A stochastic control approach to coding with feedback over degraded broadcast channels

In this paper we attempt to further demonstrate connections between information theory and control, in a networked setting. Specifically, we 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, we look at tightness conditions from the converse of the degraded broadcast channel with feedback, that inspires our scheme. Second, we develop an equivalent stochastic control problem and show that the scheme we propose is optimal from an average-reward stochastic control perspective. Finally, we prove this scheme achieves any rate in the capacity region by constructing a Lyapunov function that operates on post...

• Type: Journal
• Year: 2010
• Where: CDC
• Authors: Siva K. Gorantla, Todd P. Coleman
• Keywords: Capacity Region, CDC 2010, Control Systems, Feedback, Stochastic Control