  Traditionally, the capacity region of a coherent fading multiple access
channel (MAC) is analyzed in two popular contexts. In the first, a centralized
system with full channel state information at the transmitters (CSIT) is
assumed, and the communication parameters like transmit power and data-rate are
jointly chosen for every fading vector realization. On the other hand, in
fast-fading links with distributed CSIT, the lack of full CSI is compensated by
performing ergodic averaging over sufficiently many channel realizations.
Notice that the distributed CSI may necessitate decentralized power-control for
optimal data-transfer. Apart from these two models, the case of slow-fading
links and distributed CSIT, though relevant to many systems, has received much
less attention.
  In this paper, a block-fading AWGN MAC with full CSI at the receiver and
distributed CSI at the transmitters is considered. The links undergo
independent fading, but otherwise have arbitrary fading distributions. The
channel statistics and respective long-term average transmit powers are known
to all parties. We first consider the case where each encoder has knowledge
only of its own link quality, and not of others. For this model, we compute the
adaptive capacity region, i.e. the collection of average rate-tuples under
block-wise coding/decoding such that the rate-tuple for every fading
realization is inside the instantaneous MAC capacity region. The key step in
our solution is an optimal rate allocation function for any given set of
distributed power control laws at the transmitters. This also allows us to
characterize the optimal power control for a wide class of fading models.
Further extensions are also proposed to account for more general CSI
availability at the transmitters.
