# Fundamental limits of remote estimation of autoregressive Markov processes under communication constraints

arXiv: https://arxiv.org/abs/1505.04829 · HTML: https://mlsanity.com/paper/1505.04829/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 May 2015.

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

- [Semantic-Aware Remote Estimation of Multiple Markov Sources Under Constraints](https://mlsanity.com/paper/2403.16855/) (2024)
- [Semantic Text Transmission via Prediction with Small Language Models: Cost-Similarity Trade-off](https://mlsanity.com/paper/2403.00290/) (2024)

## Abstract (arXiv)

The fundamental limits of remote estimation of Markov processes under communication constraints are presented. The remote estimation system consists of a sensor and an estimator. The sensor observes a discrete-time Markov process, which is a symmetric countable state Markov source or a Gauss-Markov process. At each time, the sensor either transmits the current state of the Markov process or does not transmit at all. Communication is noiseless but costly. The estimator estimates the Markov process based on the transmitted observations. In such a system, there is a trade-off between communication cost and estimation accuracy. Two fundamental limits of this trade-off are characterized for infinite horizon discounted cost and average cost setups. First, when each transmission is costly, we characterize the minimum achievable cost of communication plus estimation error. Second, when there is a constraint on the average number of transmissions, we characterize the minimum achievable estimation error. Transmission and estimation strategies that achieve these fundamental limits are also identified.