Plausible Deniability over Broadcast Channels

In this paper, we introduce the notion of Plausible Deniability in an information theoretic framework. We consider a scenario where an entity that eavesdrops through a broadcast channel summons one of the parties in a communication protocol to reveal their message (or signal vector). It is desirable that the summoned party have the option to reveal as little of the true message as possible by producing a fake output that is likely plausible given the eavesdropper's observation. We examine three variants of this problem -- Transmitter Deniability, Receiver Deniability, and Message Deniability. In the first setting, the transmitter is summoned to produce the transmitted codeword on the channel. Similarly, in the second and third settings, the receiver and the message sender are required to produce the received codeword and the message respectively. For each of these settings, we examine the maximum communication rate that allows a minimum amount of plausible deniability. For the Transmitter and Receiver Deniability problems, we give an achievable region for general broadcast channels that is shown to be tight for the Transmitter Deniability problem when the channel is degraded. For the Message Deniability problem, we fully characterise the rate region for general broadcast channels.