  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. The two users are allowed to receive
channel outputs, and hence may obtain the confidential information sent by each
other from channel outputs they receive. However, 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, i.e., the
entropy rate of the confidential information conditioned on channel outputs at
the wire-tapper. The performance measure of interest for the GMAC with
confidential messages is the rate-equivocation tuple that includes the common
rate, two private rates and two equivocation rates as components. The set that
includes all these achievable rate-equivocation tuples is referred to as the
capacity-equivocation region. The GMAC with one confidential message set is
first studied, where only one user (user 1) has private (confidential)
information for the destination. Inner and outer bounds on the
capacity-equivocation region are derived, and the capacity-equivocation are
established for some classes of channels including the Gaussian GMAC.
Furthermore, 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. For the GMAC with two confidential message sets, where both
users have confidential messages for the destination, an inner bound on the
capacity-equivocation region is obtained.
