  We study the diversity-multiplexing tradeoff (DMT) for the slow fading
interference channel with a relay (ICR). We derive four inner bounds on the DMT
region: the first is based on the compress-and-forward (CF) relaying scheme,
the second is based on the decode-and-forward (DF) relaying scheme, and the
last two bounds are based on the half-duplex (HD) and full-duplex (FD)
amplify-and-forward (AF) schemes. For the CF and DF schemes, we find conditions
on the channel parameters and the multiplexing gains, under which the
corresponding inner bound achieves the optimal DMT region. We also identify
cases in which the DMT region of the ICR corresponds to that of two parallel
slow fading relay channels, implying that interference does not decrease the
DMT for each pair, and that a single relay can be DMT-optimal for two pairs
simultaneously. For the HD-AF scheme we derive conditions on the channel
coefficients under which the proposed scheme achieves the optimal DMT for the
AF-based relay channel. Lastly, we identify conditions under which adding a
relay strictly enlarges the DMT region relative to the interference channel
without a relay.
