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

Capacity Bounds and Lattice Coding for the Star Relay Network