Successive refinement with common receiver reconstructions

We study the variant of the successive refinement problem where the receivers require identical reconstructions.We characterize the rate region when the joint support of the source and the side information variables is the Cartesian product of their individual supports. The characterization indicates that the side information can be fully used to reduce the communication rates via binning; however, the reconstruction functions can depend only on the Gács-Körner common randomness shared by the two receivers. Unlike existing (inner and outer) bounds to the rate region of the general successive refinement problem, the characterization for the variant studied requires only one auxiliary random variable.