LQG control approach to Gaussian broadcast channels with feedback

The problem of communicating over an N-user additive white Gaussian noise broadcast channel with feedback is studied from a control theoretic perspective. We construct a code for this channel and characterize the set of achievable rates using the theory of linear quadratic Gaussian control. In the special case of a two-receiver channel with independent Gaussian noises, the rate region achieved by this code includes a previous result by Elia and is strictly greater than the rate region achieved by Ozarow and Leung. We establish that there exists a specific correlation among the noises at the receivers for which the ratio of the sum-rate achieved by our code and sum-rate capacity without feedback is N in the limit as the available power at the transmitter tends to infinity. This generalizes a previous result by Gastpar and Wigger for the two-user broadcast channel to the case of N receivers.