As a typical model of multicast network, wireless butterfly networks (WBNs) have been studied for modelling the scenario when two source nodes wish to convey data to two destination nodes via an intermediary node namely relay node. In the context of wireless communications, when receiving two data packets from the two source nodes, the relay node can employ either physical-layer network coding or analogue network coding on the combined packet prior to forwarding to the two destination nodes. Evaluating the energy efficiency of these combination approaches, energy-delay trade-off (EDT) is worth to be investigated and the relay placement should be taken into account in the practical network design. This chapter will first investigate the EDT of network coding in the WBNs. Based on the derived EDT, algorithms that optimize the relay position will be developed to either minimize the transmission delay or minimize the energy consumption subject to constraints on power allocation and location of nodes. Furthermore, considering an extended model of the WBN, the relay placement will be studied for a general wireless multicast network with multiple source, relay and destination nodes
