Capacity for the doubly dirty multiple access channel with partial side information at the transmitters

In this study, the authors establish achievable rate and capacity regions for three kinds of Gaussian multiple access channels (MACs) with side information (SI) partially (estimated or sensed version) and non-causally known at the transmitters. Actually, the authors show that the lattice strategy is optimal for Gaussian MACs with partial SI, the same as it is for Gaussian MACs with full SI studied by Philosof-Zamir. The rate and capacity regions, while showing that partiality in SI reduces the achievable rates, subsumes directly the Philosof-Zamir rate regions and also the Gueguen-Sayrac work and the Costa theorem indirectly as special cases.