  We consider the problem of finding optimal, fair and distributed power-rate
strategies to achieve the sum capacity of the Gaussian multiple-access
block-fading channel. In here, the transmitters have access to only their own
fading coefficients, while the receiver has global access to all the fading
coefficients. Outage is not permitted in any communication block. The resulting
average sum-throughput is also known as `power-controlled adaptive
sum-capacity', which appears as an open problem in literature.
  This paper presents the power-controlled adaptive sum-capacity of a
wide-class of popular MAC models. In particular, we propose a power-rate
strategy in the presence of distributed channel state information (CSI), which
is throughput optimal when all the users have identical channel statistics. The
proposed scheme also has an efficient implementation using successive
cancellation and rate-splitting. We propose an upperbound when the channel laws
are not identical. Furthermore, the optimal schemes are extended to situations
in which each transmitter has additional finite-rate partial CSI on the link
quality of others.
