{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,2]],"date-time":"2026-05-02T22:32:57Z","timestamp":1777761177254,"version":"3.51.4"},"reference-count":205,"publisher":"Emerald","issue":"2","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2022,4,28]]},"abstract":"<jats:p>Common information is ubiquitous in information theory and related areas such as theoretical computer science and discrete probability. However, because there are multiple notions of common information, a unified understanding of the deep interconnections between them is lacking. This monograph seeks to fill this gap by leveraging a small set of mathematical techniques that are applicable across seemingly disparate problems.<\/jats:p>\n                  <jats:p>In Part I, we review the operational tasks and properties associated with Wyner\u2019s and G\u00e1cs\u2013K\u00f6rner\u2013Witsenhausen\u2019s (GKW\u2019s) common information. In Part II, we discuss extensions of the former from the perspective of distributed source simulation. This includes the R\u00e8nyi common information which forms a bridge between Wyner\u2019s common information and the exact common information. Via a surprising equivalence between the R\u00e8nyi common information of order \u221e and the exact common information, we demonstrate the existence of a joint source in which the exact common information strictly exceeds Wyner\u2019s common information. Other closely related topics discussed in Part II include the channel synthesis problem and the connection of Wyner\u2019s and exact common information to the nonnegative rank of matrices.<\/jats:p>\n                  <jats:p>In Part III, recognizing that GKW\u2019s common information is zero for most non-degenerate sources, we examine it with a more refined lens via the Non-Interactive Correlation Distillation (NICD) problem in which we quantify the agreement probability of extracted bits from a bivariate source. We extend this to the noise stability problem which includes as special cases the k-user NICD and q-stability problems. This allows us to seamlessly transition to discussing their connections to various conjectures in information theory and discrete probability, such as the Courtade\u2013Kumar, Li\u2013M\u00e8dard and Mossell\u2013O\u2019Donnell conjectures. Finally, we consider functional inequalities (e.g., the hypercontractivity and Brascamp\u2013Lieb inequalities), which constitute a further generalization of the noise stability problem in which the Boolean functions therein are replaced by nonnnegative functions. We demonstrate that the key ideas behind the proofs in Part III can be presented in a pedagogically coherent manner and unified via information-theoretic and Fourier-analytic methods.<\/jats:p>","DOI":"10.1561\/0100000122","type":"journal-article","created":{"date-parts":[[2022,4,28]],"date-time":"2022-04-28T03:26:26Z","timestamp":1651116386000},"page":"107-389","source":"Crossref","is-referenced-by-count":24,"title":["Common Information, Noise Stability, and Their Extensions"],"prefix":"10.1108","volume":"19","author":[{"given":"Lei","family":"Yu","sequence":"first","affiliation":[{"name":"Nankai University School of Statistics and Data Science, LPMC, KLMDASR, and LEBPS, ,","place":["China"]}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Vincent Y. F.","family":"Tan","sequence":"additional","affiliation":[{"name":"National University of Singapore Department of Mathematics, Department of Electrical and Computer Engineering, Institute of Operations Research and Analytics, ,","place":["Singapore"]}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"140","published-online":{"date-parts":[[2022,4,28]]},"reference":[{"key":"2026032712181594700_ref001","first-page":"925","article-title":"Spreading of sets in product spaces and hypercontraction of the Markov operator","author":"Ahlswede","year":"1976","journal-title":"Annals of Probability"},{"key":"2026032712181594700_ref002","first-page":"664","volume-title":"General Theory of Information Transfer and Combinatorics","author":"Ahlswede","year":"-"},{"issue":"8","key":"2026032712181594700_ref003","doi-asserted-by":"crossref","first-page":"4417","DOI":"10.1109\/TIT.2014.2323418","article-title":"Moderate deviations in channel coding","volume":"60","author":"Altu\u011f","year":"2014","journal-title":"IEEE Transactions on Information Theory"},{"issue":"11","key":"2026032712181594700_ref004","doi-asserted-by":"crossref","first-page":"6979","DOI":"10.1109\/TIT.2018.2861013","article-title":"A variational characterization of R\u00e9nyi divergences","volume":"64","author":"Anantharam","year":"2018","journal-title":"IEEE