{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,24]],"date-time":"2025-10-24T08:30:26Z","timestamp":1761294626230,"version":"3.37.3"},"reference-count":63,"publisher":"Institute of Electrical and Electronics Engineers (IEEE)","issue":"10","license":[{"start":{"date-parts":[[2023,10,1]],"date-time":"2023-10-01T00:00:00Z","timestamp":1696118400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/ieeexplore.ieee.org\/Xplorehelp\/downloads\/license-information\/IEEE.html"},{"start":{"date-parts":[[2023,10,1]],"date-time":"2023-10-01T00:00:00Z","timestamp":1696118400000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-029"},{"start":{"date-parts":[[2023,10,1]],"date-time":"2023-10-01T00:00:00Z","timestamp":1696118400000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-037"}],"funder":[{"name":"6G Future Lab Bavaria funded by the Bavarian State Ministry of Science and the Arts"},{"name":"Project 6G-Life funded by the Germany Federal Ministry for Education and Research"},{"DOI":"10.13039\/501100001659","name":"German Research Foundation","doi-asserted-by":"publisher","award":["421682817","509917421"],"award-info":[{"award-number":["421682817","509917421"]}],"id":[{"id":"10.13039\/501100001659","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["IEEE Trans. Inform. Theory"],"published-print":{"date-parts":[[2023,10]]},"DOI":"10.1109\/tit.2023.3293311","type":"journal-article","created":{"date-parts":[[2023,7,7]],"date-time":"2023-07-07T18:29:10Z","timestamp":1688754550000},"page":"6231-6250","source":"Crossref","is-referenced-by-count":3,"title":["Stability of Bernstein\u2019s Theorem and Soft Doubling for Vector Gaussian Channels"],"prefix":"10.1109","volume":"69","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5093-3640","authenticated-orcid":false,"given":"Mohammad Mahdi","family":"Mahvari","sequence":"first","affiliation":[{"name":"Institute for Communications Engineering, School of Computation, Information and Technology, Technical University of Munich (TUM), Munich, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3904-9181","authenticated-orcid":false,"given":"Gerhard","family":"Kramer","sequence":"additional","affiliation":[{"name":"Institute for Communications Engineering, School of Computation, Information and Technology, Technical University of Munich (TUM), Munich, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"263","reference":[{"key":"ref1","doi-asserted-by":"publisher","DOI":"10.2307\/2371328"},{"issue":"3","key":"ref2","first-page":"21","article-title":"On a property characterizing Gauss\u2019 law","volume":"217","author":"Bernshtein","year":"1941","journal-title":"Trudy Leningr. Bolitekhn."},{"key":"ref3","doi-asserted-by":"publisher","DOI":"10.2307\/1401511"},{"key":"ref4","first-page":"217","article-title":"On a property of the normal distribution","volume":"89","author":"Skitovich","year":"1953","journal-title":"DAN SSSR"},{"key":"ref5","doi-asserted-by":"publisher","DOI":"10.1214\/aoms\/1177704579"},{"key":"ref6","doi-asserted-by":"publisher","DOI":"10.1007\/BF01233426"},{"key":"ref7","doi-asserted-by":"publisher","DOI":"10.1016\/0001-8708(76)90184-5"},{"key":"ref8","doi-asserted-by":"publisher","DOI":"10.1016\/0022-1236(91)90155-X"},{"key":"ref9","first-page":"1","article-title":"An extremal inequality related to hypercontractivity of Gaussian random variables","volume-title":"Proc. Inf. Theory Appl. Workshop","author":"Nair"},{"key":"ref10","doi-asserted-by":"publisher","DOI":"10.1109\/ALLERTON.2014.7028531"},{"key":"ref11","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2017.2779745"},{"key":"ref12","article-title":"Information-theoretic perspectives on Brascamp\u2013Lieb inequality and its reverse","author":"Liu","year":"2017","journal-title":"arXiv:1702.06260"},{"article-title":"Information theory from a functional viewpoint","year":"2018","author":"Liu","key":"ref13"},{"key":"ref14","doi-asserted-by":"publisher","DOI":"10.3390\/e20060418"},{"key":"ref15","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2022.3192913"},{"key":"ref16","article-title":"Entropy inequalities and Gaussian comparisons","author":"Aras","year":"2022","journal-title":"arXiv:2206.14182"},{"key":"ref17","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2014.2304457"},{"key":"ref18","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2016.2606502"},{"key":"ref19","doi-asserted-by":"publisher","DOI":"10.1109\/NCC.2017.8077079"},{"key":"ref20","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2019.2892107"},{"key":"ref21","doi-asserted-by":"publisher","DOI":"10.1109\/ISIT50566.2022.9834787"},{"key":"ref22","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2019.2957808"},{"key":"ref23","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2022.3163647"},{"key":"ref24","doi-asserted-by":"publisher","DOI":"10.1109\/ISIT45174.2021.9518133"},{"key":"ref25","doi-asserted-by":"publisher","DOI":"10.1109\/ISIT44484.2020.9174395"},{"key":"ref26","doi-asserted-by":"publisher","DOI":"10.1109\/ITW44776.2019.8989086"},{"key":"ref27","doi-asserted-by":"publisher","DOI":"10.3390\/info11120553"},{"key":"ref28","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2021.3107215"},{"article-title":"Secret