The Gaussian multiple access diamond channel

In this paper, we study the capacity of the diamond channel. We focus on the special case where the channel between the source node and the two relay nodes are two separate links of finite capacity and the link from the two relay nodes to the destination node is a Gaussian multiple access channel. We call this model the Gaussian multiple access diamond channel. We first propose an upper bound on the capacity. This upper bound is a single-letterization of the n-letter upper bound proposed by Traskov and Kramer, which is tighter than the cut-set bound. Next, we provide a lower bound based on sending correlated codes through the multiple access channel. Since the upper and lower bounds take on similar forms, it is expected that they coincide for certain channel parameters. To show this, we further focus on the symmetric case where the separate links to the relays are of the same capacity and the power constraints of the two relays are the same. For the symmetric case, we give necessary and sufficient conditions that the upper and lower bounds meet. Thus, for a Gaussian multiple access diamond channel that satisfies these conditions, we have found its capacity.