On the Capacity of the Carbon Copying onto Dirty Paper Channel

Abstract

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.