On the sum-rate capacity of a 2-user Multiple Access Wiretap Channel with one secret user

We consider a 2-user Gaussian Multiple-Access Wiretap channel (MA-WC), with the unintended receiver having access to signal from only one of the two transmitters. We have characterized the sum-rate capacity of this channel within .5 bits and proved that Gaussian signalling at the transmitters is approximate sum-rate capacity optimal. For the scenario when the additive noise plus the signal from first transmitter have a combined strength poorer than the additive noise of the evesdropper, the above sum-rate capacity characterization leads to an approximate capacity region characterization for the channel. It is shown that, under this circumstances, a timesharing scheme between the two users can achieve the capacity region of the channel within .25 bits. It has been proved (Xie and Ulukus, ISIT 2013 [1]) recently that on a Multiple-Access Wiretap channel interference alignment (IA) is necessary to achieve optimal performance. Our channel model is an interesting variation of the MA-WC for which IA is not necessary and independent Gaussina signalling is sufficient to achieve the optimal sum-rate within .5 bits.