Approximate secrecy capacity region of an asymmetric MAC wiretap channel within 1/2 bits

Abstract

We consider a 2-user Gaussian Multiple-Access Wiretap channel (GMAC-WT), with the Eavesdropper (E) having access to signal from only one (say, T2) of the two transmitters. We characterize the capacity region of this channel approximately within. 5 bits, where the approximation is in terms of only T1's rate or the sum-rate depending on the relative strength of the eavesdropper's channel. However, the approximation is. 5 bits independent of channel coefficients or operating Signal-to-Noise Ratios (SNR). To prove this approximate result we propose two different coding schemes, namely, the power adaptation and the time sharing coding schemes and derive their corresponding achievable rate regions. Both of them use Gaussian input distribution. To establish the approximate capacity, we first derive supersets to the capacity region and then show that corresponding to each rate pair at the boundary of these supersets there exists an achievable rate pair in one of the aforementioned achievable rate regions which are within 1/2 bits to the former pair. In comparison to a very recent result (Xie and Ulukus, ISIT 2013) on a GMAC-WT showing the requirement of interference alignment (IA) to achieve even the degrees of freedom performance, the result of this paper is surprising: our channel model is an interesting variation of the GMAC-WT for which IA is not necessary and Gaussian signalling is sufficient to achieve the entire capacity region within. 5 bits.