{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,25]],"date-time":"2026-04-25T14:42:06Z","timestamp":1777128126146,"version":"3.51.4"},"reference-count":19,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2020,12,26]],"date-time":"2020-12-26T00:00:00Z","timestamp":1608940800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100000781","name":"European Research Council","doi-asserted-by":"publisher","award":["ERC Advanced Grant N. 789190, CARENET"],"award-info":[{"award-number":["ERC Advanced Grant N. 789190, CARENET"]}],"id":[{"id":"10.13039\/501100000781","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Coded Caching, proposed by Maddah-Ali and Niesen (MAN), has the potential to reduce network traffic by pre-storing content in the users\u2019 local memories when the network is underutilized and transmitting coded multicast messages that simultaneously benefit many users at once during peak-hour times. This paper considers the linear function retrieval version of the original coded caching setting, where users are interested in retrieving a number of linear combinations of the data points stored at the server, as opposed to a single file. This extends the scope of the authors\u2019 past work that only considered the class of linear functions that operate element-wise over the files. On observing that the existing cache-aided scalar linear function retrieval scheme does not work in the proposed setting, this paper designs a novel coded caching scheme that outperforms uncoded caching schemes that either use unicast transmissions or let each user recover all files in the library.<\/jats:p>","DOI":"10.3390\/e23010025","type":"journal-article","created":{"date-parts":[[2020,12,27]],"date-time":"2020-12-27T20:04:58Z","timestamp":1609099498000},"page":"25","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["Cache-Aided General Linear Function Retrieval"],"prefix":"10.3390","volume":"23","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-4671-3287","authenticated-orcid":false,"given":"Kai","family":"Wan","sequence":"first","affiliation":[{"name":"Electrical Engineering and Computer Science Department, Technische Universit\u00e4t Berlin, 10587 Berlin, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Hua","family":"Sun","sequence":"additional","affiliation":[{"name":"Department of Electrical Engineering, University of North Texas, Denton, TX 76203, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Mingyue","family":"Ji","sequence":"additional","affiliation":[{"name":"Electrical and Computer Engineering Department, University of Utah, Salt Lake City, UT 84112, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Daniela","family":"Tuninetti","sequence":"additional","affiliation":[{"name":"Electrical and Computer Engineering Department, University of Illinois Chicago, Chicago, IL 60607, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Giuseppe","family":"Caire","sequence":"additional","affiliation":[{"name":"Electrical Engineering and Computer Science Department, Technische Universit\u00e4t Berlin, 10587 Berlin, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2020,12,26]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Borst, S., Gupta, V., and Walid, A. (2010, January 14\u201319). Distributed caching algorithms for content distribution networks. Proceedings of the 2010 Proceedings IEEE INFOCOM, San Diego, CA, USA.","DOI":"10.1109\/INFCOM.2010.5461964"},{"key":"ref_2","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_3","unstructured":"Wan, K., Tuninetti, D., and Piantanida, P. (2016, January 11\u201314). On the Optimality of Uncoded Cache Placement. Proceedings of the IEEE Information Theory Workshop (ITW), Cambridge, UK."},{"key":"ref_4","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":"2020. 66","author":"Wan","year":"2020","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"1281","DOI":"10.1109\/TIT.2017.2785237","article-title":"The Exact Rate-Memory Tradeoff for Caching with Uncoded Prefetching","volume":"64","author":"Yu","year":"2018","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_6","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_7","doi-asserted-by":"crossref","unstructured":"Wan, K., Sun, H., Ji, M., Tuninetti, D., and Caire, G. (2020). On Optimal Load-Memory Tradeoff of Cache-Aided Scalar Linear Function Retrieval. arXiv.","DOI":"10.1109\/ISIT44484.2020.9173997"},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Wan, K., and Caire, G. (2020). On Coded Caching with Private Demands. IEEE Trans. Inf. Theory.","DOI":"10.1109\/ITA50056.2020.9244946"},{"key":"ref_9","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_10","doi-asserted-by":"crossref","first-page":"8179","DOI":"10.1109\/TCOMM.2019.2940671","article-title":"On the Optimality of D2D Coded Caching With Uncoded Cache Placement and One-Shot Delivery","volume":"67","author":"Yapar","year":"2019","journal-title":"IEEE Trans. Commun."},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Yan, Q., and Tuninetti, D. (2020). Fundamental Limits of Caching for Demand Privacy against Colluding Users. arXiv.","DOI":"10.1109\/JSAIT.2021.3053372"},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Yan, Q., and Tuninetti, D. (2020). Key Superposition Simultaneously Achieves Security and Privacy in Cache-Aided Linear Function Retrieval. arXiv.","DOI":"10.1109\/TIFS.2021.3127018"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"5524","DOI":"10.1109\/TIT.2016.2599110","article-title":"Finite-Length Analysis of Caching-Aided Coded Multicasting","volume":"2016. 62","author":"Shanmugam","year":"2016","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Wan, K., Sun, H., Ji, M., Tuninetti, D., and Caire, G. (2020). Cache-Aided Matrix Multiplication Retrieval. arXiv.","DOI":"10.1109\/ISIT44484.2020.9173997"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"1479","DOI":"10.1109\/TIT.2010.2103753","article-title":"Index Coding with Side Information","volume":"57","author":"Birk","year":"2011","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"319","DOI":"10.1109\/LCOMM.2015.2388477","article-title":"Index Coding with Coded Side-Information","volume":"19","author":"Lee","year":"2015","journal-title":"IEEE Commun. Lett."},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Jia, Z., and Jafar, S.A. (2019). Cross Subspace Alignment Codes for Coded Distributed Batch Computation. arXiv.","DOI":"10.1109\/ICC40277.2020.9149322"},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Chang, W., and Tandon, R. (2019). On the Upload versus Download Cost for Secure and Private Matrix Multiplication. arXiv.","DOI":"10.1109\/ITW44776.2019.8989342"},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Kakar, J., Khristoforov, A., Ebadifar, S., and Sezgin, A. (2019). Uplink-downlink tradeoff in secure distributed matrix multiplication. arXiv.","DOI":"10.1109\/ISIT44484.2020.9174509"}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/23\/1\/25\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T10:46:28Z","timestamp":1760179588000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/23\/1\/25"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,12,26]]},"references-count":19,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2021,1]]}},"alternative-id":["e23010025"],"URL":"https:\/\/doi.org\/10.3390\/e23010025","relation":{},"ISSN":["1099-4300"],"issn-type":[{"value":"1099-4300","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,12,26]]}}}