  This work studies the Gaussian interference channel (IC) with a relay, which
transmits and receives in a band that is orthogonal to the IC. The channel
associated with the relay is thus an out-of-band relay channel (OBRC). The
focus is on a symmetric channel model, in order to assess the fundamental
impact of the OBRC on the signal interaction of the IC, in the simplest
possible setting. First, the linear deterministic model is investigated and the
sum capacity of this channel is established for all possible channel
parameters. In particular, it is observed that the impact of OBRC, as its links
get stronger, is similar to that of output feedback for the IC. The insights
obtained from the deterministic model are then used to design achievable
schemes for the Gaussian model. The interference links are classified as
extremely strong, very strong, strong, moderate, weak, and very weak. For
strong and moderate interference, separate encoding is near optimal. For very
strong and extremely strong interference, the interference links provide side
information to the destinations, which can help the transmission through the
OBRC. For weak or very weak interference, an extension of the Han-Kobayashi
scheme for the IC is utilized, where the messages are split into common and
private. To achieve higher rates, it is beneficial to further split the common
message into two parts, and the OBRC plays an important role in decoding the
common message. It is shown that our strategy achieves the symmetric capacity
to within 1.14625 bits per channel use with duplexing factor 0.5, and 1.27125
bits per channel use for arbitrary duplexing factors, for all channel
parameters. An important observation from the constant gap result is that
strong interference can be beneficial with the presence of an OBR.
