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arXiv 2301.06150cs.ITmath.IT
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通过随机延迟信道最小化错误信息年龄

Minimizing Age of Incorrect Information over a Channel with Random Delay

University of Maryland(马里兰大学)

Yutao Chen, Anthony Ephremides

AI总结:

本文研究了在随机延迟信道中通过阈值策略最小化错误信息年龄的问题,提出了可计算的相对值迭代算法,并证明了最优策略为阈值τ=1。

摘要:

我们考虑一个发射机-接收机对在一个分槽时间系统中。发射机观察一个动态源,并通过一个无错误通信信道发送更新到远程接收机,该信道具有随机延迟。我们考虑两种情况。在第一种情况下,更新保证在一定数量的时间槽内被送达。在第二种情况下,一旦传输时间超过预定值,更新就会被立即丢弃。接收机使用接收到的更新来估计动态源的状态。在本文中,我们采用错误信息年龄(AoII)作为性能度量,并研究优化发射机在每个时间槽中的行动以最小化AoII的问题。我们首先使用马尔可夫决策过程来表征优化问题,并研究阈值策略的性能,该策略规定只有在传输允许且AoII超过阈值τ时,发射机才发送更新。通过深入研究系统演变的特点,我们利用马尔可夫链精确计算阈值策略所达到的预期AoII。然后,我们证明了最优策略的存在,并提供了一种可计算的相对值迭代算法来估计最优策略。此外,通过利用策略改进定理,我们理论证明,在一个易于验证的条件下,最优策略是阈值策略,其中τ=1。最后,给出了数值结果以突出最优策略的性能。

英文摘要:

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.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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