【作者】 王芳；

【导师】 岳殿武；

【作者基本信息】 大连海事大学 ， 通信与信息系统， 2006， 硕士

【摘要】 自1948年Shannon提出并证明了著名的有扰信道编码定理以来,人们一直在努力寻找一个更能逼近Shannon理论极限的好码。从早期的分组码、代数码、RS码、卷积码,直到今天的Turbo码和低密度奇偶校验码(low density parity check codes,简称LDPC码),系统性能与Shannon极限间的差距越来越小。Turbo码和LDPC码的出现,可以说是信道编码理论在通信领域中一次大的飞跃。由于LDPC码比Turbo码还具有更多的优点,所以目前人们的注意力更集中在了LDPC码上。 作为一种新的编码技术,LDPC码无论是在编译码方面还是在其应用方面,都引来无数学者的注意。本文对LDPC码进行了系统研究。首先从校验矩阵和二分图两方面介绍了LDPC码的定义,然后讨论了LDPC码的结构及其编码思想,给出了LDPC码的一些原始构造方法,并根据LDPC码的特点及目前LDPC码编码时存在的缺点,设计了基于单位矩阵的LDPC码。该构造方式利用了分组交织器,使得构造出来的LDPC码含有很少的环。利用MATLAB对该码进行了仿真,仿真结果表明:该码在系统性能上要比其它的LDPC码有一定的改善;最后本文讨论了LDPC码在IEEE802.16a中的应用以及LDPC码在图像传输中的应用。 LDPC码由于其性能的优越性及其在数学分析上的相对简单性,已经引起了编码学术界的广泛兴趣。而且,对LDPC码的研究也给其他编码带来了新的血液,使得人们对Turbo码等其他编码技术有了新的认识。相信这样一种具有卓越性能的编码方式必将在理论上有更进一步的发展并在实际中得到广泛的应用。更多还原

【Abstract】 Since Shannon proposed and proved famous coding theorem in 1948, people have been making great efforts to look for a kind of good code, whose performance could approach to the Shannon’s theoretical limit. From early block codes, algebra codes, RS codes and convolutional codes to Turbo codes and low density parity check codes (LDPC codes);the coded system performance is closing to the theoretical limit. The appearance of the two codes is a great breakthough on channel coding theorem in the field of communication. But because the performance of LDPC codes is superior to that of Turbo codes, people’s attention is more mainly focused on LDPC code rather than Turbo codes at the moment.As a new coding technology, LDPC codes arouse many scholars’ concern not in the hand of coding and decoding, but in the hand of application. This paper gives a systematic investigation of LDPC codes. First, the definitions of LDPC codes are introduced from the aspect of parity matrix and bipartite graph. Then the structures of LDPC codes and the thought of their encoding and decoding are discussed. Some original methods of constructing LDPC codes are presented. On the base of the characteristic of LDPC code and the disadvantage of coding, a kind of LDPC codes based on identity matrix is designed, which can make use of block interleavers to reduce the cycles. It shows by the MATLAB simulation that the error performance is improved with the new kind of LDPC codes. Finally, the applications of LDPC codes to IEEE802.16a and picture transmit are discussed.LDPC codes have raised a large interest in the coding community with its excellent performance and relative simple analysis in mathematics. The study on LDPC codes gives new blood to other coding schemes, bring new recognize to other codes such as Turbo codes. Such codes with excellent performance must be developed further in theory and be widely used in practice.更多还原