基于图论的纠正同步错误的译码算法研究

发布时间：2018-05-31 02:38

本文选题：同步错误 + 级联码　；参考：《天津大学》2014年硕士论文

【摘要】：在数字通信系统中,同步是信息可靠传输的重要条件。针对同步错误信道,由Davey和Mackay提出的DM级联码方案中,内码采用水印码,外码采用多进制低密度奇偶校验(Low-Density Parity-Check,LDPC)码,可同时纠正同步错误与替代错误,是非常有效的同步错误纠错方案。本文针对采用水印码与特殊类型多进制LDPC码的级联码方案,研究其改进的译码算法。针对DM构造中多进制LDPC码的编码复杂度高的问题,本文将一类可高效编码的多进制LDPC码,即多进制环码,引入DM级联码中,可以显著降低级联码编码器的处理复杂度。进一步,针对该类LDPC码,提出了一种改进的译码算法,该算法将LDPC码的校验矩阵分解成两个子矩阵,并分别采用置信度传播(Belief Propagation,BP)算法与对数域最大后验概率(Maximum A Posteriori,MAP)算法对其进行译码。仿真结果表明,相较于BP算法,提出的改进算法在低迭代次数时有明显的性能增益。进一步,本文将多进制环码及其改进的译码算法分别用作DM构造的外码与外译码器,并分析了改进的译码算法与原始算法的复杂度。对一次迭代,改进算法增加了复杂度,但是改进算法可以降低迭代次数,因此整体的系统复杂度需要整体优化。仿真结果表明,采用多进制环码作为外码的DM级联码方案可有效纠正BIDS信道下的同步错误和替代错误。
[Abstract]:Synchronization is an important condition for reliable transmission of information in digital communication systems. For synchronous error channel, in the scheme of DM concatenated code proposed by Davey and Mackay, watermark code is used in inner code and low density parity check Low-Density Parity-Check-Based LDPC-code is used in outer code. Synchronization errors and substitution errors can be corrected simultaneously. Is a very effective synchronization error correction scheme. In this paper, the improved decoding algorithm is studied for concatenated codes using watermark codes and special types of multiary LDPC codes. In order to solve the problem of high coding complexity of multiary LDPC codes in DM construction, this paper introduces a class of efficient multiary LDPC codes into DM concatenated codes, which can significantly reduce the processing complexity of concatenated encoders. Furthermore, an improved decoding algorithm is proposed for this kind of LDPC codes, which decomposes the check matrix of LDPC codes into two submatrices. The confidence propagation algorithm (BP) and the maximum posterior probability (Maximum A Posteriorion MAP) algorithm are used to decode the algorithm. The simulation results show that compared with BP algorithm, the proposed improved algorithm has obvious performance gain at low iteration times. Furthermore, this paper uses the multiary ring code and its improved decoding algorithm as DM constructed outer codes and external decoders, and analyzes the complexity of the improved decoding algorithm and the original algorithm. For one iteration, the improved algorithm increases the complexity, but the improved algorithm can reduce the number of iterations, so the overall system complexity needs global optimization. The simulation results show that the scheme of DM concatenated codes using multiary ring codes as outer codes can effectively correct synchronization errors and substitution errors in BIDS channels.
【学位授予单位】：天津大学
【学位级别】：硕士
【学位授予年份】：2014
【分类号】：TN911.22

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