{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,21]],"date-time":"2026-04-21T10:57:46Z","timestamp":1776769066841,"version":"3.51.2"},"reference-count":15,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2022,1,13]],"date-time":"2022-01-13T00:00:00Z","timestamp":1642032000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Information"],"abstract":"<jats:p>In this work, we propose both an improvement and extensions of a reverse Jensen inequality due to Wunder et al. (2021). The new proposed inequalities are fairly tight and reasonably easy to use in a wide variety of situations, as demonstrated in several application examples that are relevant to information theory. Moreover, the main ideas behind the derivations turn out to be applicable to generate bounds to expectations of multivariate convex\/concave functions, as well as functions that are not necessarily convex or concave.<\/jats:p>","DOI":"10.3390\/info13010039","type":"journal-article","created":{"date-parts":[[2022,1,13]],"date-time":"2022-01-13T10:57:37Z","timestamp":1642071457000},"page":"39","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Reversing Jensen\u2019s Inequality for Information-Theoretic Analyses"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9547-3243","authenticated-orcid":false,"given":"Neri","family":"Merhav","sequence":"first","affiliation":[{"name":"The Viterbi Faculty of Electrical and Computer Engineering, Technion\u2014Israel Institute of Technology, Haifa 3200003, Israel"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,1,13]]},"reference":[{"key":"ref_1","unstructured":"Cover, T.M., and Thomas, J.A. (2006). Elements of Information Theory, John Wiley & Sons. [2nd ed.]."},{"key":"ref_2","unstructured":"Jebara, T., and Pentland, A. (2000, January 1). On reversing Jensen\u2019s inequality. Proceedings of the 13th International Conference on Neural Information Processing Systems (NIPS 2000), Denver, CO, USA."},{"key":"ref_3","first-page":"5","article-title":"Further reverse results for Jensen\u2019s discrete inequality and applications in information theory","volume":"2","author":"Budimir","year":"2001","journal-title":"J. Inequal. Pure Appl. Math."},{"key":"ref_4","first-page":"107","article-title":"On a new converse of Jensen\u2019s inequality","volume":"85","year":"2009","journal-title":"Math. Publ. L\u2019Institut Math."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"496821","DOI":"10.1155\/2010\/496821","article-title":"Some reverses of the Jensen inequality for functions of selfadjoint operators in Hilbert spaces","volume":"2010","author":"Dragomir","year":"2010","journal-title":"J. Inequal. Appl."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"177","DOI":"10.1017\/S0004972712001098","article-title":"Some reverses of the Jensen inequality with applications","volume":"87","author":"Dragomir","year":"2013","journal-title":"Bull. Aust. Math. Soc."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"114","DOI":"10.1007\/s13398-020-00843-1","article-title":"New converses of Jensen inequality via Green functions with applications","volume":"114","author":"Khan","year":"2020","journal-title":"Rev. Real Acad. Cienc. Exactas Fis. Nat. Ser. A Mat."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"2577","DOI":"10.1002\/mma.6066","article-title":"Converses of Jensen inequality derived from the Green functions with applications in information theory","volume":"43","author":"Khan","year":"2020","journal-title":"Math. Methods Appl. Sci."},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Wunder, G., Gro\u03b2, B., Fritschek, R., and Schaefer, R.F. (2021, January 17\u201321). A reverse Jensen inequality result with application to mutual information estimation. Proceedings of the 2021 IEEE Information Theory Workshop (ITW 2021), Kanazawa, Japan. Available online: https:\/\/arxiv.org\/pdf\/2111.06676.pdf.","DOI":"10.1109\/ITW48936.2021.9611449"},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Ali, M.A., Budak, H., and Zhang, Z. (2021). A new extension of quantum Simpson\u2019s and quantum Newton\u2019s inequalities for quantum differentiable convex functions. Math. Methods Appl. Sci., 1\u201319.","DOI":"10.1515\/math-2021-0015"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"899","DOI":"10.1007\/s10957-020-01726-6","article-title":"Some new quantum Hermite-Hadamard like inequalities for co-ordinated convex functions","volume":"186","author":"Budak","year":"2020","journal-title":"J. Optim. Theory Appl."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"114","DOI":"10.1109\/TIT.2019.2920538","article-title":"Universal randomized guessing with application to asynchronous decentralized brute-force attacks","volume":"66","author":"Merhav","year":"2020","journal-title":"IEEE Trans. Inform. Theory"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"199","DOI":"10.1109\/TIT.1981.1056331","article-title":"The performance of universal encoding","volume":"27","author":"Krichevsky","year":"1981","journal-title":"IEEE Trans. Inform. Theory"},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Dong, A., Zhang, H., Wu, D., and Yuan, D. (2015, January 6\u20139). Logarithmic expectation of the sum of exponential random variables for wireless communication performance evaluation. Proceedings of the 2015 IEEE 82nd Vehicular Technology Conference (VTC2015-Fall), Boston, MA, USA.","DOI":"10.1109\/VTCFall.2015.7391010"},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Tse, D., and Viswanath, P. (2005). Fundamentals of Wireless Communication, Cambridge University Press.","DOI":"10.1017\/CBO9780511807213"}],"container-title":["Information"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2078-2489\/13\/1\/39\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,13]],"date-time":"2025-10-13T14:02:19Z","timestamp":1760364139000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2078-2489\/13\/1\/39"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,1,13]]},"references-count":15,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2022,1]]}},"alternative-id":["info13010039"],"URL":"https:\/\/doi.org\/10.3390\/info13010039","relation":{},"ISSN":["2078-2489"],"issn-type":[{"value":"2078-2489","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,1,13]]}}}