Extended Mappings for Wireless Network Coded Butterfly Network

The authors consider the application of wireless network coding to a "Butterfly" wireless network, comprising two sources and two destinations sharing a single relay. They obtain upper bounds on the end to end capacity of the network in terms of the codebook cardinalities, allowing the use of an extended rather than a minimal hierarchical mapping at the relay and assuming that partial complementary side information is available at each destination directly from its complementary source. They further show that this bound may be achieved using a linear mapping at the relay.