Submitted to the IEEE Transactions on Information Theory , April 2006 Generalized Multiple Access Channels with Confidential Messages 1 2

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, 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. 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. These bounds match partially, and hence the capacity-equivocation region is partially characterized. Furthermore, the outer bound provides a tight converse to the secrecy capacity region, which is the set of all achievable rates with user 2 being perfectly ignorant of confidential messages of user 1, thus establishing the secrecy capacity region. A class of degraded GMACs with one confidential message set is further studied, and the capacity-equivocation region and the secrecy capacity region are established. These capacity results are further explored via two example degraded channels: the binary GMAC and the Gaussian GMAC. For both channels, the capacity-equivocation regions are obtained. In particular, the capacity-equivocation region of the degraded Gaussian GMAC is shown to apply to non-physically-degraded Gaussian channels as well. 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. The secrecy rate region is derived, where each user’s confidential information is perfectly hidden from the other user. It is demonstrated that for the case of two confidential message sets there is a trade-off between the two equivocation rates The material in this paper has been submitted in part to the IEEE International Symposium on Information Theory, Seattle, Washington, July 2006. This research was supported by the National Science Foundation under Grant ANI-03-38807. The authors are with the Department of Electrical Engineering, Princeton University, Engineering Quadrangle, Olden Street, Princeton, NJ 08544; e-mail: {yingbinl,poor}@princeton.edu 1 corresponding to the two confidential message sets, and this trade-off can be achieved by using codebooks that achieve different boundary points of the corresponding MAC.