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摘要：循环码是线性分组码的一个重要子类。因为循环码拥有其它码类所没有的非常优良的代数结构，而且它具有其它码类所没有的良好的循环特性，所以它的编码和伴随式可以通过简单的反馈移位寄存器来实现，并且可以通过很多种简单有效的方法来实现它的译码。现在人们在循环码的领域已经取得了很大的进展，比如说循环码理论的研究，并且对其理论进行实践。从循环码研究的开始到现在，循环码已经成为了现代科技理论中理论最为成熟、研究最为深入、使用最为广泛的一类线性分组码。34840
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BCH码是一类最为重要的循环码，这种码可以是二进制码，也可以是非二进制码。作为循环码中最为重要的一个子类，它具有很强的纠错能力，并且它的构造方便。与循环码相同，BCH码的编码和译码容易实现。不过BCH码最为突出的一点是它能够纠正多个随机错误。
RS码是BCH码的重要子类。它是一种特殊的非二进制码，同样地，它继承了BCH码应有的能力，也就是很强的纠错能力。
本课题研究仿真的编码就是循环码、BCH码和RS码。
论文在分析讨论循环码、BCH码和RS码的基本理论的同时，使用MATLAB软件对这三种编码进行了性能仿真，从而来验证它们的纠错能力。
毕业论文关键字：循环码；BCH码；RS码
Cyclic code performance simulation based on MATLAB
Abstract：Cyclic code is an important subclass of linear block codes. Because cyclic code with other algebraic structure code class is not very good, and it has good circulation of other types of codes have no features, so its encoding and valet can be done by simple feedback shift register, and can be a lot of kinds of simple and effective method to realize its decoding. Now people in the field of cyclic code has made great progress, such as the theoretical study of cyclic code and its theory to practice. Till now, since the beginning of the cyclic code research theory of cyclic code has become the modern science and technology in the most mature, the most thorough study, the most widely used type of linear block codes.
BCH code is a kind of the most important cyclic code, the code can be a binary code, can also is a binary code. As one of the most important subclasses in the cyclic code, it has a strong ability of error correction, and its construction is convenient. The same as the cyclic code, to achieve the coding and decoding of BCH code. But the most prominent BCH code is more than it can correct random errors.
RS code is an important subclass of BCH code. It is a special kind of binary code, in the same way, it inherits the BCH code should have the ability, is also a strong error correction capability.
This topic research the simulation code is cyclic code, BCH code and RS code.
Papers discussed in analysis of cyclic code, BCH code, and the basic theory of RS code at the same time, the use of MATLAB software for the three coding performance simulation, thus to validate their error correction ability.
Key Words: cyclic code；BCH Code；RS Code
目录
第一章 绪论 6
1.1 课题研究现状和水平 6
1.2 数字通信系统的信道模型 6
1.3 论文内容介绍 7
第二章 纠错编码简介 8
2.1 纠错编码的历史发展 8
2.2 纠错编码的基本概念和分类 8
2.3 差错控制系统的分类 9
第三章 线性分组码基础 10
3.1 线性分组码的基本概念 10
3.2 线性分组码的编码 11
3.2.1 一致校验矩阵 12
3.2.2 生成矩阵 12