On the multicast throughput for half-duplex butterfly network using deterministic approach

This paper considers the multicast throughput of a special butterfly network which is made up of two sources, two destinations and a half-duplex relay. Each destination requires to decode the data from two independent sources. All the nodes are assumed to be half-duplex. When the relay transmits signal, other nodes of the system should keep in receiving state to reduce processing complexity and interference. First, we present an explicit expression of the maximal multicast throughput in deterministic butterfly network which is derived from Aves-timehr, Diggavi and Tse´s deterministic model. Based on the result obtained in deterministic butterfly network, we propose a near-optimal transmitting and decoding policy to approach the maximal throughput by using network coding in Gaussian butterfly network. Finally, we evaluate the gap between our achievable rate region with an outer bound and show it consists of a constant item which is less than 2.45 bits and a variable item which only exists in some cases and increases logarithmically with the signal to noise ratio (SNR) over all the links.