{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T00:47:20Z","timestamp":1760143640041,"version":"build-2065373602"},"reference-count":12,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2024,2,25]],"date-time":"2024-02-25T00:00:00Z","timestamp":1708819200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"2022GXNSFDA035087, NSFC","award":["62061004"],"award-info":[{"award-number":["62061004"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>In a hierarchical caching system, a server is connected to multiple mirrors, each of which is connected to a different set of users, and both the mirrors and the users are equipped with caching memories. All the existing schemes focus on single file retrieval, i.e., each user requests one file. In this paper, we consider the linear function retrieval problem, i.e., each user requests a linear combination of files, which includes single file retrieval as a special case. We propose a new scheme that reduces the transmission load of the first hop by jointly utilizing the two layers\u2019 cache memories, and we show that our scheme achieves the optimal load for the second hop in some cases.<\/jats:p>","DOI":"10.3390\/e26030195","type":"journal-article","created":{"date-parts":[[2024,2,26]],"date-time":"2024-02-26T06:50:23Z","timestamp":1708930223000},"page":"195","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Hierarchical Cache-Aided Networks for Linear Function Retrieval"],"prefix":"10.3390","volume":"26","author":[{"given":"Lingyu","family":"Zhang","sequence":"first","affiliation":[{"name":"Guangxi Key Laboratory of Multi-Source Information Mining & Security, Guangxi Normal University, Guilin 541004, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0009-0000-2146-657X","authenticated-orcid":false,"given":"Yun","family":"Kong","sequence":"additional","affiliation":[{"name":"The Department of Electrical Engineering, University of North Texas, Denton, TX 76207, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4383-9995","authenticated-orcid":false,"given":"Youlong","family":"Wu","sequence":"additional","affiliation":[{"name":"The School of Information Science and Technology, ShanghaiTech University, Shanghai 201210, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0360-0610","authenticated-orcid":false,"given":"Minquan","family":"Cheng","sequence":"additional","affiliation":[{"name":"Guangxi Key Laboratory of Multi-Source Information Mining & Security, Guangxi Normal University, Guilin 541004, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2024,2,25]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"2856","DOI":"10.1109\/TIT.2014.2306938","article-title":"Fundamental limits of caching","volume":"60","author":"Niesen","year":"2014","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"647","DOI":"10.1109\/TIT.2018.2870566","article-title":"Characterizing the rate-memory tradeoff in cache networks within a factor of 2","volume":"65","author":"Yu","year":"2019","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"1318","DOI":"10.1109\/TIT.2020.2967753","article-title":"An index coding approach to caching with uncoded cache placement","volume":"66","author":"Wan","year":"2020","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Wan, K., Ji, M., Piantanida, P., and Tuninetti, D. (2018, January 20\u201324). Caching in combination networks: Novel multicast message generation and delivery by leveraging the network topology. Proceedings of the 2018 IEEE International Conference on Communications, Kansas City, MO, USA.","DOI":"10.1109\/ICC.2018.8422197"},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Ji, M., Tulino, A.M., Llorca, J., and Caire, G. (2015, January 8\u201311). Caching in combination networks. Proceedings of the 2015 49th Asilomar Conference on Signals, Systems & Computers, Pacific Grove, CA, USA.","DOI":"10.1109\/ACSSC.2015.7421346"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"849","DOI":"10.1109\/TIT.2015.2504556","article-title":"Fundamental limits of caching in wireless D2D networks","volume":"62","author":"Ji","year":"2016","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"9595","DOI":"10.1109\/TWC.2023.3272348","article-title":"Distributed Deep Multi-Agent Reinforcement Learning for Cooperative Edge Caching in Internet-of-Vehicles","volume":"22","author":"Zhou","year":"2023","journal-title":"IEEE Trans. Wireless Commun."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"1326","DOI":"10.1109\/TNSE.2023.3255544","article-title":"Cost Minimization-Oriented Computation Offloading and Service Caching in Mobile Cloud-Edge Computing: An A3C-Based Approach","volume":"10","author":"Zhou","year":"2023","journal-title":"IEEE Trans. Netw. Sci. Eng"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"3212","DOI":"10.1109\/TIT.2016.2557804","article-title":"Hierarchical coded caching","volume":"62","author":"Karamchandani","year":"2016","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Wang, K., Wu, Y., Chen, J., and Yin, H. (2019, January 7\u201312). Reduce transmission delay for caching-aided two-layer networks. Proceedings of the 2023 IEEE International Symposium on Information Theory, Paris, France.","DOI":"10.1109\/ISIT.2019.8849624"},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Kong, Y., Wu, Y., and Cheng, M. (2023, January 26\u201329). Combinatorial designs for coded caching on hierarchical networks. Proceedings of the IEEE Conference on Wireless Communications and Networking, Glasgow, UK.","DOI":"10.1109\/WCNC55385.2023.10118860"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"4001","DOI":"10.1109\/TIT.2021.3066005","article-title":"On the optimal load-memory tradeoff of cache-aided scalar linear function retrieval","volume":"67","author":"Wan","year":"2021","journal-title":"IEEE Trans. Inf. 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