Research on construction of Binary Random Linear Code for Syndrome Coding in Physical Layer Security

In the aspects of increasing system security by syndrome coding, extant research aims at improving system structure and increasing channel difference. However, it is urgent and necessary to design a kind of secure code by using characteristics of the code itself. This paper proposed an algorithm of syndrome coding of binary random linear codes with physical layer security. Based on the analysis of system security, we deducted the formula of the wiretap’s equivocation. Based on the basic idea of syndrome coding, we constructed the parity check matrix of the code and proposed a construction algorithm on consider of minimum distance optimization. The algorithm guarantees the minimum distance of the code reaching the biggest during the extension of parity check matrix. The simulation results show that compared with Best Known Code (BKC) and Best Equivocation Code (BEC) of same length and rate, the newly constructed code by this paper provides better security. It is also superior to BEC code from the aspect of efficiency of algorithm.