Time-Division is Optimal for Covert Communication over Some Broadcast Channels

TL;DR

This paper demonstrates that for covert communication over certain broadcast channels, a simple time-division approach achieves optimal throughput under the square root law, contrasting with non-covert scenarios.

Contribution

It establishes the optimality of time-division strategies for covert broadcast channels where the no-input symbol is non-redundant, a novel result in covert communication theory.

Findings

Time-division achieves optimal covert throughput for certain broadcast channels.

The optimal covert throughput scales with the square root of the number of channel uses.

Using separate point-to-point codes in a time-division manner is optimal for these channels.

Abstract

We consider a covert communication scenario where a transmitter wishes to communicate simultaneously to two legitimate receivers while ensuring that the communication is not detected by an adversary, the warden. The legitimate receivers and the adversary observe the transmission from the transmitter via a three-user discrete or Gaussian memoryless broadcast channel. We focus on the case where the "no-input" symbol is not redundant, i.e., the output distribution at the warden induced by the no-input symbol is not a mixture of the output distributions induced by other input symbols, so that the covert communication is governed by the square root law, i.e., at most $\Theta(\sqrt{n})$ bits can be transmitted over $n$ channel uses. We show that for such a setting, a simple time-division strategy achieves the optimal throughputs for a non-trivial class of broadcast channels; this is not true for communicating over broadcast channels without the covert communication constraint. Our result implies that a code that uses two separate optimal point-to-point codes each designed for the constituent channels and each used for a fraction of the time is optimal in the sense that it achieves the best constants of the $\sqrt{n}$-scaling for the throughputs. Our proof strategy combines several elements in the network information theory literature, including concave envelope representations of the capacity regions of broadcast channels and El Gamal's outer bound for more capable broadcast channels.