题 目：
毕业论文
LDPC码的编译码算法研究
摘 要
低密度奇偶校验码（Low Density Parity Check Codes，简称LDPC码），本质上是一种线性分组码，更接近香农限。目前的研究均表明LDPC 码是信道编码中纠错能力最强的一种码,其译码器结构简单,在深空探测、卫星通信等领域可得到广泛的应用。文章介绍了LDPC 码,综述了其编码方法和译码方法。在编码方法中分别描述了校验矩阵的构造和基于校验矩阵的编码算法，对LDPC 码的快速编码方法进行分析。在译码方法中主要论述了消息传递译码算法、置信传播译码方法、最小和译码算法、比特翻转译码算法和加权比特翻转译码方法。对部分LDPC码的编译码就行了仿真，同时对LDPC 码的编译码方法的发展及应用前景作了分析。
本文的重点是对LDPC码的编译码算法的论述与研究，介绍LDPC码的基本原理和分类，分别从基于生成矩阵和基于校验矩阵详细讨论了LDPC码编码算法，简单介绍了线性分组码编码，LU分解法，RU分解法。并用简明例子对RU算法做了清晰的解释。对译码大致做了解释：分为软判决译码（MP算法）和硬判决译码（比特翻转算法和加权比特翻转算法）。在本文的最后用AWGN信道下LDPC码的性能仿真，主要是针对比特翻转算法进行仿真。做出理论比较。
关键词：LDPC码 编译码 MATLAB
Title：Encoding and Decoding Algorithms of LDPC Codes
Abstract：LDPC code, namely Low Density Parity Check Code, is a kind of
linear block codes in nature, and the decoding performance of LDPC is more nearer to the Shannon limit. With it s best performance and simple decoder structure, LDPC codes will be widely used in deep space exploration, satellite communications and other fields. While briefly introducing LDPC codes are introduced briefly, this paper summarizes the encoding and decoding algorithms. The encoding algorithm is described in two steps: the const ruction of parity-check matrix and the encoding method based on parity-check matrix. Analyze the rapidly coding method for LDPC code. As to decoding algorithm, MP decoding method, BP decoding method, Min-Sum decoding method, Bit-Flipping method and Weighted Bit-Flipping method are discussed. Emulate for the LDPC codes .The development and application of encoding and decoding methods is analyzed as well.
This article focuses on encoding and decoding algorithms of LDPC codes，According to the different methods of decoding algorithm, and makes the theoretical MATLAB simulation.
Key words：LDPC codes encoding and decoding MATLAB
目 录
1 引言......................................................................................................................... 1 2 LDPC码概述 .......................................................................................................... 3 2.1 线性分组码 ......................................................................................................... 3 2.2 低密度奇偶校验码(LDPC码) ......................................................................... 3 2.2.1 LDPC码定义 ................................................................................................. 3 3 LDPC码的编码算法 .............................................................................................. 6 3.1 基于生成矩阵的编码算法 (线性分组码编码) ............................................... 6 3. 2基于校验矩阵的编码算法 (LU 分解法) .......................................................... 6 3.3基于校验矩阵的编码算法(RU算法) ................................................................ 6 4 LDPC码的译码概述 .......................................................................................... 10 4.1 MP算法集 ....................................................................................................... 11 4.2 硬判决译码算法 ............................................................................................... 12 4.2.1 比特翻转算法 ................................................................................................ 12 4.2.2加权比特翻转译码算法 ................................................................................. 13 5 AWGN信道下LDPC码的性能仿真 .............................................................. 14 5.1 仿真软件简介（MATLAB&SIMULINK） ........................................................ 14 5.2 仿真与结果分析 ............................................................................................... 15 5.3 译码仿真系统框图及系统总流程图 ............................................................... 15 5.4 BF算法及其改进算法仿真 ............................................................................ 16 结 论.......................................................................................................................... 17 致 谢.......................................................................................................................... 18 参考文献 ..................................................................................................................... 18 代码.............................................................................................................................. 19