Multicast for asymmetrical half-duplex butterfly network: A deterministic approach

We investigate the multicast throughput of asymmetrical butterfly network which consists of two sources, two destinations and a half-duplex relay, where each destination needs to decode the data from two independent sources. In order to reduce processing complexity and multiple interference, other nodes should keep silent when the relay transmits signals. We first present an explicit expression of the deterministic maximal multicast throughput by using Avestimehr, Diggavi and Tse´s deterministic approach. With the insight of the obtained result, we put forward a near-optimal network coding strategy to approach the maximal multicast throughput of this network. Finally, we compare our achievable rate region with an outer bound and show the gap between them is less than a constant 2.45 bits in some cases.