准循环LDPC码的构造算法研究

发布时间：2018-08-31 20:03

【摘要】：LDPC(Low-Density Parity-Check,低密度奇偶校验)码是目前公认的纠错性能最好的信道编码技术之一,该码可以应用在几乎所有的信道上,同时其校验矩阵H的结构非常地简单,具有逼近香农极限的纠错性能。在实际的工程实现中,编译码器的实现都非常简单并且可以使用并行操作节省资源。QC-LDPC码是一类结构化的LDPC码,由于其校验矩阵H独有的准循环特性,使其可以实现线性复杂度的编码。本文的主要内容是对准循环LDPC码构造算法的理论研究及性能分析,主要工作包括:(1)主要从LDPC码的定义出发、通过对构造算法、编译码算法的深入分析,以及准循环LDPC码的基本概念,对LDPC码的基本理论作了一个系统的、详细而深入的分析研究,以达到可以从整体把握LDPC码;(2)基于BIBD的准循环LDPC码的构造算法。首先介绍了文献中传统的基于BIBD构造LDPC码的算法,通过使用关联矩阵在区组和校验矩阵之间建立联系;然后,介绍了一种通过用位置矢量代替关联矩阵,将区组中的元素分别与校验矩阵建立关系的改进算法,这样构造的校验矩阵对列进行了4:1的扩展,使列重降为原来的1/4;上面两种算法都是基于有限域中的加法运算实现的,用本原元的幂乘运算代替元素的加法运算,得到了一种基于乘法群和BIBD的构造准循环LDPC码的算法。通过对三种算法进行的性能仿真实验,结果表明:在高斯白噪声信道下,两种改进算法在纠错性能上都有所提高;在进行迭代译码时,第二种改进算法相比前两种算法的的收敛速度快。(3)基于PEG算法的准循环LDPC码。基于Tanner图的PEG构造算法是随机构造算法中性能最优的一种,非常适用于构造码长较短的LDPC码字。通过用单位循环置换矩阵对基于PEG算法构造的基矩阵进行扩展,可以得到一种具有准循环特性的校验矩阵,并且通过改变扩展子矩阵的大小,可以应用这种改进的PEG算法构造任意码长的码字,使得PEG算法不再受限于码字的长度。同时,通过对基矩阵中短环上对应的子矩阵的移位参数的修正,可以增大构造的校验矩阵的围长,改善构造的LDPC码字的纠错性能。仿真结果表明,通过矩阵扩展的PEG算法构造的LDPC码的纠错性能和基于传统的PEG算法构造的LDPC码的性能非常相近。同时子矩阵的存在,可以使得LDPC码的参数选择变得更为灵活,并且这种改进的算法构造的校验矩阵在结构上具有准循环的特性,简化编译码过程。
[Abstract]:LDPC (Low-Density Parity-Check, low density parity check) code is one of the most widely accepted channel coding techniques with the best error-correcting performance. It can be used in almost all channels, and the structure of the check matrix H is very simple. It has the error correction performance of approaching Shannon limit. In practical engineering implementation, the implementation of encoder and decoder is very simple and can save resources by parallel operation. QC-LDPC code is a kind of structured LDPC code. So that it can achieve linear complexity coding. The main content of this paper is the theoretical research and performance analysis of the alignment cyclic LDPC code construction algorithm. The main work includes: (1) from the definition of LDPC code, through the construction algorithm, coding and decoding algorithm in-depth analysis, And the basic concept of quasi-cyclic LDPC code, this paper makes a systematic, detailed and in-depth analysis of the basic theory of LDPC code, so that we can grasp the LDPC code from the whole. (2) the construction algorithm of quasi-cyclic LDPC code based on BIBD. This paper first introduces the traditional algorithm of constructing LDPC code based on BIBD in the literature, establishes the relation between block and check matrix by using the correlation matrix, and then introduces a method of replacing the correlation matrix with position vector. The improved algorithm which establishes the relation between the elements in block groups and the check matrix respectively, expands the column 4:1 and reduces the column weight to 1 / 4. The above two algorithms are realized based on the addition operation in the finite domain. An algorithm for constructing quasi-cyclic LDPC codes based on multiplicative group and BIBD is obtained by replacing the addition operation of elements with the power multiplication operation of primitive elements. The simulation results of the three algorithms show that the performance of the two improved algorithms is improved in Gao Si white noise channel, and the performance of iterative decoding is improved. The second improved algorithm is faster than the former two algorithms. (3) Quasi-cyclic LDPC codes based on PEG algorithm. The PEG construction algorithm based on Tanner graph is one of the best random construction algorithms, which is very suitable for constructing LDPC codewords with short code length. By using the unit cyclic permutation matrix to extend the base matrix based on the PEG algorithm, a kind of check matrix with quasi-cyclic property can be obtained, and the size of the extended submatrix can be changed. The improved PEG algorithm can be used to construct code words of arbitrary code length, so that the PEG algorithm is no longer limited by the length of the codeword. At the same time, by modifying the shift parameter of the submatrix corresponding to the short ring in the base matrix, the girth of the constructed check matrix can be increased, and the error correction performance of the constructed LDPC codeword can be improved. The simulation results show that the error-correcting performance of the LDPC codes constructed by the matrix extended PEG algorithm is very similar to that of the LDPC codes constructed by the traditional PEG algorithm. At the same time, the existence of submatrix can make the parameter selection of LDPC code more flexible. Moreover, the improved algorithm has the property of quasi-cyclic structure and simplifies the encoding and decoding process.
【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

【相似文献】