【作者】 郝永杰；

【导师】 蒋建国； 吴从中；

【作者基本信息】 合肥工业大学 ， 电路与系统， 2007， 硕士

【摘要】 在数字通信中，纠错码技术得到了广泛的应用。作为一种性能优异的纠错码，RS码在实际应用中发挥着重要的作用。本论文的内容主要在于对RS码的算法、RS码在某些移动信道中的应用进行研究，并讨论RS码在DSP上编程实现的一些相关问题。在本课题的研究中，选择了两个RS码作为研究对象，它们分别是RS(15，9，7)码和RS(255，223，33)码。这两个码的性能和参数存在着很大的差异，其应用背景也有所不同：RS(15，9，7)码用于允许较高编码冗余度的场合；其编译码速度较快。RS(255，223，33)码适用于低冗余度的场合；但其编译码速度较慢。本文的工作主要集中在以下几个方面：1．对RS码的原理和常用编译码算法进行了简单的介绍；2．基于错误图样重量分布的规律，提出了一种改进的RS码译码流程，并将其应用到RS(15，9，7)码的译码中。理论分析和实验都表明，改进译码流程比传统译码流程节省约30％～50％的计算量；3．根据相关文献中提供的算法思想，推导出GF(2~8)有限域上的快速傅立叶变换公式和拉格朗日插值公式，并将它们应用到RS(255，223，33)码的快速编码和伴随式计算中，使这两步的计算量降低到原来的10％～30％；4．讨论了RS码在TI TMS320C64x DSP上编程实现的相关问题(如用二表法实现有限域上的乘方运算)，并结合64xDSP的硬件结构和特点，对编译码过程中的某些算法进行了程序优化设计(如结合64x的有限域乘法器和流水线结构设计有限域上的求逆算法等)；5．根据相关文献提供的信道参数，用隐Markov模型对不同调制方式、不同传信率及不同环境下的八个移动数字信道进行仿真。利用仿真的结果，分析RS(15，9，7)码和RS(255，223，33)码在这些信道中的纠错性能。实验表明，在结合适当的交织以后，两个RS码在这些信道中都能得到较好的纠错效果。本文最后对全文的工作作了总结和展望，指出了以后的研究方向和工作重点。更多还原

【Abstract】 The technology of error-correcting code has been widely used in the digital communication. As a good error-correcting code, RS code has been having a desired effect on many applications. So this thesis mainly researches on the algorithm of RS code and its application in some mobile channels, and discusses some issues about the implement on DSP of RS code.During the research, two different types of RS code are selected as the studying objects. They are (15,9,7)RS code and (255,223,33)RS code.There are many differences between them concern their parameters and performances, so they have been used in different applications: RS(15,9,7) is suit for the application that allows high redundancy,but it has a high encoding-decoding speed; RS(255.223,33) is suit for the application of low redundancy,but it’s slow when encoding-decoding. In this paper, several points are focused, which are listed below:1. Principle and algorithm of RS code is introduced first;2. An improved flow of RS decoding is proposed in this thesis. For (15,9,7)RS code, using this improved flow can reduce about 30%～50% of the computational complexity compare with the traditional one;3. Basd on the idel of correlative thesis, we conclude the formula of DFT and Lagrange interpolation over GF(2~8) by program, and then use them to encoding the (255,223,33)RS code and computing its syndromes, and reduce 70%～80% of the computational complexity of these two steps;4. Discuss some issues about the implement on TI TMS320C64x DSP of RS code(eg.algorithm for power operation over GF(2~8)). Optimize some steps of encoding and decoding combined with the characteristic of 64x DSP.5. Based on the parameters provided by correlative thesis, eight digital mobile channels with different modulation,different data rata and different environment are simulated, using Markov model. Using the result of simulation, the performance of (15,9,7)RS code and (255,223,33)RS code in these channels are analysised. Experiment shows that combined with proper interlace, these two codes are both effective in these channels.At last, conclusions and the direction of future improvement are summarized.更多还原