The capacity of a broadcast channel with Gaussian jamming and a friendly eavesdropper

A friendly eavesdropper assists communication in a broadcast scenario in which one transmitter wishes to send a common message to two receivers in the presence of a malicious jammer. The jammer attempts to disrupt communication by transmitting a high power Gaussian signal, whereas the friendly eavesdropper `hears' the jammer's transmission and sends an assisting signal to the destinations over an orthogonal channel in order to help them alleviate the jammer's impact. We derive an expression for capacity, i.e., the maximum data rate that can be reliably communicated from the transmitter to the receivers and we show that it is optimal for the friendly eavesdropper to send a Gaussian description of the jamming signal with the help of a scheme based on a modified compress-and-forward relaying that uses a list decoding procedure.