Covert Communication With Mismatched Decoders

TL;DR

This paper investigates the limits of covert communication when the receiver's decoder is mismatched or sub-optimal, providing bounds on the maximum reliable and covert data transmission rates under these conditions.

Contribution

It derives the first single-letter bounds on covert communication throughput with mismatched decoders, applicable to specific channel and decoding metric scenarios.

Findings

Bounds match for binary-input binary-output channels

Bounds are tight for erasures-only decoding metrics

Introduces novel coding and analysis techniques for mismatched decoding in covert settings

Abstract

This paper considers the problem of covert communication 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 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 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 proof of the upper bound relies on a non-trivial combination of analytical techniques for the problems of covert communication and mismatched decoding.