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This connection provides an organizational framework for assessing existing bounds on these functions. In particular, we show that the best-known bounds of Xie et al. are nonredundant when examined through this connection.<\/jats:p>","DOI":"10.3390\/e27040441","type":"journal-article","created":{"date-parts":[[2025,4,20]],"date-time":"2025-04-20T20:31:36Z","timestamp":1745181096000},"page":"441","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["A Constrained Talagrand Transportation Inequality with Applications to Rate-Distortion-Perception Theory"],"prefix":"10.3390","volume":"27","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5255-4564","authenticated-orcid":false,"given":"Li","family":"Xie","sequence":"first","affiliation":[{"name":"School of Information and Electronics, Beijing Institute of Technology, Beijing 100081, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Liangyan","family":"Li","sequence":"additional","affiliation":[{"name":"Department of Electrical and Computer Engineering, McMaster University, Hamilton, ON L8S 4K1, Canada"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8084-9332","authenticated-orcid":false,"given":"Jun","family":"Chen","sequence":"additional","affiliation":[{"name":"Department of Electrical and Computer Engineering, McMaster University, Hamilton, ON L8S 4K1, Canada"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0772-2914","authenticated-orcid":false,"given":"Lei","family":"Yu","sequence":"additional","affiliation":[{"name":"School of Statistics and Data Science, LPMC, KLMDASR, and LEBPS, Nankai University, Tianjin 300071, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Zhongshan","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Cyberspace Science and Technology, Beijing Institute of Technology, Beijing 100081, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2025,4,19]]},"reference":[{"key":"ref_1","unstructured":"Cover, T.M., and Thomas, J.A. 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