Multi-access fading channels: delay-limited capacities

We consider the multi-access, white-noise, fading channel, and introduce a notion of delay-limited capacity, which is the maximum rate achievable with delay independent of how slow the fading is. We characterize the delay-limited capacity region and the associated optimal power allocation schemes. We show that successive decoding is optimal, and the optimal decoding order and power allocation can be found explicitly as a function of the fading states; this is a consequence of an underlying polymatroid structure that we exploit.