The secrecy capacity region of a special class of multiple access channels

We study the problem of secure communications over the multiple access channel where there is one eavesdropper in the system and the eavesdropper can only overhear the transmitted signal of one of the transmitters. This channel model can be seen as a special case of both scenarios currently studied in the literature for multiple access channels with secrecy constraints. In this simplified model, we obtain the secrecy capacity region if the multiple access channel satisfies certain conditions. We also compare the capacity regions of this special class of multiple access channels with and without secrecy constraints to illustrate the price paid for secrecy.