Secure Polar Coding for the Two-Way Wiretap Channel

This paper studies polar coding for secure communications over the general two-way wiretap channel, where two legitimate users communicate with each other simultaneously while a passive eavesdropper overhears a combination of their exchanged signals. The legitimate users wish to design a coding scheme such that the interference between their codewords can be leveraged to jam the eavesdropper. This security method is called coded cooperative jamming. Inspired by recent studies on polar coding for asymmetric channels, Slepian-Wolf coding, multiple access channels and wiretap channels, we design a polar code-based cooperative jamming code that achieves the whole secrecy rate region of the two-way wiretap channel under the strong secrecy criterion. To make proper alignment of polar indices, a multi-block method is used. We show that as the blocklength and the number of chained blocks increase, the rate of randomness required to be shared between two legitimate users becomes negligible. For the special case when the eavesdropper channel is degraded with respect to both legitimate channels, a simplified scheme is proposed which can simultaneously ensure reliability and weak secrecy within a single transmission block. An example of the binary erasure channel case is given to demonstrate the performance of our scheme.