{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,22]],"date-time":"2026-04-22T18:37:40Z","timestamp":1776883060625,"version":"3.51.2"},"reference-count":30,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2021,11,25]],"date-time":"2021-11-25T00:00:00Z","timestamp":1637798400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>In this paper, we study a slotted-time system where a base station needs to update multiple users at the same time. Due to the limited resources, only part of the users can be updated in each time slot. We consider the problem of minimizing the Age of Incorrect Information (AoII) when imperfect Channel State Information (CSI) is available. Leveraging the notion of the Markov Decision Process (MDP), we obtain the structural properties of the optimal policy. By introducing a relaxed version of the original problem, we develop the Whittle\u2019s index policy under a simple condition. However, indexability is required to ensure the existence of Whittle\u2019s index. To avoid indexability, we develop Indexed priority policy based on the optimal policy for the relaxed problem. Finally, numerical results are laid out to showcase the application of the derived structural properties and highlight the performance of the developed scheduling policies.<\/jats:p>","DOI":"10.3390\/e23121572","type":"journal-article","created":{"date-parts":[[2021,11,29]],"date-time":"2021-11-29T05:23:02Z","timestamp":1638163382000},"page":"1572","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":26,"title":["Scheduling to Minimize Age of Incorrect Information with Imperfect Channel State Information"],"prefix":"10.3390","volume":"23","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3992-5468","authenticated-orcid":false,"given":"Yutao","family":"Chen","sequence":"first","affiliation":[{"name":"Department of Electrical and Computer Engineering, University of Maryland, College Park, MD 20742, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Anthony","family":"Ephremides","sequence":"additional","affiliation":[{"name":"Department of Electrical and Computer Engineering, University of Maryland, College Park, MD 20742, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2021,11,25]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"2215","DOI":"10.1109\/TNET.2020.3005549","article-title":"The age of incorrect information: A new performance metric for status updates","volume":"28","author":"Maatouk","year":"2020","journal-title":"IEEE\/ACM Trans. Netw."},{"key":"ref_2","unstructured":"Uysal, E., Kaya, O., Ephremides, A., Gross, J., Codreanu, M., Popovski, P., Assaad, M., Liva, G., Munari, A., and Soleymani, T. (2021). Semantic communications in networked systems. arXiv."},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Kam, C., Kompella, S., and Ephremides, A. (2020, January 6\u20139). Age of incorrect information for remote estimation of a binary markov source. Proceedings of the IEEE INFOCOM 2020-IEEE Conference on Computer Communications Workshops (INFOCOM WKSHPS), Toronto, ON, Canada.","DOI":"10.1109\/INFOCOMWKSHPS50562.2020.9162726"},{"key":"ref_4","unstructured":"Maatouk, A., Assaad, M., and Ephremides, A. (2020). The age of incorrect information: An enabler of semantics-empowered communication. arXiv."},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Chen, Y., and Ephremides, A. (2021). 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