On the Capacity of the Dirty Paper Channel with Fast Fading and Discrete Channel States

Abstract

Interference pre-cancellation as in the "writing onto dirty paper" channel crucially depends on the transmitter having exact knowledge of the way in which input and channel state combine to produce the channel output. The presence of even a small amount of uncertainty in such knowledge, gravely hampers the ability of the encoder to pre-code its transmissions 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 have very high precision, a condition which is generally unattainable in wireless environments. In this paper we show that state decoding, instead of state pre-cancellation, can be approximately optimal for a channel with discrete states when only partial channel knowledge is available. More specifically, we consider a variation of the "writing onto dirty paper" channel in which a discrete-valued state sequence is multiplied by a fast fading process and derive conditions on the fading distribution for which state decoding closely approaches capacity. This channel model is a special case of the Gelf\'and-Pinsker channel and our results show an instance of this problem in which state decoding is approximately optimal.