# Online variable-length source coding for minimum bitrate LQG control

arXiv: https://arxiv.org/abs/2304.00593 · HTML: https://mlsanity.com/paper/2304.00593/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 6 of its 28 references that are in the map.
- First posted on arXiv 2 Apr 2023.

## Builds on (most cited first, 6 of 6)

- [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)
- [Rate of Prefix-free Codes in LQG Control Systems](https://mlsanity.com/paper/1604.01227/) (2016)
- [Algorithms for Optimal Control with Fixed-Rate Feedback](https://mlsanity.com/paper/1809.04917/) (2018)
- [Time-invariant Prefix Coding for LQG Control](https://mlsanity.com/paper/2204.00588/) (2022)
- [A Lower-bound for Variable-length Source Coding in Linear-Quadratic-Gaussian Control with Shared Randomness](https://mlsanity.com/paper/2203.12467/) (2022)

## Abstract (arXiv)

We propose an adaptive coding approach to achieve linear-quadratic-Gaussian (LQG) control with near-minimum bitrate prefix-free feedback. Our approach combines a recent analysis of a quantizer design for minimum rate LQG control with work on universal lossless source coding for sources on countable alphabets. In the aforementioned quantizer design, it was established that the quantizer outputs are an asymptotically stationary, ergodic process. To enable LQG control with provably near-minimum bitrate, the quantizer outputs must be encoded into binary codewords efficiently. This is possible given knowledge of the probability distributions of the quantizer outputs, or of their limiting distribution. Obtaining such knowledge is challenging; the distributions do not readily admit closed form descriptions. This motivates the application of universal source coding. Our main theoretical contribution in this work is a proof that (after an invertible transformation), the quantizer outputs are random variables that fall within an exponential or power-law envelope class (depending on the plant dimension). Using ideas from universal coding on envelope classes, we develop a practical, zero-delay version of these algorithms that operates with fixed precision arithmetic. We evaluate the performance of this algorithm numerically, and demonstrate competitive results with respect to fundamental tradeoffs between bitrate and LQG control performance.