  A Gaussian interference channel (IC) aided by a half-duplex relay is
considered, in which the relay receives and transmits in an orthogonal band
with respect to the IC. The system thus consists of two parallel channels, the
IC and the channel over which the relay is active, which is referred to as
Out-of-Band Relay Channel (OBRC). The OBRC is operated by separating a multiple
access phase from the sources to the relay and a broadcast phase from the relay
to the destinations. Conditions under which the optimal operation, in terms of
the sum-capacity, entails either signal relaying and/or interference forwarding
by the relay are identified. These conditions also assess the optimality of
either separable or non-separable transmission over the IC and OBRC.
Specifically, the optimality of signal relaying and separable coding is
established for scenarios where the relay-to-destination channels set the
performance bottleneck with respect to the source-to-relay channels on the
OBRC. Optimality of interference forwarding and non-separable operation is also
established in special cases.
