Covert Communication with Mismatched Decoders

This paper considers the problem of covert communication over binary-input discrete memoryless channels with mismatched decoding, in which a sender wishes to reliably communicate with a receiver whose decoder is fixed and possibly suboptimal, and simultaneously to ensure that the communication is covert with respect to a warden. We present single-letter lower and upper bounds on the information-theoretically optimal throughput as a function of the given decoding metric, channel laws, and the desired level of covertness. These bounds match when the decoding metric is particularized to the erasures-only metric, yielding an exact single-letter expression for the so-called covert erasures-only capacity. The lower bound is obtained based on a modified random coding union bound with pulse position modulation (PPM) codebooks, coupled with a nonstandard expurgation argument. The proof of the upper bound relies on a non-trivial combination of analytical techniques for the problems of covert communication and mismatched decoding.