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