We present a joint PHY/MAC architecture (DCC-MAC) for 802.15.4a-like networks based on PPM-UWB. Unlike traditional approaches it fully utilizes the specific nature of UWB to achieve high rates at low protocol complexity. It is the first MAC protocol that adapts the channel code (and thus the bit rate) to interference from concurrent transmissions instead of enforcing exclusion. In order to avoid a complex mutual exclusion protocol at the MAC layer, we propose an interference mitigation scheme. The scheme is based on a modification of the physical layer that cancels much of the interfering energy, in particular from nearby interferers. We further use dynamic channel coding to combat the remaining interference. Sources constantly adjust their channel codes to the level of interference and send incremental redundancy as required. Contention between sources sending to the same destination is solved by a "private MAC" protocol that involves only the nodes that want to talk to the same destination. The private MAC does not use any common channel; this avoids the issues of hidden and exposed terminals altogether. We show by simulation that our MAC protocol fully satisfies the application requirements of 802.15.4a in terms of link lengths, rates and mobility. We further show that it achieves a significant increase in network throughput, compared to traditional MAC protocols like 802.15.4, that are separated from the physical layer.