A New Outer Bound for the Secrecy Capacity Region of the Gaussian Two-Way Wiretap Channel

We investigate the fundamental communication limits when messages are sent via a Gaussian two-way channel, which must at the same time be kept secret from an external eavesdropper. In this two-way wiretap channel that models two legitimate transceivers and an eavesdropping receiver, there are two techniques to provide confidentiality for the messages: one entails the legitimate nodes to jam the eavesdropper, i.e., cooperative jamming, while the other entails generating keys from the feedback signals received by the two legitimate nodes and using them to encrypt the messages. Previous work has shown that both methods can be used concurrently to improve the secrecy rates of a channel with a degradedness condition. In this work, we consider the general case, and derive a new outer bound for the secrecy capacity region of this channel. A case is identified where the loss in secrecy rate, due to ignoring the backward (feedback) link at each legitimate transmitter from the other, is bounded by a constant which only depends on the channel gains. This is the case when the power of the two legitimate nodes increases proportionally. In all other cases, we show that ignoring feedback signals causes unbounded loss in the secrecy rate. The loss is measured as the gap between the achievable rate when the feedback signals are taken into account, and the upper bound when the feedback is not used, and hence is not affected by the choice of the achievable scheme. This result therefore establishes that, for the Gaussian two-way channel with an external eavesdropper, the encoders need to be designed with memory. This is in contrast to the result for this channel in the absence of an eavesdropper.