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 sub-optimal, and simultaneously to ensure that the communication is covert with respect to a warden. We present a single-letter lower bound and two single-letter 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 for a variety of scenarios of interest, such as (i) when the channel between the sender and receiver is a binary-input binary-output channel, and (ii) when the decoding metric is particularized to the so-called erasures-only metric. The lower bound is obtained based on a modified random coding union bound with pulse position modulation (PPM) codebooks, coupled with a non-standard expurgation argument. The upper bounds are based on the idea of translating the mismatched-decoding error of the original channel to the decoding error of an auxiliary channel.