory is first introduced in this thesis together with the main research aspects of LDPC codes. Based on the basic principles and concepts of LDPC codes, the constructions of parity-check matrixes and the encoding and decoding algorithms are detailed subsequently. A girth detection method of LDPC codes and its application are proposed and discussed in this thesis particularly.It’s an important way to analyze the performance of LDPC codes with the parameters and feature of the parity-check matrixes. Factors related are the size of the parity-check matrixes, the row and column weight, girth and the number of short cycles in the matrixes. Girth is directly related to the minimum distance of the code and matrixes with higher girth will have better error-correcting ability. But it will be more difficult to construct parity-check matrixes when pursuing higher girth. Due to the short cycles in parity-check matrix, when decoded with iterative decoding method soft information comes out from a node will return back to itself after several iterations and so the performance is depressed.A girth detection method base on linked list is proposed in this thesis. A linked list is obtained by expanding the non-zero elements in parity-check matrixes into a layered structure. All the cycles can be detected by comparing nodes in different layers and the girth is the length of the shortest cycle. The exact number of different length of cycles is also given in the algorithm. Matrixes with different number of cycles are obtained using sub-block cyclic-shift factor replacing method and their performance is analyzed. Simulation results show that the number of cycle with special length affects the performance of the code only at a given signal-to-noise ratio (SNR). Matrixes with reduced number of the shortest length don’t have performance improvement. Other parameters should be considered when analyzing and design the parity-check matrix such as minimum distance. Research focused on this issue isn’t much at present and much more work can be done in the future.更多还原