Covert Communication over a Physically Degraded Relay Channel with Non-Colluding Wardens

We analyze a physically degraded relay channel, in which the transmitter sends a covert message to the legitimate receiver with the help of a relay. Two wardens, who do not collude with each other, monitor communication from the transmitter and the relay, respectively, through two Discrete Memoryless Channels (DMCs) to detect the presence of a covert message. The objective of the transmitter is to deliver the covert message successfully to the receiver without exceeding the covertness threshold of either warden. We identify the optimal asymptotic scaling of message and key bits and the dependence of the covert throughput on the two covertness thresholds.