Multiple user writing on dirty paper

Writing on dirty paper, a variation of the standard additive white Gaussian noise (AWGN) channel with the channel output is considered. The Gaussian noise noncausally known at the transmitter does not affect the capacity of the AWGN channel. This is known as WDP property. The WDP property for three Gaussian multiple user channels with known capacity region is established. The achievable rate regions of corresponding discrete channels is proved. Although those regions may be suboptimal in general, they turn out to be optimal for these Gaussian channels. Alternative proofs can be obtained by successive uses of Costa´s WDP coding scheme, from which the WDP property can be established for more general noise and state distributions.