{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,23]],"date-time":"2025-10-23T11:25:36Z","timestamp":1761218736212,"version":"build-2065373602"},"reference-count":48,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2025,6,11]],"date-time":"2025-06-11T00:00:00Z","timestamp":1749600000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["62231022"],"award-info":[{"award-number":["62231022"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>A composite source model consists of an intrinsic state and an extrinsic observation. The fundamental performance limit of reproducing the intrinsic state is characterized by the indirect rate\u2013distortion function. In a remote classification application, a source encoder encodes the extrinsic observation (e.g., image) into bits, and a source decoder plays the role of a classifier that reproduces the intrinsic state (e.g., label of image). In this work, we characterize the general structure of the optimal transition probability distribution, achieving the indirect rate\u2013distortion function. This optimal solution can be interpreted as a \u201csoft classifier\u201d, which generalizes the conventionally adopted \u201cclassify-then-compress\u201d scheme. We then apply the soft classification to aid the lossy compression of the extrinsic observation of a composite source. This leads to a coding scheme that exploits the soft classifier to guide reproduction, outperforming existing coding schemes without classification or with hard classification.<\/jats:p>","DOI":"10.3390\/e27060620","type":"journal-article","created":{"date-parts":[[2025,6,11]],"date-time":"2025-06-11T11:18:40Z","timestamp":1749640720000},"page":"620","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Soft Classification in a Composite Source Model"],"prefix":"10.3390","volume":"27","author":[{"given":"Yuefeng","family":"Cao","sequence":"first","affiliation":[{"name":"Department of Electronic Engineering and Information Science, University of Science and Technology of China, Hefei 230026, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1062-9342","authenticated-orcid":false,"given":"Jiakun","family":"Liu","sequence":"additional","affiliation":[{"name":"Department of Electronic Engineering and Information Science, University of Science and Technology of China, Hefei 230026, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Wenyi","family":"Zhang","sequence":"additional","affiliation":[{"name":"Department of Electronic Engineering and Information Science, University of Science and Technology of China, Hefei 230026, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2025,6,11]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"293","DOI":"10.1109\/TIT.1962.1057738","article-title":"Information transmission with additional noise","volume":"8","author":"Dobrushin","year":"1962","journal-title":"IRE Trans. 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