# Time-invariant Prefix Coding for LQG Control

arXiv: https://arxiv.org/abs/2204.00588 · HTML: https://mlsanity.com/paper/2204.00588/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 45 references that are in the map.
- First posted on arXiv 1 Apr 2022.

## Builds on (most cited first, 13 of 13)

- [Convergence of Langevin MCMC in KL-divergence](https://mlsanity.com/paper/1705.09048/) (2017)
- [Rate-cost tradeoffs in control](https://mlsanity.com/paper/1612.02126/) (2016)
- [LQG Control with Minimum Directed Information: Semidefinite Programming Approach](https://mlsanity.com/paper/1510.04214/) (2015)
- [Wireless Control for Smart Manufacturing: Recent Approaches and Open Challenges](https://mlsanity.com/paper/2010.09087/) (2020)
- [Zero-Delay Rate Distortion via Filtering for Vector-Valued Gaussian Sources](https://mlsanity.com/paper/1810.00298/) (2018)
- [Rate of Prefix-free Codes in LQG Control Systems](https://mlsanity.com/paper/1604.01227/) (2016)
- [The Time-Invariant Multidimensional Gaussian Sequential Rate-Distortion Problem Revisited](https://mlsanity.com/paper/1711.09853/) (2017)
- [Algorithms for Optimal Control with Fixed-Rate Feedback](https://mlsanity.com/paper/1809.04917/) (2018)
- [A Characterization of the Minimal Average Data Rate that Guarantees a Given Closed-Loop Performance Level](https://mlsanity.com/paper/1407.0118/) (2014)
- [Exact minimum number of bits to stabilize a linear system](https://mlsanity.com/paper/1807.07686/) (2018)
- [Comments on "A Framework for Control System Design Subject to Average Data-Rate Constraints"](https://mlsanity.com/paper/2103.12897/) (2021)
- [Robustness to Incorrect Priors and Controlled Filter Stability in Partially Observed Stochastic Control](https://mlsanity.com/paper/2110.03720/) (2021)
- [Stabilizing Error Correction Codes for Controlling LTI Systems over Erasure Channels](https://mlsanity.com/paper/2201.05488/) (2022)

## Built on by (most cited first, 2 of 2)

- [Online variable-length source coding for minimum bitrate LQG control](https://mlsanity.com/paper/2304.00593/) (2023)
- [Reinforcement Learning for Jointly Optimal Coding and Control Policies for a Controlled Markovian System over a Communication Channel](https://mlsanity.com/paper/2411.13884/) (2024)

## Abstract (arXiv)

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