Perfect Secrecy in Physical-Layer Network Coding Systems from Structured Interference

Physical-layer network coding (PNC) has been proposed for next generation networks. In this paper, we investigate PNC schemes with embedded perfect secrecy by exploiting structured interference in relay networks with two users and a single relay. In a practical scenario where both users employ finite and uniform signal input distributions, we establish upper bounds (UBs) on the achievable perfect secrecy rates and make these explicit when pulse amplitude modulation modems are used. We then describe two simple, explicit encoders that can achieve perfect secrecy rates close to these UBs with respect to an untrustworthy relay in the single antenna and single relay setting. Last, we generalize our system to a multiple-input multiple-output relay channel, where the relay has more antennas than the users and study optimal precoding matrices, which maintain a required secrecy constraint. Our results establish that the design of PNC transmission schemes with enhanced throughput and guaranteed data confidentiality is feasible in next generation systems.