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The classical writing on dirty paper capacity result establishes that fullinterference pre-cancellation can be attained in Gelfand-Pinsker problem withadditive state and additive white Gaussian noise. This result holds under theidealized assumption that perfect channel knowledge is available at bothtransmitter and receiver. While channel knowledge at the receiver can beobtained through pilot tones, transmitter channel knowledge is harder toacquire. For this reason, we are interested in characterizing the capacityunder the more realistic assumption that only partial channel knowledge isavailable at the transmitter. We study, more specifically, the dirty paperchannel in which the interference sequence in multiplied by fading valueunknown to the transmitter but known at the receiver. For this model, weestablish an approximate characterization of capacity for the case in whichfading values vary greatly in between channel realizations. In this regime,which we term the strong fading regime, the capacity pre-log factor is equal tothe inverse of the number of possible fading realizations.

On Capacity of the Dirty Paper Channel with Fading Dirt in the Strong Fading Regime