We study the diversity-multiplexing tradeoff (DMT) for the slow fadinginterference channel with a relay (ICR). We derive four inner bounds on the DMTregion: 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 thelast 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 conditionson the channel parameters and the multiplexing gains, under which thecorresponding inner bound achieves the optimal DMT region. We also identifycases in which the DMT region of the ICR corresponds to that of two parallelslow fading relay channels, implying that interference does not decrease theDMT for each pair, and that a single relay can be DMT-optimal for two pairssimultaneously. For the HD-AF scheme we derive conditions on the channelcoefficients under which the proposed scheme achieves the optimal DMT for theAF-based relay channel. Lastly, we identify conditions under which adding arelay strictly enlarges the DMT region relative to the interference channelwithout a relay.
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