  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.
