Achievable rate regions for Dirty Tape Channels and “joint writing on Dirty paper and Dirty Tape”

We consider the Gaussian Dirty Tape Channel (DTC) Y = X + S + Z, where S is an additive Gaussian interference known causally to the transmitter. The general expression max
_{PU,f(·),X = f(U, S)}
I(U; Y) is proposed for the capacity of this channel. For linear assignment to f(-), i.e., X = U - βS, this expression leads to the compensation strategy proposed previously by Willems to obtain an achievable rate for the DTC. We show that linear assignment to f(·) is optimal under the condition that there exists a real number β* such that the pair (X + β S, U) is independent of the interference S. Furthermore, by applying a time-sharing technique to the achievable rate derived by linear assignment to f (·), an improved lower bound on the capacity of DTC is obtained. We also consider the Gaussian multiple access channel with additive interference, and study two different scenarios for this system. In the first case, both transmitters know interference causally while in the second, one transmitter has access to the interference noncausally and the other causally. Achievable rate regions for these two scenarios are then established.