  We consider transmission over the ergodic fading multi-antenna broadcast
(MIMO-BC) channel with partial channel state information at the transmitter and
full information at the receiver. Over the equivalent {\it non}-fading channel,
capacity has recently been shown to be achievable using transmission schemes
that were designed for the ``dirty paper'' channel. We focus on a similar
``fading paper'' model. The evaluation of the fading paper capacity is
difficult to obtain. We confine ourselves to the {\it linear-assignment}
capacity, which we define, and use convex analysis methods to prove that its
maximizing distribution is Gaussian. We compare our fading-paper transmission
to an application of dirty paper coding that ignores the partial state
information and assumes the channel is fixed at the average fade. We show that
a gain is easily achieved by appropriately exploiting the information. We also
consider a cooperative upper bound on the sum-rate capacity as suggested by
Sato. We present a numeric example that indicates that our scheme is capable of
realizing much of this upper bound.
