On the role of feedback in two-way secure communication

For bi-directional communication, the most general form of encoders should consider the signals received in the past as inputs. However, in practice, it would also be highly desirable if feedback could be ignored for encoding purposes since this would lead to a simple system design. In this work, we investigate the question of whether and how much loss in secrecy rate would be incurred, if such an approach were taken. To do so, we investigate the role of feedback in secrecy for two three-node two-way channel models. First, we show that feedback is indeed useful for a class of full-duplex two-way wire-tap channels. In this case, when feedback is ignored, the channel is equivalent to a Gaussian degraded relay channel with confidential messages to the relay. The usefulness of feedback is demonstrated by deriving an upper bound for this channel when feedback is ignored, and then proving that, when feedback is used, a secrecy rate higher than this upper bound is achievable. Secondly, we consider the half-duplex Gaussian two-way relay channel where there is an eavesdropper co-located with the relay node, and find that the impact of feedback is less pronounced compared to the previous scenario. Specifically, the loss in secrecy rate, when ignoring the feedback, is quantified to be less than 0.5 bit per channel use when the power of the relay goes to infinity. We also show that this rate region is achievable under a simple time sharing scheme with cooperative jamming, which, with its simplicity and near-optimum performance, is a viable alternative to an encoder using feedback.