高斯Wiretap模型下基于部分陪集的无线物理层强安全编码

A Wireless Physical Layer Coding Method Achieving Strong Security Based on Partitioning Coset for the Gaussian Wiretap Model

针对无线物理层安全编码不能保证信息在有噪信道下进行强安全传输的问题,该文提出一种基于部分陪集的强安全编码方法。首先证明了当且仅当陪集母码的对偶码的最小汉明距离大于信息泄露位数时,利用部分陪集编码能够保证信息的强安全传输;然后证明了陪集编码的一系列性质,基于这些性质可以将陪集间最小汉明距离计算降低为1次查表运算,进而设计了一种基于树形深度优先的最大可用陪集集合搜索算法;最后分析得出一些典型线性分组码的抗窃听信道信息泄露和抗合法信道传输噪声的能力,以及相应的最大可用陪集集合。当陪集母码为BCH(15,11)的对偶码时,与传统陪集编码方案相比,该方法对合法信道的信道质量要求降低了5 dB,同时能够保证信息传输的强安全性。

To solve the problem of that the wireless physical layer secrecy coding can not achieve strong security while the legal channel is noisy, a strong security coding method is proposed based on partitioning coset. First, it is proved that if and only if the minimum Hamming distance of the dual code of the coset mother code is larger than the number of leak bits, the method can keep strong security. It is also proved that many properties of partitioning coset can help to decrease the calculation complexity to one time table search to get the Hamming distance among cosets, and a search algorithm is proposed based on tree deep priority to get maximum available coset set. Finally, the abilities of anti-information leakage in eavesdropper channel, the anti-noise in legal channel, and the corresponding maximum available coset set of typical linear block codes is presented. Compared with the traditional method, the proposed method reduces the requirement of the legal channel quality with 5 dB while keeping strong security when the mother code is the dual code of BCH（15,11）.