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

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).