We consider the Gaussian interference channel (IC) with an out-of-band
relay (OBR). The relay works in bands orthogonal to the IC. The focus
is on a symmetric channel model, in order to demonstrate the
fundamental impact of the OBR on the signal interaction of the IC, in
the simplest possible setting. The linear deterministic model is first
investigated and the sum capacity of this channel is established for
all possible channel parameters. The insights obtained from the
deterministic model are then used to design achievable schemes for the
Gaussian model. Specifically, we classify the interference links as
extremely strong, very strong, strong, moderate, weak, and very
weak. We design achievable schemes for each channel setting to combat
or utilize interference to increase the achievable rates. For very
weak or weak interference, we show that the out-of-band relay is
useful to further mitigate the interference. For very strong and
extremely strong interference, we show that the interference can be
utilized to further increase the achievable rates with the presence of
the out-of-band relay. For moderate and strong interference, we show
that separate encoding is near optimal, i.e., there is no need to use
the out-of-band relay to combat or utilize the interference. By
deriving outerbounds for the channel model, we show that our strategy
achieves the symmetric capacity to within 1.14625 bits per channel use
for all channel parameters.