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In this work, we study an LQG control system where one of two feedback channels is discrete and incurs a communication cost. We assume that a decoder (co-located with the controller) can make noiseless measurements of a subset of the state vector (referred to as side information) meanwhile a remote encoder (co-located with a sensor) can make arbitrary measurements of the entire state vector, but must convey its measurements to the decoder over a noiseless binary channel. Use of the channelarXiv:2101.09329v3 fatcat:vbwjnygkezf6zkkrjrzpctiw4m