Error Exponent for Covert Communications over Discrete Memoryless Channels

We define and study the error exponent of covert communications over binary-input Discrete Memoryless Channels (DMCs). Our main result consists of upper and lower bounds for the exponent, which match in a regime that we explicitly characterize. While our proofs follow standard techniques, the vanishing rate regime inherent to covert communications and the low-weight of codewords introduces specific technical challenges. In particular, the lower bound of the error exponent follows from a non-standard constant-composition ensemble instead of an independent and identically distributed (i.i.d.) ensemble, and the upper bound requires a careful treatment that does not appear in the traditional analysis of error exponent.