Capacity Bounds for Backhaul-Supported Wireless Multicast Relay Networks with Cross-Links

We investigate the capacity bounds for a wireless multicast relay network where two sources simultaneously multicast to two destinations through Gaussian channels with the help of a full-duplex relay node. All the individual channel gains are assumed to be time-invariant and known to every nodes in the network. The transmissions from two sources and from the relay use the same channel resource (i.e. co-channel transmission) and the two source nodes are connected with an orthogonal error-free backhaul. This multicast relay network is generic in the sense that it can be extended to more general networks by tuning the channel gains within the range [0, ∞). By extending the proof of the converse developed by Cover and El Gamal for the Gaussian relay channel, we characterize the cut-set bound for this multicast relay network. We also present a lower bound by using decoding-and-forward relaying combined with network beam-forming.