Achievable Rate Regions for Dirty Tape Channels and "Joint Writing on Dirty Paper and Dirty Tape"

TL;DR

This paper derives the capacity and achievable rate regions for Gaussian Dirty Tape Channels with causal interference knowledge, demonstrating the optimality of linear strategies and improving lower bounds through time-sharing, also extending results to multi-user scenarios.

Contribution

It establishes the optimality of linear assignment strategies for the DTC and introduces improved lower bounds via time-sharing, also analyzing multi-user interference scenarios.

Findings

Linear assignment to f(.) is optimal under certain conditions.

Time-sharing improves the achievable rate lower bounds.

Achievable rate regions are characterized for multi-user interference scenarios.

Abstract

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]\_top(P_U,f(.),X=f(U,S))I(U;Y) is presented for the capacity of this channel. For linear assignment to f(.), i.e. X=U-{\beta}S, 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 {\beta}^* such that the pair (X+{\beta}^* S,U) is independent of 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.