Optimal codes for information-theoretically covert communication

Abstract

We consider a problem of coding for covert communication, which involves ensuring reliable communication between two legitimate parties while simultaneously guaranteeing a low probability of detection by an eavesdropper. Specifically, we develop an optimal low-complexity coding scheme that achieves the information-theoretic limits of covert communication over binary-input discrete memoryless channels. We first demonstrate the non-triviality of designing codes for covert communication by showing the impossibility of achieving information-theoretic limits using linear codes without a shared secret key for a regime in which information theory proves the possibility of covert communication without a secret key. We then circumvent this impossibility by introducing non-linearity into the coding scheme through the use of pulse position modulation (PPM) and multilevel coding (MLC). This MLC-PPM scheme exhibits several appealing properties; in particular, for an appropriate decoder, the channel at a given level is independent of the total number of levels and the codeword length. We exploit these properties to show how one can use families of channel capacity- and channel resolvability-achieving codes to concretely instantiate a covert communication scheme. Further, we extend the MLC-PPM scheme using bi-orthogonal PPM symbols to achieve information-theoretic limits of covert communication over additive white Gaussian channels. Finally, we illustrate the application of this scheme for the secret-key generation problem with a covertness constraint.