On the capacity of the carbon copying onto dirty paper channel

Costa's 'writing on dirty paper' capacity result establishes that full state pre-cancellation can be attained in the Gel'fand-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: here a common message is to be decoded at M receivers, each observing the sum of the channel input, Gaussian noise and one of M possible state sequences. As in the Gel'fand-Pinsker channel, the state sequences are anti-causally known at the encoder, which can thus pre-code its transmissions so as to minimize the adverse effects of the channel states. In this paper we derive the capacity to within 2.25 bits-per-channel-use of the M-user 'carbon copying onto dirty paper' channel in which the state sequences are Gaussian distributed with the same variance and the same pairwise correlation.