LDPC码及其在安全通信中的应用研究

发布时间：2018-03-21 09:43

本文选题：LDPC码　切入点：QC-LDPC码　出处：《电子科技大学》2017年硕士论文　论文类型：学位论文

【摘要】：随着信息技术的快速发展及其对通信网络的依赖,通信系统的可靠性和安全性变得越来越重要。LDPC码是一类接近香农限的好码,目前在DVB-S2和IEEE802.16e等通信标准中得到了广泛应用。QC-LDPC码是一类易于存储、编译码可由简单硬件电路实现的LDPC码,该类码的一些构造方法在相同编码参数下可得到大量的性能等价码,不仅纠错性能优异,而且也非常适用于安全通信领域。McEliece在1978年第一次打破传统思想,将编码与加密相结合,提出了基于Goppa码的McEliece公钥加密体制,简称M公钥加密体制,Rao利用该思想设计了M对称加密体制,但这两类体制只是基于纠错码构建的加密方案,没有纠错能力。王新梅对M对称加密体制进行修改,提出了同时具备加密和纠错能力的MC分组加密纠错体制。但是目前基于M体制的纠错加密方案存在密钥开销大且只适用于二进制对称信道的缺点,阻碍了其大围实际应用。本文以LDPC码在安全通信中的应用为课题,重点研究了基于QC-LDPC码的安全可靠传输方案以及适用于安全通信的QC-LDPC码构造方法。本文首先分析了LDPC码和QC-LDPC码的特点、编译码方法、构造方法以及目前基于M体制的纠错加密方案的基本原理及其缺陷。然后利用基于RDF(Random Difference Families)的组合设计构造法在相同的编码参数下,可以得到大量等价QC-LDPC码的特点,设计了两个基于QC-LDPC码的安全可靠传输方案。这两个方案一方面通过通信双方随机同步改变加密编码矩阵G'=S·G·P的方式,保证了系统的安全性;另一方面通过使用简单的密钥参数控制置换矩阵P和校验矩阵H的生成和同步变化,降低了密钥开销。另外这两个方案保留了 LDPC码的软判决译码优势,在AWGN信道中也能正确解密。最后结合基于RDF的组合设计思想和IEEE 802.16e标准中的随机构造方法,对基于RDF的组合设计法构造法进行了改进,提出了一种新的适用于安全通信的QC-LDPC码的构造方法。相比基于RDF的组合设计构造法,新方法在相同编码参数下能得到更多性能等价的校验矩阵;设计更加灵活,能够构造出任意码长、码率、度分布的码字;纠错性能更优异,构造码字的纠错能力与PEG算法以及IEEE 802.16e标准构造的码字的纠错能力几乎相同。
[Abstract]:With the rapid development of information technology and its dependence on communication network, the reliability and security of communication system become more and more important. LDPC code is a kind of good code close to Shannon limit. At present, QC-LDPC codes are widely used in communication standards such as DVB-S2 and IEEE802.16e. QC-LDPC codes are a kind of LDPC codes that are easy to store and can be realized by simple hardware circuits. Some construction methods of this kind of codes can obtain a large number of equal-performance codes under the same coding parameters. Not only the error correction performance is excellent, but also very suitable for the secure communication field. McEliece broke the traditional thought for the first time in 1978, combining the code with the encryption, proposed the McEliece public key encryption system based on the Goppa code. The M-symmetric encryption scheme is designed by Rao, a public key cryptosystem for short, but these two schemes are only based on error-correcting codes and have no error-correcting ability. Wang Xinmei modifies the M-symmetric encryption system. A MC block encryption and error correction scheme with both encryption and error correction capability is proposed. However, the current error correction encryption scheme based on M system has the disadvantages of high key overhead and only suitable for binary symmetric channels. This paper focuses on the application of LDPC code in secure communication. In this paper, the secure and reliable transmission scheme based on QC-LDPC code and the construction method of QC-LDPC code suitable for secure communication are studied. Firstly, the characteristics of LDPC code and QC-LDPC code, the encoding and decoding method are analyzed. The construction method and the basic principle and defects of the current error-correcting encryption scheme based on M system are presented. Then, by using the combination design construction method based on RDF(Random Difference families, we can obtain a large number of equivalent QC-LDPC codes under the same coding parameters. Two secure and reliable transmission schemes based on QC-LDPC code are designed. On the other hand, by using simple key parameters to control the generation and synchronization of permutation matrix P and check matrix H, the key overhead is reduced. The other two schemes retain the advantages of soft decision decoding of LDPC codes. It can also be decrypted correctly in AWGN channel. Finally, combining the idea of combination design based on RDF and the random construction method in IEEE 802.16e standard, the method of combination design based on RDF is improved. A new method for constructing QC-LDPC codes for secure communication is proposed. Compared with the combinatorial design method based on RDF, the new method can obtain more performance equivalent check matrices under the same coding parameters, and the design is more flexible. Code words with arbitrary code length, rate and degree distribution can be constructed, and the error-correcting ability of constructing codewords is almost the same as that of PEG algorithm and IEEE 802.16e standard.
【学位授予单位】：电子科技大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：TN911.22

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