Two-way source coding with a helper

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.