On the Role of Age and Semantics of Information in Remote Estimation of Markov Sources

This paper investigates the semantics-aware remote estimation of a finite-state Markov chain. We employ the maximum a posteriori (MAP) estimator and aim to devise a transmission policy to optimize estimation performance subject to a transmission frequency constraint. We leverage two metrics, namely the Age of Consecutive Error (AoCE) and the Age of Information (AoI), to quantify, respectively, the significance of estimation error at the transmitter and the predictability of outdated information at the receiver. The optimal transmission problem is formulated as a constrained Markov decision process (CMDP) with unbounded costs. We show the existence of an optimal simple mixture policy, which randomly selects between two deterministic switching policies with a fixed probability. Notably, each switching policy triggers a transmission only when the AoCE exceeds a threshold value that depends on both the AoI and the instantaneous estimation error. We further derive sufficient conditions under which the switching policy reduces to a simple threshold policy; that is, it admits identical thresholds for all estimation errors. Leveraging these results, we develop an efficient structure-aware algorithm, Insec-SPI, that computes the optimal policy with reduced computation overhead. Our results demonstrate that incorporating both AoI and AoCE yields significantly improved estimation quality compared to using either metric alone.