This paper investigates the Age of Incorrect Information (AoII) in a communication system whose channel suffers a random delay. We consider a slotted-time system where a transmitter observes a dynamic source and decides when to send updates to a remote receiver through the communication channel. The threshold policy, under which the transmitter initiates transmission only when the AoII exceeds the threshold, governs the transmitter's decision. In this paper, we analyze and calculate the performance of the threshold policy in terms of the achieved AoII. Using the Markov chain to characterize the system evolution, the expected AoII can be obtained precisely by solving a system of linear equations whose size is finite and depends on the threshold. We also give closed-form expressions of the expected AoII under two particular thresholds. Finally, calculation results show that there are better strategies than the transmitter constantly transmitting new updates.

翻译：本文研究了通信系统中因信道随机延迟导致的错误信息年龄（AoII）问题。我们考虑一个时隙系统，其中发射机观测动态源，并决定何时通过通信信道向远程接收器发送更新。阈值策略控制发射机的决策，即仅当AoII超过阈值时发射机才启动传输。本文以实现的AoII为指标，分析并计算了阈值策略的性能。通过利用马尔可夫链刻画系统演化，精确期望AoII可通过求解一组线性方程组获得，该方程组规模有限且取决于阈值。我们还给出了两种特定阈值下期望AoII的闭式表达式。最后，计算结果表明存在优于发射机持续传输新更新策略的方案。