The Heegard-Berger problem with common receiver reconstructions

The variant of the Heegard-Berger problem where the receivers require identical reconstructions is studied, and the rate-distortion function for the following three settings is derived: (a) the encoder is also required to generate the reconstructions common to the receivers; (b) the side information at the receivers are physically degraded; and (c) the side information at the receivers are stochastically degraded, and the source satisfies a particular full-support condition. The characterizations indicate that the receiver side information can be fully exploited to perform Wyner-Ziv-style binning. However, the reconstruction functions can depend only on the randomness common to the receivers in the Gács-Körner sense.