Two-Way Lossy Compression Via A Relay With Self Source

We consider interactive source coding of two sources through a relay which also has a source. Alice and Bob have no direct links and wish to exchange their sources with fidelity via an intermediary, Ryan. Ryan also has an individual source and seeks to communicate it to Alice and Bob. We develop inner and outer bounds for the optimal rate-distortion region of this problem, which coincide in certain lossless cases, e.g., when the sources of Alice and Bob are conditionally independent given the source of Ryan or when two of the sources are functions of the third one. The bounds heavily make use of Wyner-Ziv and Berger-Tung coding and often rely on linear network coding. Our results highlight the dual role of the relaying source, which, on one hand, facilitates compression rate savings for the other two sources by helping as side information, and on the other hand, requires additional rate for its own description.