# Sequential Source Coding for Stochastic Systems Subject to Finite Rate Constraints

arXiv: https://arxiv.org/abs/1906.04217 · HTML: https://mlsanity.com/paper/1906.04217/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Jun 2019.

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

- [On the Choice of Perception Loss Function for Learned Video Compression](https://mlsanity.com/paper/2305.19301/) (2023)
- [On Self-Adaptive Perception Loss Function for Sequential Lossy Compression](https://mlsanity.com/paper/2502.10628/) (2025)

## Abstract (arXiv)

In this paper, we revisit the sequential source coding framework to analyze fundamental performance limitations of discrete-time stochastic control systems subject to feedback data-rate constraints in finite-time horizon. The basis of our results is a new characterization of the lower bound on the minimum total-rate achieved by sequential codes subject to a total (across time) distortion constraint and a computational algorithm that allocates optimally the rate-distortion for any fixed finite-time horizon. This characterization facilitates the derivation of analytical, non-asymptotic, and finite-dimensional lower and upper bounds in two control-related scenarios. (a) A parallel time-varying Gauss-Markov process with identically distributed spatial components that is quantized and transmitted through a noiseless channel to a minimum mean-squared error (MMSE) decoder. (b) A time-varying quantized LQG closed-loop control system, with identically distributed spatial components and with a random data-rate allocation. Our non-asymptotic lower bound on the quantized LQG control problem, reveals the absolute minimum data-rates for (mean square) stability of our time-varying plant for any fixed finite time horizon. We supplement our framework with illustrative simulation experiments.