Time-Invariant Prefix Coding for LQG Control

Motivated by control with communication constraints, in this work we develop a time-invariant data compression architecture for linear-quadratic-Gaussian (LQG) minimum bitrate prefix-free feedback. For any fixed performance, the approach propose nearly achieves known directed information (DI) lower bounds on time-average expected codeword length. We refine analysis of classical achievability approach, which required quantized plant measurements to be encoded via time-varying lossless source code. prove that sequence random variables describing quantizations has limiting distribution and may code optimized without added time-asymptotic redundancy. Our result follows from analyzing long-term stochastic behavior system, permits us additionally guarantee length (as opposed length) is almost surely within few bits DI. To our knowledge, first literature. The originally published version supplementary material included proof contained an error turned out inconsequential. This updated preprint corrects error, appeared under Lemma A.7.