利用LDPC编码冗余位译码的恢复性.docx

摘要随着信息化的发展，人们对信号传输的要求越来越苛刻。一方面人们要减少成本加快信息传输速率，一方面还要加强信号可信度，所以对于信道编码方法的研究对信号最后的性能至关重要。本文首先从编码思想入手，介绍了信道编码的多种分类和基本理论。然后具体介绍了一种常见的优秀码，线性分组系统码即是LDPC编码。接着着重讨论了该编码在编码性能上的优势，并根据编码理论校验矩阵编码恒等为零，和系统码信源位置保持一致的性质，用Gallager规则矩阵生成法和比特填充法生成了两种LDPC编码。之后为了观察编码的恢复性能，用BP译码方式估值，而用Punctured LDPC方式恢复系统码。最后通过matlab仿真和理论分析两个方面研究了Punctured LDPC译码恢复方式的理论可行性和适用条件。发现Punctured LDPC译码不能良好的恢复码率高于0.5的编码，所以存在一定局限性。关键词：系统码 Gallager规则矩阵生成法 比特填充法 BP译码ABSTRACTWiththe developmentofinformation technology, peoples demands for signal transmission become increasingly harsh. On the one hand, people want higher transmission ratebut reduce the cost. On the one hand, it is necessary to strengthen the credibility of the signal. So the research on themethodof channel coding is very important.Firstly, this paper begins with the coding theory, and introduces the variety of channel coding and basic theories. Then we introduced a kind of common excellent code, the code of linear block system, LDPC code.Then we emphasized that the code in the coding performance advantage, according to the coding theory that the parity check matrix of the code is always zero, and the location of code system keep the same. Weuse Gallager Rule matrix generation method and Bit Filling Method to generate the two LDPC codes. In order to observe the recovery performance of the coding, We used BP decoding method and the Punctured LDPCto recover the system code.Finally, we simulation and analysis through MATLAB. We foundthat the recovery rate of Punctured LDPC decoding has some limitations. Itdoesn`t work when transmission rate higher than 0.5.key word: The generation of code Gallager Rule BP decoding目录第一章编码介绍11.1信道编码的介绍11.1.1概述和模型11.1.2主流道编码类别的介绍31.2信道编码理论41.2.1编码理论介绍41.2.2编码译码原则5第二章 LDPC码基础和编码72.1 LDPC码的定义与性质72.1.1 线性分组码72.1.2 LDPC码的定义与其描述92.2 LDPC码的节点和Tanner图102.2.1 校验矩阵的Tanner图102.2.2 度数分布和循环112.3规则LDPC码和不规则LDPC码12第三章 LDPC和AWGN信道后的接收143.1 H矩阵的构造143.1.1 Gallager构造法生成规则LDPC码校验矩阵143.1.2 比特填充法构造非规则LDPC码校验矩阵153.2 LDPC基于高斯消去的直接编码18