本文選題：LDPC碼　切入點(diǎn)：QC-LDPC碼　出處：《電子科技大學(xué)》2017年碩士論文　論文類型：學(xué)位論文

【摘要】：隨著信息技術(shù)的快速發(fā)展及其對通信網(wǎng)絡(luò)的依賴,通信系統(tǒng)的可靠性和安全性變得越來越重要。LDPC碼是一類接近香農(nóng)限的好碼,目前在DVB-S2和IEEE802.16e等通信標(biāo)準(zhǔn)中得到了廣泛應(yīng)用。QC-LDPC碼是一類易于存儲、編譯碼可由簡單硬件電路實(shí)現(xiàn)的LDPC碼,該類碼的一些構(gòu)造方法在相同編碼參數(shù)下可得到大量的性能等價(jià)碼,不僅糾錯性能優(yōu)異,而且也非常適用于安全通信領(lǐng)域。McEliece在1978年第一次打破傳統(tǒng)思想,將編碼與加密相結(jié)合,提出了基于Goppa碼的McEliece公鑰加密體制,簡稱M公鑰加密體制,Rao利用該思想設(shè)計(jì)了M對稱加密體制,但這兩類體制只是基于糾錯碼構(gòu)建的加密方案,沒有糾錯能力。王新梅對M對稱加密體制進(jìn)行修改,提出了同時具備加密和糾錯能力的MC分組加密糾錯體制。但是目前基于M體制的糾錯加密方案存在密鑰開銷大且只適用于二進(jìn)制對稱信道的缺點(diǎn),阻礙了其大圍實(shí)際應(yīng)用。本文以LDPC碼在安全通信中的應(yīng)用為課題,重點(diǎn)研究了基于QC-LDPC碼的安全可靠傳輸方案以及適用于安全通信的QC-LDPC碼構(gòu)造方法。本文首先分析了LDPC碼和QC-LDPC碼的特點(diǎn)、編譯碼方法、構(gòu)造方法以及目前基于M體制的糾錯加密方案的基本原理及其缺陷。然后利用基于RDF(Random Difference Families)的組合設(shè)計(jì)構(gòu)造法在相同的編碼參數(shù)下,可以得到大量等價(jià)QC-LDPC碼的特點(diǎn),設(shè)計(jì)了兩個基于QC-LDPC碼的安全可靠傳輸方案。這兩個方案一方面通過通信雙方隨機(jī)同步改變加密編碼矩陣G'=S·G·P的方式,保證了系統(tǒng)的安全性;另一方面通過使用簡單的密鑰參數(shù)控制置換矩陣P和校驗(yàn)矩陣H的生成和同步變化,降低了密鑰開銷。另外這兩個方案保留了 LDPC碼的軟判決譯碼優(yōu)勢,在AWGN信道中也能正確解密。最后結(jié)合基于RDF的組合設(shè)計(jì)思想和IEEE 802.16e標(biāo)準(zhǔn)中的隨機(jī)構(gòu)造方法,對基于RDF的組合設(shè)計(jì)法構(gòu)造法進(jìn)行了改進(jìn),提出了一種新的適用于安全通信的QC-LDPC碼的構(gòu)造方法。相比基于RDF的組合設(shè)計(jì)構(gòu)造法,新方法在相同編碼參數(shù)下能得到更多性能等價(jià)的校驗(yàn)矩陣;設(shè)計(jì)更加靈活,能夠構(gòu)造出任意碼長、碼率、度分布的碼字;糾錯性能更優(yōu)異,構(gòu)造碼字的糾錯能力與PEG算法以及IEEE 802.16e標(biāo)準(zhǔn)構(gòu)造的碼字的糾錯能力幾乎相同。
[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.
【學(xué)位授予單位】：電子科技大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2017
【分類號】：TN911.22

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