  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.
