  Consider the two-way rate-distortion problem in which a helper sends a common
limited-rate message to both users based on side information at its disposal.
We characterize the region of achievable rates and distortions where a Markov
form (Helper)-(User 1)-(User 2) holds. The main insight of the result is that
in order to achieve the optimal rate, the helper may use a binning scheme, as
in Wyner-Ziv, where the side information at the decoder is the "further" user,
namely, User 2. We derive these regions explicitly for the Gaussian sources
with square error distortion, analyze a trade-off between the rate from the
helper and the rate from the source, and examine a special case where the
helper has the freedom to send different messages, at different rates, to the
encoder and the decoder.
