The Generalized Multiple Access Channel with Confidential Messages
  A discrete memoryless generalized multiple access channel (GMAC) with confidential messages is studied, where two users attempt to transmit common information to a destination and each user also has private (confidential) information intended for the destination. This channel generalizes the multiple access channel (MAC) in that the two users also receive channel outputs. It is assumed that each user views the other user as a wire-tapper, and wishes to keep its confidential information as secret as possible from the other user. The level of secrecy of the confidential information is measured by the equivocation rate. The performance measure of interest is the rate-equivocation tuple that includes the common rate, two private rates and two equivocation rates as components. The set that includes all achievable rate-equivocation tuples is referred to as the capacity-equivocation region. For the GMAC with one confidential message set, where only one user (user 1) has private (confidential) information for the destination, inner and outer bounds on the capacity-equivocation region are derived. The secrecy capacity region is established, which is the set of all achievable rates with user 2 being perfectly ignorant of confidential messages of user 1. Furthermore, the capacity-equivocation region and the secrecy capacity region are established for the degraded GMAC with one confidential message set. For the GMAC with two confidential message sets, where both users have confidential messages for the destination, inner bounds on the capacity-equivocation region and the secrecy capacity region are obtained. 
Yingbin Liang and H. Vincent Poor