The "writing dirty paper" capacity result crucially dependents on the perfectchannel knowledge at the transmitter as the presence of even a smalluncertainty in the channel realization gravely hampers the ability of thetransmitter to pre-code its transmission against the channel state. This isparticularly disappointing as it implies that interference pre-coding inpractical systems is effective only when the channel estimates at the usershave very high precision, a condition which is generally unattainable inwireless environments. In this paper we show that substantial improvements arepossible when the state sequence is drawn from a discrete distribution, such asa constrained input constellation, for which state decoding can beapproximately optimal. We consider the "writing on dirty paper" channel inwhich the state sequence is multiplied by a fast fading process and deriveconditions on the fading and state distributions for which state decodingclosely approaches capacity. These conditions intuitively relate to the abilityof the receiver to correctly identify both the input and the state realizationdespite of the uncertainty introduced by fading.
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