The General Gaussian Multiple Access and Two-Way Wire-Tap Channels: Achievable Rates and Cooperative Jamming
Abstract
We consider the General Gaussian Multiple Access Wire-Tap Channel (GGMAC-WT) and the Gaussian Two-Way Wire-Tap Channel (GTW-WT). In the GGMAC-WT, multiple users communicate with an intended receiver in the presence of an intelligent and informed eavesdropper who receives their signals through another GMAC. In the GTW-WT, two users communicate with each other with an eavesdropper listening through a GMAC. We consider a secrecy measure that is suitable for this multi-terminal environment, and identify achievable such secrecy regions for both channels using Gaussian codebooks. In the special case where the GGMAC-WT is degraded, we show that Gaussian codewords achieve the strong secret key sum-capacity. For both GGMAC-WT and GTW-WT, we find the power allocations that maximize the achievable secrecy sum-rate, and find that the optimum policy may prevent some terminals from transmission in order to preserve the secrecy of the system. Inspired by this construct, we next propose a new scheme which we call cooperative jamming, where users who are not transmitting according to the sum-rate maximizing power allocation can help the remaining users by "jamming" the eavesdropper. This scheme is shown to increase the achievable secrecy sum-rate, and in some cases allow a previously non-transmitting terminal to be able to transmit with secrecy. Overall, our results point out that for wire-tap channels, multiple-access allows the users to be able to help each other to achieve a positive secrecy rate collectively. Furthermore, the cooperative jamming scheme allows terminals that cannot participate in communication with secrecy to help enlarge the achievable region for the remaining terminals. In other words, we see that cooperation among users can be very valuable for achieving secrecy for the system.Keywords
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