1、摘摘 要要 1948年信息论和编码理论的奠基人克劳德香农提出了著名的 有噪信道编码定理， 该定理促进了基于高斯噪声的编码理论的快速发 展。 然而，传统的基于高斯噪声的信道研究与现实中多数信道为脉 冲噪声环境的现实并不相符，因此，脉冲噪声环境下编码信道抗噪声 性能研究有重要的理论意义和应用意义。 许多研究表明, 法国数学家利维于1925年提出的稳定分布模 型是一种能够比较合理描述这类噪声的模型。 本文以稳定分布和信 道编码理论为基础，并以稳定分布噪声为脉冲噪声模型， 研究了脉 冲噪声环境下编码信道（循环码和卷积码）的抗噪声性能。研究结果 表明， 脉冲噪声对编码信道所造成的误码影响比高斯噪声所造成
2、的误 码影响大得多， 且高斯噪声所造成的误码率在信噪比较小的情况下即 可达到0，远小于脉冲噪声所要求的信噪比。 【关键字关键字】 ：稳定分布，编码信道，抗噪声性能，循环码，卷积码 1 2 Abstract In 1948, Claude Shannon, the founder of information theory and coding theory，proposed the well-known noisy channel coding theorem， which contributed to the rapid development of coding theory based
3、on Gaussian noise. However, the traditional research based on Gaussian noise is not consistent with the reality that the majority of the channels are in the impulse noise environment. Therefore, the research of anti-noise performance of the channel coding in the Impulse noise environment has importa
4、nt theoretical and applied significance. Many studies show that the -stable distribution which was proposed by the French mathematician Levy in 1925 is a more appropriate description of these noises. The anti-noise performance of the coding channel(cyclic code and convolution code) based on the theo
5、ry of -stable distribution and coding channel is researched here. The noises which follow the -stable distribution are used as the impulse noises in this paper. Studies show that, alpha noises make much bigger influence than the Gauss noises to the coding channel when the SNR is big. BER caused by G
6、auss noises can achieve zero when the SNR is much smaller than by alpha noises. 【Keywords】: -stable distribution，Coding channel，Anti-noise performance，Impulse noise environment，Cyclic code， Convolution code 3 目目 录录 第一章 绪论. 1 第二章 信道编码 . 3 2.1 信道编码的概念 . 3 2.2 信道编码的特点 . 4 2.3 信道编码的分类 . 5 2.4 线性分组码 6 2.5 卷积码 . 8 第三章 稳定分布 13 3.1 稳定分布的提出 13 3.2 稳定分布 . 14 3.2.1 稳定分布的概念 . 14 3.2.2 稳定分布模型. 15 3.2.3 稳定分布的几种特殊情况 . 16 3.2.4 广义中心极限定理 . 17 3.3 稳定分布随机变量的产生 . 18 3.4 分数低阶 稳定分布噪声条件下混合信
