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Recent theoretical results show that it is optimal to allow interfering sources to transmit simultaneously as long as they are outside a well-defined exclusion region around a destination and to adapt the rate to interference. In contrast, interference from inside the exclusion region needs to be controlled. Furthermore, when a source transmits, it should do so at maximum power. Based on these theoretical findings, we propose a cross-layer design of MAC and physical layer and present a fully distributed, rate adaptive MAC protocol for ultra-wide band (UWB) where sources constantly adapt their channel codes (and thus their rate) to the level of interference experienced at the destination. To mitigate the interference of sources inside the exclusion region, we propose a specific demodulation scheme that cancels most of the interfering energy. This scheme is entirely local to a destination and involves no protocol action. In contrast, existing MAC designs for UWB are either based on mutual exclusion, where no other communication is possible within the same collision domain, or based on power control. Through simulation we show that we achieve a significant increase in network throughput compared to traditional MAC proposals. Overall, we find that existing proposals do not fully take advantage of the specific nature of an ultra-wide band physical layer.