Lossy broadcasting with common transmitter-receiver reconstructions

We consider a variant of Wyner-Ziv (WZ) coding over a broadcast channel where a source is to be communicated over a broadcast channel to two receivers that have side-information correlated with the source. In this variant, the transmitter and the receivers have to generate reconstructions that are (almost always) identical to one another, and each reconstruction meets a certain fidelity constraint. We present a complete characterization of the capacity region for the problem.