结构化LDPC码及在编码调制系统中的应用

发布时间：2018-08-28 17:30

【摘要】：结构化LDPC(Low-Density Parity-Check,LDPC)码是一种逼近香农限的实用好码,工程中通常用结构化的方法进行构造。而准循环LDPC(Quasi-Cyclic LDPC,QC-LDPC)码因为其校验矩阵具有准循环的特性在实际应用中具有很大的发展潜力和研究价值。LDPC码与BICM-ID系统相结合在不同信道条件下都能获得很好的性能表现,是目前编码调制系统的热门技术之一。本文主要工作及创新点如下:(1)改进了一种基于有限域子集的QC-LDPC码构造方法。本文在有限域的基础上,利用两个有限域元素子集构造QC-LDPC码,在复杂度和性能表现之间取得了一定的平衡,并且能够获得较大的围长,仿真表明性能表现比一般的有限域方法更为优异。(2)改进了一种简单有效的掩模矩阵构造方法。在用有限域进行构造的过程中,无法保证校验矩阵的稀疏特性,因此需要采用掩模(masking)技术降低它的密度。针对用PEG算法进行掩模矩阵的构造在矩阵较小时效果不好的缺陷,改进了一种掩模矩阵构造法,在扩大了围长的同时减少了短环的数量。改进后构造的准循环LDPC码性能表现更加优秀。(3)设计了一种等概非均匀的星座图,将其应用到BICM-ID系统中,并与采用非等概映射的BICM-ID系统进行了性能比较。传统的通信系统中调制器并不具备任何成形增益,而本文通过几何成形和概率成形两个方面的优化设计获得成形增益。在几何成形方面,设计了一种等概非均匀的星座图,将空间上的星座点分布近似服从离散高斯分布,从而获得性能增益。与传统的QAM星座相比可以获得更为优异的性能表现。在概率成形方面,设计了一种非等概映射规则。该规则使各个星座点被使用的概率近似服从离散高斯分布,同时让每个星座点集合内部以及星座点之间的汉明距离最小化以降低错误概率。仿真结果证明这两种方法都给整个BICM-ID系统带来了一定的性能提升。
[Abstract]:Structured LDPC (Low-Density Parity-Check,LDPC) codes are practical codes that approach the Shannon limit and are usually constructed by structured methods in engineering. The quasi-cyclic LDPC (Quasi-Cyclic LDPC,QC-LDPC) code has great development potential and research value in practical application because of its quasi-cyclic property of check matrix. The combination of LDPC code and BICM-ID system can achieve good performance under different channel conditions. It is one of the most popular technologies in the coding modulation system. The main works and innovations of this paper are as follows: (1) an improved method for constructing QC-LDPC codes based on finite field subsets is proposed. In this paper, based on finite field, QC-LDPC codes are constructed by using two subsets of finite field elements, which achieve a certain balance between complexity and performance, and can obtain large girth. Simulation results show that the performance is better than the conventional finite field method. (2) A simple and effective mask matrix construction method is improved. In the process of constructing the finite field, the sparse property of the check matrix can not be guaranteed, so the mask (masking) technique is needed to reduce its density. Aiming at the disadvantage of constructing mask matrix with PEG algorithm, a mask matrix construction method is improved, which not only widens the girth but also reduces the number of short rings. The performance of the improved quasi-cyclic LDPC codes is better. (3) an equal-non-uniform constellation diagram is designed and applied to the BICM-ID system, and the performance of the BICM-ID system with non-equal-almost mapping is compared. In the traditional communication system, the modulator does not have any shaping gain, but in this paper, the shaping gain is obtained by the optimal design of geometric shaping and probabilistic shaping. In geometric shaping, an equal-inhomogeneous constellation diagram is designed to approximate the constellation point distribution from the discrete Gao Si distribution to obtain the performance gain. Compared with the traditional QAM constellation, it can get better performance. In the aspect of probabilistic shaping, we design a kind of non-equal-probability mapping rule. The rule approximates the probability of each constellation to be used from discrete Gao Si and minimizes the hamming distance within and between constellation points to reduce the error probability. The simulation results show that both of these two methods can improve the performance of the whole BICM-ID system.
【学位授予单位】：华侨大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：TN911.22

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