State Masking Over a Two-State Compound Channel

We consider the fundamental limits of reliable communication over a two-state compound channel when the state of the channel needs to be masked. Our model is closely related to an area of study known as covert communication, a setting in which the transmitter wishes to communicate to legitimate receiver(s) while ensuring that the communication is not detected by an adversary. Our main contribution is the establishment of upper and lower bounds on the throughput-key length region when the constraint that quantifies how much the states are masked is defined to be the total variation distance between the channel output distributions of the two states. When length of the key is sufficiently large, we provide sufficient conditions for the bounds to coincide. Our results follow the so-called square-root law and hence are reminiscent of results in covert communications. Numerical examples, including that of a Gaussian channel, are provided to illustrate our results.