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Costa's "writing on dirty paper" capacity result establishes that full statepre-cancellation can be attained in Gelfand-Pinsker channel with additive stateand additive Gaussian noise. The "carbon copy onto dirty paper" channel is theextension of Costa's model to the compound setting: M receivers each observethe sum of the channel input, Gaussian noise and one of M Gaussian statesequences and attempt to decode the same common message. The state sequencesare all non-causally known at the transmitter which attempts to simultaneouslypre-code its transmission against the channel state affecting each output. Inthis correspondence we derive the capacity to within 2.25 bits-per-channel-useof the carbon copying onto dirty paper channel in which the state sequences arestatistically equivalent, having the same variance and the same pairwisecorrelation. For this channel capacity is approached by letting the channelinput be the superposition of two codewords: a base codeword, simultaneouslydecoded at each user, and a top codeword which is pre-coded against the staterealization at each user for a portion 1/M of the time. The outer bound relieson a recursive bounding in which incremental side information is provided ateach receiver. This result represents a significant first step towarddetermining the capacity of the most general "carbon copy onto dirty paper"channel in which state sequences appearing in the different channel outputshave any jointly Gaussian distribution.

The Carbon Copy onto Dirty Paper Channel with Statistically Equivalent States