Approximate capacity of the symmetric half-duplex Gaussian butterfly network

In this paper we study the capacity of the half-duplex wireless butterfly network, in which a relay node facilitates the communication between two interfering transmitter-receiver pairs. We use the deterministic approach to make progress towards approximating the capacity region of this network. We use the insights obtained from the analysis of the corresponding deterministic problem to derive a new upper bound on the capacity of this network. We also propose a transmission strategy and show that for symmetric channel gains the gap between its achievable rate region and the upper bound is at most equation bits/sec/Hz per user.