| Abstract: | We investigate the multicast throughput of a butterfly network, which may be a promising topology for network coding application in next‐generation wireless communication systems. The butterfly network consists of two sources, two destinations and a relay, where each destination requires decoding of data from two independent sources. It is assumed that all the nodes are operated in half‐duplex mode. Each end‐to‐end packet transmission should be completed in a two‐phase period. In order to reduce processing complexity and multiple interference, other nodes should keep silent when the relay transmits a signal. By using Avestimehr, Diggavi and Tse's deterministic model, we first introduce a deterministic butterfly network and demonstrate that its maximal multicast rate region can be achieved by employing a network coding policy. According to the results obtained in deterministic case, we then put forward a near‐optimal design on the transmitted signal and decoding scheme for Gaussian scenarios based on a nested lattice code. It is proved that the gap between the achievable rate region and an outer bound is less than 3bits/s/Hz, which is not related to the signal‐to‐noise ratio. That is, the proposed scheme can approach the maximal multicast throughput. Finally, numerical results demonstrate that the gap is robust to both channel gains and time division of the two phases. Copyright © 2014 John Wiley & Sons, Ltd. |
