Age of Incorrect Information for Generic Discrete-Time Markov Sources

2026-03-30

AI Summary

This work addresses the problem of information inaccuracy in real-time monitoring systems caused by channel noise and transmission constraints, aiming to minimize the duration of inaccurate information under a rate constraint. The problem is formulated as a constrained Markov decision process, and a novel class of multi-threshold scheduling policies is proposed, where thresholds depend on the source state, receiver state, and packet count. Theoretically, the optimal policy is shown to be a randomized mixture of two stationary policies, and—for the first time—a closed-form expression for the performance of this policy class is derived. An efficient algorithm combining relative value iteration with binary search is developed to satisfy the rate constraint, alongside a low-complexity single-threshold approximation. Experiments demonstrate that the proposed multi-threshold policy achieves near-optimal performance and significantly outperforms periodic scheduling, while the single-threshold scheme retains strong performance with substantially reduced complexity.

Abstract

This work introduces a framework for analyzing the Age of Incorrect Information (AoII) in a real-time monitoring system with a generic discrete-time Markov source. We study a noisy communication system employing a hybrid automatic repeat request (HARQ) protocol, subject to a transmission rate constraint. The optimization problem is formulated as a constrained Markov decision process (CMDP), and it is shown that there exists an optimal policy that is a randomized mixture of two stationary policies. To overcome the intractability of computing the optimal stationary policies, we develop a multiple-threshold policy class where thresholds depend on the source, the receiver, and the packet count. By establishing a Markov renewal structure induced by threshold policies, we derive closed-form expressions for the long-term average AoII and transmission rate. The proposed policy is constructed via a relative value iteration algorithm that leverages the threshold structure to skip computations, combined with a bisection search to satisfy the rate constraint. To accommodate scenarios requiring lower computational complexity, we adapt the same technique to produce a simpler single-threshold policy that trades optimality for efficiency. Numerical experiments exhibit that both thresholdbased policies outperform periodic scheduling, with the multiplethreshold approach matching the performance of the globally optimal policy.

Problem

• Age of Incorrect Information
• Markov source
• real-time monitoring
• transmission rate constraint
• HARQ

Innovation

• Age of Incorrect Information
• Markov decision process
• threshold policy
• HARQ
• Markov renewal