{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,24]],"date-time":"2025-10-24T08:30:18Z","timestamp":1761294618457,"version":"build-2065373602"},"reference-count":31,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2023,6,11]],"date-time":"2023-06-11T00:00:00Z","timestamp":1686441600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"JSPS KAKENHI","award":["JP20K04462","JP18H01438"],"award-info":[{"award-number":["JP20K04462","JP18H01438"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>The utilization of databases such as IoT has progressed, and understanding how to protect the privacy of data is an important issue. As pioneering work, in 1983, Yamamoto assumed the source (database), which consists of public information and private information, and found theoretical limits (first-order rate analysis) among the coding rate, utility and privacy for the decoder in two special cases. In this paper, we consider a more general case based on the work by Shinohara and Yagi in 2022. Introducing a measure of privacy for the encoder, we investigate the following two problems: The first problem is the first-order rate analysis among the coding rate, utility, privacy for the decoder, and privacy for the encoder, in which utility is measured by the expected distortion or the excess-distortion probability. The second task is establishing the strong converse theorem for utility\u2013privacy trade-offs, in which utility is measured by the excess-distortion probability. These results may lead to a more refined analysis such as the second-order rate analysis.<\/jats:p>","DOI":"10.3390\/e25060921","type":"journal-article","created":{"date-parts":[[2023,6,12]],"date-time":"2023-06-12T02:28:42Z","timestamp":1686536922000},"page":"921","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Utility\u2013Privacy Trade-Offs with Limited Leakage for Encoder"],"prefix":"10.3390","volume":"25","author":[{"given":"Naruki","family":"Shinohara","sequence":"first","affiliation":[{"name":"Department of Computer and Network Engineering, The University of Electro-Communications, 1-5-1 Chofugaoka, Chofu 182-8585, Tokyo, Japan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Hideki","family":"Yagi","sequence":"additional","affiliation":[{"name":"Department of Computer and Network Engineering, The University of Electro-Communications, 1-5-1 Chofugaoka, Chofu 182-8585, Tokyo, Japan"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,6,11]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"918","DOI":"10.1109\/TIT.1983.1056749","article-title":"A source coding problem for sources with additional outputs to keep secret from the receiver or wiretappers","volume":"29","author":"Yamamoto","year":"1983","journal-title":"IEEE Trans. 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