On secure signaling for the Gaussian multiple access wire-tap channel

We consider the Gaussian Multiple Access Wire-Tap Channel (GMAC-WT) where multiple users communicate with the intended receiver in the presence of an intelligent and informed wire-tapper (eavesdropper). The wire-tapper receives a degraded version of the signal at the receiver. We assume that the wire-tapper is as capable as the intended receiver, and there is no other shared secret key. We consider two different secure communication scenarios: (i) keeping the wire-tapper totally ignorant of the message of any group of users even if the remaining users are compromised, (ii) using the secrecy of the other users to ensure secrecy for a group of users. We first derive the outer bounds for the secure rate region. Next, using Gaussian codebooks, we show the achievability of a secure rate region for each measure in which the wire-tapper is kept perfectly ignorant of the messages. We also find the power allocations that yield the maximum sum rate, and show that upper bound on the secure sum rate can be achieved by a TDMA scheme. We present numerical results showing the new rate region and compare it with that of the Gaussian Multiple-Access Channel (GMAC) with no secrecy constraints.