On the Sum-Capacity of Degraded Gaussian Multiaccess Relay Channels

The sum-capacity is studied for a K-user degraded Gaussian multiaccess relay channel (MARC) where the multiaccess signal received at the destination from the K sources and relay is a degraded version of the signal received at the relay from all sources, given the transmit signal at the relay. An outer bound on the capacity region is developed using cutset bounds. An achievable rate region is obtained for the decode-and-forward (DF) strategy. It is shown that for every choice of input distribution, the rate regions for the inner (DF) and outer bounds are given by the intersection of two K-dimensional polymatroids, one resulting from the multiaccess link at the relay and the other from that at the destination. Although the inner and outer bound rate regions are not identical in general, for both cases, a classical result on the intersection of two polymatroids is used to show that the intersection belongs to either the set of active cases or inactive cases, where the two bounds on the K-user sumrate are active or inactive, respectively. It is shown that DF achieves the capacity region for a class of degraded Gaussian MARCs in which the relay has a high SNR link to the destination relative to the multiaccess link from the sources to the relay. Otherwise, DF is shown to achieve the sum-capacity for an active class of degraded Gaussian MARCs for which the DF sum-rate is maximized by a polymatroid intersection belonging to the set of active cases. This class is shown to include the class of symmetric Gaussian MARCs where all users transmit at the same power. The work of L. Sankar and N. B. Mandayam was supported in part by the National Science Foundation under Grant No. ITR0205362. The work of H. V. Poor was supported by the National Science Foundation under Grants ANI-03-38807 and CNS06-25632. The material in this paper was presented in part at the Information Theory and Applications Workshop, San Diego, CA, January 2006. L. Sankar and H. V. Poor are with Princeton University. N. B. Mandayam is with the WINLAB, Rutgers University. 2 Index Terms Multiple-access relay channel (MARC), outer bounds, achievable strategies, Gaussian and degraded Gaussian MARC.