  This paper studies the interference channel with two transmitters and two
receivers in the presence of a MIMO relay in the low transmit power regime. A
communication scheme combining block Markov encoding, beamforming, and Willems'
backward decoding is used. With this scheme, we get an interference channel
with channel gains dependent on the signal power. A power allocation for this
scheme is proposed, and the achievable rate region with this power allocation
is given. We show that, at low transmit powers, with equal power constraints at
the relay and the transmitters, the interference channel with a MIMO relay
achieves a sum rate that is linear in the power. This sum rate is determined by
the channel setup. We also show that in the presence of abundant power at the
relay, the transmit strategy is significantly simplified, and the MAC from the
transmitters to the relay forms the bottle neck of the system from the sum rate
point of view.
