Research On Physical Layer Secure Coding Based On The Differences Between Channels

The physical layer security coding is a channel coding technique which guarantees both the security and reliability simultaneously. By using the inherent differences between the legal channel and the wiretap channel, it directly prevents the confidential information from being intercepted in the level of information at the physical layer. However, the following problems still exist in the current researches:(1) Random redundancy which ensures the strong security of confidential information shall reduce the actual Hamming distance between symbols, leading to the poor anti-noise performance of strong security codes;(2) Any changes of coding schemes have a same influence on the legal receiver and eavesdropper when the legal channel and the wiretap channel both are Binary Erasure Channels(BECs), leading to a lack of codes with strong security and reliability;(3) Despite that the code with strong security and reliability can be designed based on the channel polarization theory while the statistical channel state information is known, the secrecy rate is low for Polar security code;(4) The security gaps of concatenation codes are too large to discriminatorily transmit the confidential information in the legal channel and the wiretap channel.Supported by National Natural Science Foundation of China ‘Research on Physical Layer Security with Equivalent Wireless Channel Characteristic‘, the dissertiaon firstly analyses the intrinsic relationship between reliability and security based on the theories of mutual information and typical sequence. Then, with the main idea of transforming the small characteristic differences of channels to the obvious disparity of bit error rates between the legal receiver and eavesdropper, the dissertation focuses on the researches of secure and reliable codes when the legal channel is noisy for different scenarios. The main results are represented as follows:1. A coding scheme is proposed based on partitioning coset to deal with the problem of poor anti-noise performance of strong security codes while the legal channel is a Gaussian channel and the wiretap channel is a BEC. The confidential information is transmitted discriminatorily by using the different channel model. Firstly, to keep strong security, we prove that the proposed method can make the confidential information be transmitted with strong security in the BEC wiretap channel if and only if the minimum Hamming distance of the dual code which is mother code of the coset is larger than the number of leaked bits. Secondly, to improve the reliability and the effectivity, we analyze many properties of coset coding to make the calculation complexity decrease to one time of looking up table for getting the Hamming distance among cosets and prove that the largest coset set must contain the basic coset. According to the complete sub-graph theory, a search algorithm based on tree deep priority is further proposed to find the largest available coset set. At last, we provide the performances of anti-noise in the legal channel and anti-leakage in the wiretap channel, along with the corresponding largest coset set for classical coset mother code. Compared with the Wyner‘s method, the analyses and simulations show that the proposed method can reduce the requirement of legal channel quality with 5dB while keeping strong security when the coset mother code is the dual code of BCH(15, 11).2. A method is proposed based on Explosive Fountain code with Coset pre-coding to deal with the problem that the physical layer secrecy codes cannot achieve strong security and reliability when both the legal channel and the wiretap channel are BECs. The confidential information is transmitted discriminatorily by using the different erasure probability. Firstly, the reliability is ensured because of the rateless nature of fountain code. Then, a fountain code with explosive decoding process is designed by optimizing the degree distribution. By taking advantages of the random and explosive natures of the proposed method, EFC scheme can make the eavesdropper intercept few symbols. In order to keep strong security, the random redundancy is added before fountain coding to prevent the eavesdropper from recovering the confidential information from the leaked symbols. The simulation results show that EFC can match the legal channel quality adaptively to keep reliability and reduce the amount of leaked symbols to keep strong security for coset pre-coding.3. A strong security puncturing pattern is proposed for confidential information to deal with the problem that Polar security code has poor performance on transmission rate. The confidential information is transmitted discriminatorily by using the different transmission ability between logical channels after channel polarizing. Firstly, to keep strong security and reliability, a method is proposed to design the mother Polar security code based on channel polarization. Then, to improve the effectivity, three parameters are used to describe the influences of outputs on confidential information by analyzing the iterative structure of Polar encoder, and an optimized puncturing pattern is designed based on the principle of just minimizing the influence on the confidential information. Compared with the traditional method, the simulation results show that the secrecy rate increase by 12.7% while keeping strong security and reliability when the cross transition probabilities of legal channel and wiretap channel are 0.01 and 0.15 respectively.4. A concatenated security method is proposed based on balancing propagation multi-output function to deal with the problem that the error propagation ability of concatenated function is too weak to expand the traditional channel codes to security codes by reducing the security gap. The smaller the security gap is, the easier to transmit the confidential information discriminatorily by using the difference of SNR will be. Firstly, the paper points out the boundedness of the conclusion that the method based on scramble matrix has optimal error propagation. Then, a multiple input and multiple output function under the rule of error propagation is proposed based on Boolean function. The bit error rate after decoding is amplified to reduce the security gap using the designed function. To prevent the outputs being concentrated when the inputs follow uniform distribution, the function is optimized for balance property. Compared with the traditional method, the simulation results show that the error propagation capacity is much closer to the theoretical bound and the security gap decreases by 3.5 d B.