【作者】 李玉祥；

【导师】 梁国龙；

【作者基本信息】 哈尔滨工程大学 ， 信号与信息处理， 2011， 博士

【摘要】 纠错编码技术是移动通信、卫星通信、光纤通信和磁盘存储等系统中的关键技术之一,低密度奇偶校验码(Low-Density Parity-Check, LDPC)是一种性能逼近Shannon限的纠错码,也是目前被广泛关注的一种信道编码。本文以水声通信为应用背景,以LDPC码为信道编码,对水声信道中的二进制LDPC码、多进制LDPC码、MMO系统的LDPC码和高阶调制LDPC码的传输特性进行了理论分析、仿真与试验研究。本论文得到了哈尔滨工程大学中央高校基本科研业务费专项资金"LDPC码在水声通信中的应用研究”(HEUCFL20101114)的支持,主要的研究内容包括：1.二进制LDPC码与多进制LDPC码的研究。从LDPC码的构成元素来分,主要有二进制与多进制LDPC码。研究了二进制LDPC码的基本原理、编译码方法。对二进制LDPC码在水声信道中的传输性能进行了仿真,分析了码长、迭代次数的变化对译码性能的影响,为其参数的设置提供了参考依据。LDPC码与卷积码、Turbo码进行了性能的对比,表明了LDPC码在水声信道中的传输是可行的,并与现有的性能较好的码相比具有一定的优越性。多进制LDPC码同样是LDPC码研究领域中的一个热点问题,由于多进制元素能够减少校验矩阵中短环的个数而使其性能要优于二进制LDPC码,但多进制符号与二进制比特间转换矩阵的求解并没有相关的文献报道,本文首先用线性代数方法证明了多进制符号和二进制比特间转换矩阵的唯一性,然后给出了转换矩阵的求解方法,此方法还可以推广至多进制符号与二进制比特间格雷映射关系的转换。对多进制LDPC码译码算法中的难点,校验节点向变量节点的消息传递过程做了具体的分析,并对其译码性能进行了仿真。最后研究了多进制LDPC码在水声信道中的应用,表明多进制LDPC码可以应用在复杂声速分布的水声信道中。2.提出了基于模拟退火算法和信息状态转移图的度分布对设计方法。模拟退火算法是一种非导数的优化方法,在组合优化方面具有快速准确的优越性。同时利用信息状态转移图的变量节点曲线与校验节点曲线的匹配程度作为模拟退火算法寻优的目标函数,用此方法得到的变量节点曲线与校验节点曲线的匹配与用密度进化法得到的曲线匹配程度近似,表明了此方法的优化性,同时也降低了度分布参数的寻优时间。3.将LDPC码应用在MMO系统中,用因子图表示了MMO信道,提出了LDPC码与MMO系统空时分组码的联合检测迭代译码技术,通过将LDPC译码与空时分组码间的软信息进行多次迭代,增加了信道信息可靠性从而提高了译码性能。将高阶调制软信息提取的简化算法应用在高阶调制LDPC码的系统中,此简化算法将二维欧式距离简化为一维计算,结果表明软解调比硬解调获得了更多的编码增益,提高了通信系统的容量并降低了误码率。最后进行了LDPC码的湖试试验,对数据信息与图像信息进行了传输性能的测试,进一步表明了LDPC码在实际应用中的可行性。更多还原

【Abstract】 Error-correcting codes are widely applied in many fields, such as mobile communications, satellite communications, optical communications and disk recorders. Low-density parity-check (LDPC) codes belong to a family of error-correcting codes, approaching to Shannon limit. LDPC as a channel code is expected to be prosperous in underwater acoustic communication. In the dissertation, the theoretical analysis, the numerical simulation and the experimental work are utilized to study the transmission characteristics of binary LDPC codes, nonbinary LDPC codes, LDPC codes in MIMO system and LDPC Codes based on high order modulation.This thesis has been supported by the Fundamental Research Funds for the Central Universities "Study on application of LDPC Code in Underwater Acoustic Communication" (HEUCFL20101114) of Harbin Engineering University.The main contents of this thesis are as follows:1. According to the constitution element of LDPC codes, it can be usually divided into binary LDPC codes and nonbinary LDPC codes. The basic principle, encoding and decoding method of the binary LDPC codes are investigated, then the simulations are carried out to show the transmission characteristic of the binary LDPC codes in the underwater acoustic communication, the effects of the iterations times and the code length on the decoding performance are analyzed elaborately, which provides the reference for the determination of LDPC’s parameters. Being comparison with the convolution codes and Turbo codes, the transmission of LDPC codes in underwater acoustic channels is feasible. Nonbinary LDPC codes have also been attracted much attention in recent years. Nonbinary elements can reduce the number of short cycles in the check matrix, consequently nonbinary LDPC codes is superior to binary LDPC codes. However, to my knowledge, no relevant reports have been published on the solution of transfer matrix between nonbinary LDPC codes and binary LDPC codes. In this dissertation the linear algebra is used to prove the uniqueness of transfer matrix, subsequently the solution is presented. This solution is still applied to the transformation of Gray maps between the nonbinary and binary elements. As a main obstacle in nonbinary decoding algorithm, the message transmission from the check node to the variable node is studied, and simulated results are utilized to successfully recognize the decoding performance. Finally, nonbinary LDPC codes are applied in the underwater acoustic channel and the results indicate that they are ideally suitable for applications in the complex sound-speed distribution.2. The design method of degree distribution is proposed based on the simulated annealing algorithm and EXIT (Extrinsic Information Transfer Chart). The simulated annealing algorithm is a non-derivative optimization algorithm, which is fast and accurate in the aspect of combination optimization. Meanwhile, the match degree between the variable node curve and the check node curve of the EXIT is treated as the objective function of the simulated annealing algorithm optimization. The results reveal that there is a good agreement between the match degree and the density evolution and the proposed method is not only superior but also reduces the optimization time of the degree distribution parameter.3. When the LDPC codes are applied into the MIMO system and the factor graph represents the MIMO channel, a joint detection and decoding algorithm of LDPC codes and space-time block codes in MIMO system is proposed. Iterating the soft information of LDPC-MIMO can improve the reliability of channel information and the decoding performance. The simplified algorithm of soft information extraction is applied into LDPC codes system with higher-order modulation, which simplifies the two-dimensional distance into the one-dimensional calculation. The results show that the soft demodulation obtains more coding gain than the hard one, then the capacity of communication system is improved and the error rate is reduced. At last, Lake trials of the LDPC codes are performed, and the transmission performance of the data and image information is tested. The conclusion can be drawn that the LDPC codes are feasible and reliable in practical underwater acoustic applications.更多还原