Gaussian wiretap channels with correlated sources: Approaching capacity region within a constant gap

This paper studies the Gaussian wiretap channel with correlated sources available not only at the transmitter and legitimate receiver, but also the eavesdropper. In particular, we are interested in the open problem of finding the optimal auxiliary random variable, which provides a closed-form solution to the secret-message and secret-key capacity region. To do that, we first take a deterministic approach and give a precise characterization of its secrecy capacity region. Then we translate the insights gained to the Gaussian case. As a result, we provide a sub-optimal solution by employing a specified Gaussian choice of the auxiliary random variable. This suggested choice is a compromise of keeping most source information subject to the constraint imposed by the channel capability of conducting source coding. Nevertheless, it is shown to be able to approach the secrecy capacity region within half a bit as the signal-noise-ratio of the main channel is no less than 1.