Minimizing Age of Incorrect Information over a Channel with Random Delay

We consider a transmitter-receiver pair in a slotted-time system. The transmitter observes a dynamic source and sends updates to a remote receiver through an error-free communication channel that suffers a random delay. We consider two cases. In the first case, the update is guaranteed to be delivered within a certain number of time slots. In the second case, the update is immediately discarded once the transmission time exceeds a predetermined value. The receiver estimates the state of the dynamic source using the received updates. In this paper, we adopt the Age of Incorrect Information (AoII) as the performance metric and investigate the problem of optimizing the transmitter’s action in each time slot to minimize AoII. We first characterize the optimization problem using the Markov decision process and investigate the performance of the threshold policy, under which the transmitter transmits updates only when the transmission is allowed and the AoII exceeds the threshold $τ$. By delving into the characteristics of the system evolution, we precisely compute the expected AoII achieved by the threshold policy using the Markov chain. Then, we prove that the optimal policy exists and provide a computable relative value iteration algorithm to estimate the optimal policy. Furthermore, by leveraging the policy improvement theorem, we theoretically prove that, under an easily verifiable condition, the optimal policy is the threshold policy with $τ=1$. Finally, numerical results are presented to highlight the performance of the optimal policy.

💡 Research Summary

This research paper addresses a critical challenge in modern networked control systems: how to minimize the discrepancy between a remote receiver’s estimate and the actual state of a dynamic source in the presence of unpredictable communication delays. The authors focus on the “Age of Incorrect Information (AoII)” as the primary performance metric. Unlike the traditional Age of Information (AoI), which only tracks the time elapsed since the last update, AoII specifically measures the period during which the receiver’s information is inaccurate, making it a much more relevant metric for applications where the source value remains constant for periods of time.

The paper investigates a slotted-time communication system characterized by a channel with random delays. The authors explore two distinct scenarios: first, a system where updates are guaranteed to arrive within a bounded number of time slots, and second, a system where updates are discarded if the transmission delay exceeds a predefined threshold. These scenarios accurately reflect real-world constraints such as buffer limits and time-to-live (TTL) settings in packet-switched networks.

To solve the optimization problem, the authors formulate the system dynamics as a Markov Decision Process (MDP). They specifically investigate a “threshold policy,” where the transmitter decides to send an update only when the current AoII exceeds a certain threshold $\tau$. Through the use of Markov chains, the researchers are able to precisely compute the expected AoII achieved under such threshold-based strategies.

A significant mathematical contribution of this paper is the proof of the existence of an optimal policy and the development of a computable Relative Value Iteration (RVI) algorithm to approximate it. Furthermore, by applying the policy improvement theorem, the authors provide a rigorous theoretical proof that, under a verifiable condition, the optimal policy is indeed a threshold policy with $\tau=1$. This implies that the most efficient strategy is to trigger an update as soon as the information becomes incorrect.

The paper concludes with numerical simulations that demonstrate the superiority of the proposed optimal policy in reducing AoII compared to other baseline strategies. This work provides essential theoretical foundations for designing highly reliable and efficient communication protocols for next-generation technologies, such as 5G/6G networks, autonomous vehicle communications (V2X), and industrial IoT, where minimizing information error in uncertain delay environments is paramount.