In a coordination or channel synthesis problem, parties have to use communication and shared randomness to produce correlated random outputs. The question is, how much communication and/or shared randomness is required to accurately generate correlation.

In this project, we study the problem of three parties synthesizing a noisy broadcast channel. The first party observes a random variable X, and sends a common message to the other two, who have to produce random variables Y and Z according to a prescribed distribution.