Two-way source coding through a relay

A 3-node lossy source coding problem for a 2-DMS (X1, X2) is considered. Source nodes 1 and 2 observe X1 and X2, respectively, and each wishes to reconstruct the other source with a prescribed distortion. To achieve these goals, nodes 1 and 2 send descriptions of their sources to relay node 3. The relay node then broadcasts a joint description to the source nodes. A cutset outer bound and a compress-linear code inner bound are established and shown to coincide in several special cases. A compute-compress inner bound is then presented and shown to outperform the compress-linear code in some cases. An outer bound based on Kaspi's converse for the two-way source coding problem is shown to be strictly tighter than the cutset outer bound.