On the Sum-Capacity of Degraded Gaussian Multiple-Access Relay Channels

The sum-capacity is studied for a $K$-user physically degraded Gaussian multiple-access relay channel (MARC). Decode-and-forward (DF) is shown to achieve the sum-capacity and capacity region for a subclass of degraded Gaussian MARCs in which the multiple-access link from the sources to the relay is the bottleneck link. For the remaining subclass, DF is shown to achieve the $K$-user sum-capacity when the sources are symmetric, i.e., they transmit with the same transmit power. The optimality of DF is conjectured for the case of asymmetric sources.