Capacity Bounds and Lattice Coding for the Star Relay Network

A half-duplex wireless network with 6 lateral nodes, 3 transmitters and 3 receivers, and a central relay is considered. The transmitters wish to send information to their corresponding receivers via a two phase communication protocol. The receivers decode their desired messages by using side information and the signals received from the relay. We derive an outer bound on the capacity region of any two phase protocol as well as 3 achievable regions by employing different relaying strategies. In particular, we combine physical and network layer coding to take advantage of the interference at the relay, using, for example, lattice-based codes. We then specialize our results to the exchange rate. It is shown that for any snr, we can achieve within 0.5 bit of the upper bound by lattice coding and within 0.34 bit, if we take the best of the 3 strategies. Also, for high snr, lattice coding is within log(3)/4 ~ 0.4 bit of the upper bound.