光纤通信中多元LDPC码译码算法的研究及FPGA实现

发布时间：2018-04-12 22:12

本文选题：低密度奇偶校验码 + 光纤通信　；参考：《烟台大学》2017年硕士论文

【摘要】：低密度奇偶校验(Low Density Parity Check,LDPC)码是由Gallager博士提出的一种性能优良的线性分组码。它克服了其它很多纠错码的缺点,是目前发现的性能最接近香农限的信道编码。LDPC码译码算法可以通过完全并行的译码结构来降低译码延时,这在很多领域都引起了极大关注。近年来越来越多的学者开始研究LDPC码,这使得LDPC码的编译码算法不断改进。优异的性能使LDPC码在光纤通信、数字水印、水下通信以及深空通信等多个领域都得到了广泛应用。光纤通信作为一种新兴的通信技术,从开始就显示出巨大的优势。二元LDPC码在光纤通信中的应用已经十分广泛,但是多元LDPC码具有更好的性能,因此多元LDPC码更适合在光纤通信中应用。本文主要在以下几个方面进行了深入研究:1.简要介绍光纤通信的特点以及在光纤通信中应用多元LDPC码作为纠错码的优点。对多元LDPC码的基本理论包括表示方式、构造方法以及常见编码方法等进行介绍。2.详细介绍了多元LDPC码几种典型译码算法包括BP译码算法、LOG-BP译码算法、最小和译码算法、扩展最小和译码算法以及FFT-BP译码算法,并且在此基础上对多元LDPC码FFT-BP译码算法进行改进。通过对编码后的码字等间隔加入判决位的方法提高FFT-BP译码算法初始信息的准确性。改进后的FFT-BP译码算法迭代次数明显降低。3.详细介绍了有限域中加法、乘法运算的FPGA实现,并且在此基础上对多元LDPC码编码器进行设计。采用自顶向下的模块化设计思想对改进的多元LDPC码FFT-BP译码算法进行FPGA实现,并采用Modelsim仿真软件验证其准确性。4.总结论文所做的工作,指出论文中存在的不足之处,并且指明下一步的研究方向。
[Abstract]:Low Density Parity check (LDPC) code with low density parity check is a linear block code with excellent performance proposed by Dr. Gallager.It overcomes the shortcomings of many other error-correcting codes, and is that the channel coding. LDPC decoding algorithm, which has the closest performance to Shannon limit, can reduce the decoding delay by completely parallel decoding structure, which has attracted great attention in many fields.In recent years, more and more scholars have begun to study LDPC codes, which makes the encoding and decoding algorithms of LDPC codes continuously improved.With its excellent performance, LDPC codes are widely used in optical fiber communication, digital watermarking, underwater communication and deep space communication.As a new communication technology, optical fiber communication has shown great advantages from the beginning.Binary LDPC codes have been widely used in optical fiber communication, but multivariate LDPC codes have better performance, so multivariate LDPC codes are more suitable for optical fiber communication.This article mainly carries on the thorough research in the following several aspects: 1.This paper briefly introduces the characteristics of optical fiber communication and the advantages of using multiple LDPC codes as error correction codes in optical fiber communication.This paper introduces the basic theory of multivariate LDPC codes, including representation, construction and common coding methods.Several typical decoding algorithms for multivariate LDPC codes are introduced in detail, including BP decoding algorithm, minimum sum decoding algorithm, extended minimum sum decoding algorithm and FFT-BP decoding algorithm. On this basis, the FFT-BP decoding algorithm of multivariate LDPC codes is improved.The accuracy of the initial information of the FFT-BP decoding algorithm is improved by adding decision bits to the coded codewords at equal intervals.The number of iterations of the improved FFT-BP decoding algorithm is significantly reduced by .3.The FPGA implementation of addition and multiplication in finite domain is introduced in detail. On this basis, the multivariate LDPC encoder is designed.The improved FFT-BP decoding algorithm of multivariate LDPC codes is implemented by using the top-down modular design idea, and the accuracy of the algorithm is verified by Modelsim simulation software .4.The paper summarizes the work done, points out the shortcomings of the paper, and points out the next research direction.
【学位授予单位】：烟台大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：TN911.22;TN929.11

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