key agreement over Gaussian two-way wiretap channel","year":"2021","author":"Wang","key":"ref29"},{"key":"ref30","doi-asserted-by":"publisher","DOI":"10.1137\/1101016"},{"key":"ref31","doi-asserted-by":"publisher","DOI":"10.1214\/aos\/1176346604"},{"key":"ref32","doi-asserted-by":"publisher","DOI":"10.1214\/aoms\/1177730390"},{"key":"ref33","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2003.821979"},{"key":"ref34","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.27.4.222"},{"key":"ref35","doi-asserted-by":"publisher","DOI":"10.1007\/BF02924890"},{"key":"ref36","doi-asserted-by":"publisher","DOI":"10.1515\/dema-1989-0220"},{"key":"ref37","doi-asserted-by":"publisher","DOI":"10.1109\/LCOMM.2017.2689770"},{"key":"ref38","doi-asserted-by":"publisher","DOI":"10.2307\/1426390"},{"key":"ref39","doi-asserted-by":"publisher","DOI":"10.1007\/BF01180430"},{"key":"ref40","first-page":"205","article-title":"The stability problem for a theorem of Cram\u00e9r","volume":"1","author":"Sapogov","year":"1951","journal-title":"Sel. Trans. Math. Staist. Prob."},{"issue":"11","key":"ref41","first-page":"61","article-title":"The problem of stability for a theorem of Cram\u00e9r","volume":"10","author":"Sapogov","year":"1955","journal-title":"Ramer. Vestnik Leningrad Univ. Mat. Meh. Astronom."},{"volume-title":"Th\u00e9orie de l\u2019Addition des Variables Al\u00e9atoires","year":"1937","author":"L\u00e9vy","key":"ref42"},{"issue":"19","key":"ref43","first-page":"1","article-title":"On independent terms of a sum of random variables which is distributed almost normally","volume":"5","author":"Sapogov","year":"1959","journal-title":"Izv. Akad. Nauk SSSR Ser. Mat."},{"key":"ref44","doi-asserted-by":"publisher","DOI":"10.1137\/1113062"},{"issue":"3","key":"ref45","first-page":"83","article-title":"\u03b5-dependence of X\u2081+X\u2082 and X\u2081-X\u2082","volume":"25","author":"Klebanov","year":"1985","journal-title":"Litovskii Matemat. Sbornik"},{"key":"ref46","doi-asserted-by":"publisher","DOI":"10.1137\/1130043"},{"key":"ref47","doi-asserted-by":"publisher","DOI":"10.1007\/BF02432370"},{"key":"ref48","doi-asserted-by":"publisher","DOI":"10.1007\/BF01091625"},{"key":"ref49","doi-asserted-by":"publisher","DOI":"10.1515\/9783110935981"},{"key":"ref50","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511921889"},{"volume-title":"Expansions of Probability Laws","year":"1960","author":"Linnik","key":"ref51"},{"key":"ref52","doi-asserted-by":"publisher","DOI":"10.1007\/BF01676137"},{"key":"ref53","first-page":"60","article-title":"Stability of the characterization of the normal law by properties of parametric estimates of distribution density","volume-title":"Problems of Stability of Stochastic Models","author":"Klebanov"},{"key":"ref54","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-6313-5"},{"key":"ref55","doi-asserted-by":"publisher","DOI":"10.1063\/1.3034123"},{"key":"ref56","doi-asserted-by":"publisher","DOI":"10.1017\/9781108241267.002"},{"key":"ref57","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2007.894680"},{"issue":"5","key":"ref58","first-page":"153","article-title":"On the stability of the quadratic functional equation on a restricted domain","volume":"121","author":"Skof","year":"1987","journal-title":"Atti Accad. Sci. Turin Cl. Sci. Fis. Mat. Nature"},{"key":"ref59","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-1790-9"},{"key":"ref60","doi-asserted-by":"publisher","DOI":"10.1007\/s00010-016-0463-6"},{"key":"ref61","doi-asserted-by":"publisher","DOI":"10.1007\/BF01444119"},{"volume-title":"Applied Digital Information Theory I","year":"1998","author":"Massey","key":"ref62"},{"key":"ref63","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9781139030687"}],"container-title":["IEEE Transactions on Information Theory"],"original-title":[],"link":[{"URL":"http:\/\/xplorestaging.ieee.org\/ielx7\/18\/10253618\/10176134.pdf?arnumber=10176134","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,3,14]],"date-time":"2024-03-14T03:53:53Z","timestamp":1710388433000},"score":1,"resource":{"primary":{"URL":"https:\/\/ieeexplore.ieee.org\/document\/10176134\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,10]]},"references-count":63,"journal-issue":{"issue":"10"},"URL":"https:\/\/doi.org\/10.1109\/tit.2023.3293311","relation":{},"ISSN":["0018-9448","1557-9654"],"issn-type":[{"type":"print","value":"0018-9448"},{"type":"electronic","value":"1557-9654"}],"subject":[],"published":{"date-parts":[[2023,10]]}}}