Exploiting Data Significance in Remote Estimation of Discrete-State Markov Sources

TL;DR

This work addresses semantics-aware remote estimation for a binary Markov source with normal and alarm states, introducing AoMA and AoFA to capture lasting error impacts. It formulates the problem as an average-cost, countably infinite-state MDP and proves that the optimal policy has a switching structure with age-thresholds, reducing complexity to two thresholds in symmetric scenarios. A finite-state, exponentially accurate truncated MDP is proposed to enable tractable optimization, alongside an efficient $\mathcal{O}(N^2)$ policy-search algorithm and comprehensive numerical validation. The results demonstrate how content significance alters transmission strategies, improving long-horizon estimation performance under communication constraints with practical implications for semantic communications and networked control systems.

Abstract

We consider semantics-aware remote estimation of a discrete-state Markov source with both normal (low-priority) and alarm (high-priority) states. Erroneously announcing a normal state at the destination when the source is actually in an alarm state (i.e., missed alarm) incurs a significantly higher cost than falsely announcing an alarm state when the source is in a normal state (i.e., false alarm). Moreover, consecutive estimation errors may cause significant lasting impacts, such as maintenance costs and misoperations. Motivated by this, we introduce two new metrics, the Age of Missed Alarm (AoMA) and the Age of False Alarm (AoFA), to capture the lasting impacts incurred by different estimation errors. Notably, these two age processes evolve interdependently and distinguish between different error types. Our goal is to design a transmission policy that achieves an optimized trade-off between lasting impact and communication cost. The problem is formulated as a countably infinite-state Markov decision process (MDP) with an unbounded cost function. We show the existence of a simple switching policy with distinct thresholds for each age process and derive closed-form expressions for its performance. For symmetric and non-prioritized sources, we show that the optimal policy reduces to a threshold policy with identical thresholds. For numerical tractability, we propose a finite-state approximate MDP and prove that it converges exponentially fast to the original MDP in the truncation size. Finally, we develop an efficient search algorithm to compute the optimal switching policy and validate our theoretical findings with numerical results.

Figures (9)

• Figure 1: Remote estimation of a Markov source with normal and alarm states.
• Figure 2: The evolution of estimation error under different actions.
• Figure 3: State evolution of the Markov chains induced by the age-agnostic randomized policy.
• Figure 4: State evolution of MC2 induced by the switching policy.
• Figure 5: State evolution of the truncated MC2 under the switching policy.

Theorems & Definitions (21)

• Remark 1
• Definition 1
• Definition 2
• Remark 2
• Proposition 1
• Proposition 2
• Remark 3
• Definition 3
• Theorem 1
• Proposition 3