Random complex field code design for security over wiretap channels

Wiretap channel has caught a lot of attention recently in secured communications. A commonly adopted wiretap model is that the main channel is noiseless and the eavesdroppers channel is binary erasure channel (BEC). LDPC codes have been applied to achieve strong secrecy. However, it lacks design flexibility balancing on security and reliability, and cannot illustrate the fundamental tradeoffs among erasure rate, secrecy rate, and the security performance. In this paper, we propose a random complex field code (RCFC) design for such wiretap channels. The design of RCFCs is systematic and flexible for any secrecy rate. By using the proposed code design, the desired receiver can decode the confidential information without any error (in the absence of noise). Simultaneously, when the secrecy rate is below or equal to the secrecy capacity, we prove that the mutual information between the confidential message and the decoded message given by the eavesdropper converges to zero with the codeword length goes to infinity. Additionally, our RCFC design is the first one which provides a platform to tradeoff secrecy rate with the security performance.