  The "writing dirty paper" capacity result crucially dependents on the perfect
channel knowledge at the transmitter as the presence of even a small
uncertainty in the channel realization gravely hampers the ability of the
transmitter to pre-code its transmission against the channel state. This is
particularly disappointing as it implies that interference pre-coding in
practical systems is effective only when the channel estimates at the users
have very high precision, a condition which is generally unattainable in
wireless environments. In this paper we show that substantial improvements are
possible when the state sequence is drawn from a discrete distribution, such as
a constrained input constellation, for which state decoding can be
approximately optimal. We consider the "writing on dirty paper" channel in
which the state sequence is multiplied by a fast fading process and derive
conditions on the fading and state distributions for which state decoding
closely approaches capacity. These conditions intuitively relate to the ability
of the receiver to correctly identify both the input and the state realization
despite of the uncertainty introduced by fading.
