Extended Mappings for Wireless Network Coded Butterfly Network

We consider the application of wireless network coding to a “butterfly” wireless network, comprising two sources and two destinations sharing a single relay. We 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. We further show that this bound may be achieved using a linear mapping at the relay. We obtain numerical results for the mutual information on the links of the network, and hence show that the extended mapping may provide increased capacity compared to the minimal for some values of channel fading parameters. Keywords-Wireless Network Coding, Physical Layer Network Coding, Two-way relay channel, Two-source shared relay channel