纠正同步错误的广义低密度码研究

发布时间：2018-03-10 20:20

本文选题：同步错误　切入点：级联码　出处：《天津大学》2014年硕士论文　论文类型：学位论文

【摘要】：同步错误在实际的通信和存储系统中是比较常见的,例如多媒体数字水印系统和磁记录系统,主要表现为比特或符号的插入和删节。单个未被纠正的同步错误会引发一系列突发性的替代错误,直到系统恢复同步,这将造成灾难性的后果。针对同步错误,研究者们设计了一类可纠正同步错误的纠错码。其中,Davey和Mackay针对随机同步错误信道提出一种称为DM构造的级联码编译码方案,可纠正多个同步错误和替代错误,是非常具有应用前景的同步错误纠错码。然而,这种级联码采用多进制低密度奇偶校验(Low-Density Parity-Check,LDPC)码作为外码,编码复杂度较高。针对该问题,本文对DM构造的外码进行了优化设计,设计了一类特殊的广义低密度码,也即每行采用相同非零元素组的多进制LDPC码。首先,本文采用半随机构造法构造了一种低编码复杂度的多进制LDPC码。这种半随机构造法采用渐进边增长算法与准循环扩展方法对基矩阵进行扩展,并对非零元素进行了优化配置。通过优化非零元素的值,尽量消除了短环,并有效减少了低重码字的数量,改善了多进制LDPC码的性能。由于可将这种码的校验矩阵转换为重复累加码的校验矩阵的结构,因此可实现低复杂度编码。该类多进制LDPC码的每一行采用相同的非零元素组,因此是一类特殊的广义低密度码,性能优越。进一步,将DM构造的外码替换为所构造的多进制LDPC码,来纠正通信系统中的替代错误和同步错误。改进的DM构造以水印码为内码,用于推断发生同步错误的位置以恢复同步,并为外译码器提供软信息输出;以所构造的多进制LDPC码为外码,采用置信度传播迭代译码算法纠正接收序列中的插入、删节及替代错误。仿真结果表明,改进的DM构造在二进制插入、删节、替代(Binary Insertion-Deletion-Substitution,BIDS)信道下具有较好的纠错性能,且编码复杂度较低。
[Abstract]:Synchronization errors are common in real communication and storage systems, such as multimedia digital watermarking systems and magnetic recording systems. A single uncorrected synchronization error can cause a series of sudden substitution errors until the system resumes synchronization, which will have disastrous consequences. Researchers have designed a class of error-correcting codes which can correct synchronization errors, in which Davey and Mackay propose a concatenated coding and decoding scheme called DM construction for random synchronous error channels, which can correct multiple synchronization errors and substitute errors. However, this concatenated code takes Low-Density Parity-Checkcheck LDPC (LDPC) code as the outer code, which has high coding complexity. In order to solve this problem, this paper optimizes the design of the outer code constructed by DM. A special class of generalized low density codes is designed, that is, the multiary LDPC codes with the same set of nonzero elements are used in each row. In this paper, a low coding complexity multiary LDPC code is constructed by using semi-random construction method, in which the base matrix is extended by the asymptotic edge growth algorithm and the quasi-cyclic expansion method. By optimizing the value of non-zero elements, the short loop is eliminated as far as possible, and the number of low-duplication code words is reduced effectively. The performance of the multiary LDPC code is improved. Since the check matrix of this code can be converted into the structure of the check matrix of the repeated accumulative code, the low complexity coding can be realized. Each row of this kind of multiary LDPC code adopts the same set of non-zero elements. Therefore, it is a special kind of generalized low density code with superior performance. Furthermore, the outer code constructed by DM is replaced by the constructed multiary LDPC code to correct the substitution error and synchronization error in the communication system. The improved DM construction takes the watermark code as the inner code. It is used to infer the position of synchronization error to restore synchronization, and to provide soft information output for the external decoder, to use the constructed multiary LDPC code as the outer code, and to correct the insertion in the received sequence by using the confidence propagation iterative decoding algorithm. The simulation results show that the improved DM structure has better error-correcting performance and low coding complexity in binary insertion, deletion and substitution of binary Insertion-Deletion-Substitution-SubstitutionBIDSs channel.
【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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