Carbon Copying Onto Dirty Paper

A generalization of the problem of writing on dirty paper is considered in which one transmitter sends a common message to multiple receivers. Each receiver experiences on its link an additive interference, which is known noncausally to the transmitter but not to any of the receivers. In this work, we focus on the Gaussian case with two users and independent interferences. We provide upper and lower bounds on capacity. At high interference-to-noise ratios, we show that time-sharing is (asymptotically) optimal. This settles the conjecture by Steinberg and Shamai (2005). At high signal-to-noise ratios, we propose a superposition dirty paper code that achieves within 1/4 bit/symbol of capacity. An extension to the case of correlated interferences is also discussed