两种图码的BP译码算法研究

发布时间：2018-04-04 15:20

本文选题：图码　切入点：低密度奇偶校验码　出处：《西安电子科技大学》2014年硕士论文

【摘要】：低密度奇偶校验(LDPC)码和极化(Polar)码由于译码过程都是基于因子图,因此也称作图码,由于它们优越的性能,进而成为了近年来信道编码领域的研究热点。本文采用理论与仿真分析相结合的方法,对LDPC码以及Polar码的置信传播(belief propagation)译码算法做了研究与实现。主要完成了以下几个方面的工作:系统的介绍了两种图码——LDPC码和Polar码的基本概念,LDPC码的构造、编码、译码方法,介绍了Polar码的编码方法以及连续删除(successive cancellation)译码算法。通过对BP译码算法也就是和积算法(sum-product algorithm)的研究,为了降低译码复杂度,减少译码迭代次数,提出了针对LDPC码的改进算法——MSPA(Modified Sum-Product Algorithm),在译码过程中,通过比较译码迭代过程中连续多次比特信息更新前后值的差异是否满足设定条件,来确定译码停止迭代与否。改进算法主要分为两个步骤:首先,确定比特信息更新前后差值的精度;然后,进行译码迭代至连续多次满足设定精度。并且通过仿真实验分析结果验证了算法的有效性,即在保证译码性能的同时减少了译码迭代次数。此外,还针对Polar码的BP译码算法提出了一种提前终止迭代的改进译码算法——MBP(Modified Belief Propagation),改进算法利用冻结比特左右信息偏移的幅度来设定停止迭代的门限的译码方法,达到了减少了译码算法的迭代次数,同时保证了译码性能。并且通过仿真实验分析验证了改进算法的有效性。
[Abstract]:Low density parity check (LDPC) codes and polarimetric Polar codes (LDPC) codes are also called graph codes because the decoding process is based on factor graphs. Because of their superior performance, LDPC codes have become a hot research topic in the field of channel coding in recent years.In this paper, the method of combining theory with simulation analysis is used to study and implement the decoding algorithm of LDPC codes and Polar codes with confidence propagation propagation.The main work of this paper is as follows: the construction, coding and decoding methods of two kinds of graph codes (LDPC-LDPC-LDPC-codes and Polar codes) are introduced systematically. The coding method of Polar codes and the decoding algorithm of successive cancellations are introduced.In order to reduce the decoding complexity and reduce the number of decoding iterations, an improved algorithm for LDPC codes, which is called sum product algorithm, is proposed in this paper. In the process of decoding, a modified Sum-Product algorithm is proposed.By comparing whether the difference between the values before and after successive bit information updating in the iterative process of decoding meets the set conditions, it is determined whether the decoding stops the iteration or not.The improved algorithm is mainly divided into two steps: first, the accuracy of the difference before and after the bit information update is determined; then, the decoding iteration is carried out to satisfy the set accuracy several times in succession.The simulation results show that the algorithm is effective, that is, the decoding performance is guaranteed and the number of decoding iterations is reduced.In addition, an improved decoding algorithm, MBP modified Belief Propagation, is proposed for BP decoding algorithm of Polar codes. The improved decoding algorithm sets the threshold of stopping iteration by using the amplitude of the left and right information offset of frozen bits.The number of iterations of the decoding algorithm is reduced and the decoding performance is guaranteed.The effectiveness of the improved algorithm is verified by simulation experiments.
【学位授予单位】：西安电子科技大学
【学位级别】：硕士
【学位授予年份】：2014
【分类号】：TN911.22

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