Assisted sampling of correlated sources

We study a distributed sampling scenario in which two agents observing components of a correlated source must each generate components of a second correlated source. The agents are aided by an “omniscient” third terminal which observes the two input sources and transmits rate-limited messages to assist the terminals in generating the required correlation in their outputs. We identify two sub-cases of this problem based on how the generated sources must depend on the input sources.