ar X iv : c s / 05 11 09 5 v 1 [ cs . I T ] 2 8 N ov 2 00 5 1 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. Applications range from wireless multi-antenna multicasting to robust dirty paper coding. We develop results for memoryless channels in Gaussian and noiseless binary special cases. In general, we show that the availability of side information at the transmitter increases capacity relative to systems without such side information, and that the lack of side information at the receivers decreases capacity relative to systems with such side information. For the noiseless binary case, we derive the capacity when there are two receivers. When there are many receivers, we show that the side information provides a vanishingly small benefit. When the interference is large, we show that time sharing is optimal. For 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 [22]. At high signal-to-noise ratios, we propose a superposition dirty paper code that achieves within 1/4 bit/symbol of capacity. Extensions and generalizations are also discussed.

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@inproceedings{Khisti2005arXI, title={ar X iv : c s / 05 11 09 5 v 1 [ cs . I T ] 2 8 N ov 2 00 5 1 Carbon Copying Onto Dirty Paper}, author={Ashish Khisti and Uri Erez and Amos Lapidoth and Gregory W. Wornell}, year={2005} }