  Costa's "writing on dirty paper" capacity result establishes that full state
pre-cancellation can be attained in Gelfand-Pinsker channel with additive state
and additive Gaussian noise. The "carbon copy onto dirty paper" channel is the
extension of Costa's model to the compound setting: M receivers each observe
the sum of the channel input, Gaussian noise and one of M Gaussian state
sequences and attempt to decode the same common message. The state sequences
are all non-causally known at the transmitter which attempts to simultaneously
pre-code its transmission against the channel state affecting each output. In
this correspondence we derive the capacity to within 2.25 bits-per-channel-use
of the carbon copying onto dirty paper channel in which the state sequences are
statistically equivalent, having the same variance and the same pairwise
correlation. For this channel capacity is approached by letting the channel
input be the superposition of two codewords: a base codeword, simultaneously
decoded at each user, and a top codeword which is pre-coded against the state
realization at each user for a portion 1/M of the time. The outer bound relies
on a recursive bounding in which incremental side information is provided at
each receiver. This result represents a significant first step toward
determining the capacity of the most general "carbon copy onto dirty paper"
channel in which state sequences appearing in the different channel outputs
have any jointly Gaussian distribution.
