基于球形译码的RS码译码性能研究.pdf

摘 要
Reed-Solomon 码是是一种在移动动通信，深空通信，数字存储中广泛应用的非二
进制制的循环纠错码。它具有严格的代数结结构，对随机错误，突发错误和删删除错误
都有良好的纠错性能。
本文主要研究 RS 码软判判决译码算法，重点研究 RS 码的 KV 译码算法和球形
译码 SD(Sphere Decoding)算法，详细分分析了该算法的优缺缺点。基于球形译码，给给
出出了更有效的译码算法。本文的主要工作概括如下：
1. 概述了 RS 码有关代数知识，总结结了 RS 码的一些重要特性。通过介绍循环
码的概念，引出出了 BCH 码和 RS 码，阐述了二者之间的联系和区别别，并对 RS 码
的译码性能进行分分析。
2. 在了解 RS 码编编码方法的基础上，详细讨论了它的传统统译码算法。着重分分
析了 KV 算法及其多项式插插值子算法、因式分分解子算法的原理，给给出出了 KV 算法
的两个性能界，并在 AWGN 信道下进行了仿真，讨论了复杂度因子的影响，对比比
了不同码长，不同码率码字的译码性能。
3. 着重探讨 SD 球形译码算法与传统统 RS 译码算法在译码复杂度方面的优缺缺
点，并依据仿真结结果表明明，SD 算法在译码复杂度方面得到到了明明显显的改善，使得
RS 码的软判判决译码算法在保持高译码性能的同时时，有效地控制制了译码的复杂度。

关键词：Reed-Solomon 码 Berlekamp-Massey 算法 Koetter-Vardy 算法
SD 球形译码
Abstract
Reed-Solomon （RS ）code is a kind of non-binary cyclic error correcting code,
which can correct not only random errors, but also the burst errors with strong
capability. Due to this and its rigorous algebraic structure, it is widely used in mobile
communication, satellite communication, and data storage.
This thesis is mainly on the soft decision decoding of RS codes, especially on KV
algorithm and SD algorithm, and deeply analyze the advantages and disadvantages of
the algorithm. Based on Sphere Decoding, the improved algorithm of is proposed. Some
results are obtained and summarized as follow:
1. The principle of encoding for RS codes in time domain and frequency domain
coding principle is surveyed, the RS binary pattern mapping method is presented, and
the error probability of bounded distance decoding and the performance of hard
decoding are investigated.
2. Based on the analysis of RS codes’ traditional decoding algorithm, a detailed
discussion of SD is given, and the decoding complexity of SD is also investigated. The
types of impr