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In this paper the authors attempt to further demonstrate connections between information theory and control, in a networked setting. Specifically, they consider the communication problem of broadcasting to multiple receivers, when one receiver has a degraded observation of the other's, and causal feedback about channel outputs is provided by both receivers. The encoder has to make decisions on the next channel input based on feedback. In this paper, a posterior matching style feedback based encoding scheme is proposed for the problem setting which achieves the capacity region. First, they look at tightness conditions from the converse of the degraded broadcast channel with feedback that inspires their scheme. Second, they develop a stochastic control problem whose optimal value coincides with the tightness conditions.
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