Information Extraction from a Strategic Sender over a Noisy Channel

We consider a setting where a receiver tries to perfectly recover a source signal privately known to a sender who can send messages via a noisy channel. However, the sender is compromised and may have an incentive to lie about its information. We formulate the problem as a game between the sender and the receiver and show that there is a strategy for the receiver in which it can recover an exponential number of signals. We define a notion of a sender graph and the information extraction capacity of the sender which quantifies the maximum amount of information that can be extracted from the sender. We also show that the rate of information extraction is given by the minimum of the information extraction capacity of the sender and the zero-error capacity of the noisy channel.