Rate of Prefix-free Codes in LQG Control Systems with Side Information

In this work, we study LQG control systems where one of two feedback channels is discrete and incurs a communication cost, measured as time-averaged expected length of prefix-free codeword. This formulation to motivates a rate distortion problem, which we restrict to a particular policy space and express as a convex optimization. The optimization leads to a quantizer design and a subseqent achievability result.