Transactions on Information Theory"},{"key":"2026032712181594700_ref005","first-page":"3022","article-title":"On hyper- contractivity and a data processing inequality","author":"Anantharam","year":"2014"},{"key":"2026032712181594700_ref006","volume":"10","author":"An\u00e9","year":"2000","journal-title":"Sur les in\u00e9galit\u00e9s de Sobolev logarithmiques"},{"key":"2026032712181594700_ref007","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/BFb0073871","volume-title":"Lectures on Probability Theory","author":"Bakry","year":"1994"},{"key":"2026032712181594700_ref008","first-page":"91","article-title":"Functional inequalities for Markov semigroups","author":"Bakry","year":"2004","journal-title":"Probability Measures on Groups"},{"key":"2026032712181594700_ref009","volume":"348","author":"Bakry","year":"2013","journal-title":"Analysis and Geometry of Markov Diffusion Operators"},{"issue":"2","key":"2026032712181594700_ref010","doi-asserted-by":"crossref","first-page":"259","DOI":"10.1007\/s002220050026","article-title":"L\u00e9vy\u2013Gromov\u2019s isoperimetric inequality for an infinite dimensional diffusion generator","volume":"123","author":"Bakry","year":"1996","journal-title":"Inventiones Mathematicae"},{"key":"2026032712181594700_ref011","first-page":"2205","article-title":"The Courtade\u2013Kumar most informative Boolean function conjecture and a symmetrized Li\u2013M\u00e9dard conjecture are equivalent","author":"Barnes","year":"2020"},{"issue":"2","key":"2026032712181594700_ref012","doi-asserted-by":"crossref","first-page":"335","DOI":"10.1007\/s002220050267","article-title":"On a reverse form of the Brascamp\u2013Lieb inequality","volume":"134","author":"Barthe","year":"1998","journal-title":"Inventiones Mathematicae"},{"issue":"12","key":"2026032712181594700_ref013","doi-asserted-by":"crossref","first-page":"2330","DOI":"10.1016\/j.laa.2009.02.034","article-title":"Real rank versus nonnegative rank","volume":"431","author":"Beasley","year":"2009","journal-title":"Linear Algebra and its Applications"},{"issue":"12","key":"2026032712181594700_ref014","doi-asserted-by":"crossref","first-page":"7980","DOI":"10.1109\/TIT.2014.2361632","article-title":"Quantum achievability proof via collision relative entropy","volume":"60","author":"Beigi","year":"2014","journal-title":"IEEE Transactions on Information Theory"},{"issue":"4","key":"2026032712181594700_ref015","doi-asserted-by":"crossref","first-page":"2193","DOI":"10.1109\/TIT.2018.2806965","article-title":"\u03a6-entropic measures of correlation","volume":"64","author":"Beigi","year":"2018","journal-title":"IEEE Transactions on Information Theory"},{"key":"2026032712181594700_ref016","first-page":"1038","article-title":"Equivalent characterization of reverse Brascamp\u2013Lieb-type inequalities using information measures","author":"Beigi","year":"2016"},{"issue":"3","key":"2026032712181594700_ref017","doi-asserted-by":"crossref","first-page":"2926","DOI":"10.1109\/TIT.2014.2309968","article-title":"The quantum reverse Shannon theorem and resource tradeoffs for simulating quantum channels","volume":"60","author":"Bennett","year":"2014","journal-title":"IEEE Transactions on Information Theory"},{"issue":"10","key":"2026032712181594700_ref018","doi-asserted-by":"crossref","first-page":"2637","DOI":"10.1109\/TIT.2002.802612","article-title":"Entanglement-assisted capacity of a quantum channel and the reverse Shannon theorem","volume":"48","author":"Bennett","year":"2002","journal-title":"IEEE Transactions on Information Theory"},{"issue":"1","key":"2026032712181594700_ref019","doi-asserted-by":"crossref","first-page":"122","DOI":"10.1090\/S0002-9947-1941-0003498-3","article-title":"The accuracy of the Gaussian approximation to the sum of independent variates","volume":"49","author":"Berry","year":"1941","journal-title":"Transactions of the American Mathematical Society"},{"issue":"3","key":"2026032712181594700_ref020","doi-asserted-by":"crossref","first-page":"316","DOI":"10.3390\/e22030316","article-title":"Conditional R\u00e9nyi divergences and horse betting","volume":"22","author":"Bleuler","year":"2020","journal-title":"Entropy"},{"key":"2026032712181594700_ref021","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9780511977985","volume-title":"Physical-Layer Security: From Information Theory to Security Engineering","author":"Bloch","year":"2011"},{"issue":"12","key":"2026032712181594700_ref022","doi-asserted-by":"crossref","first-page":"8077","DOI":"10.1109\/TIT.2013.2283722","article-title":"Strong secrecy from channel resolvability","volume":"59","author":"Bloch","year":"2013","journal-title":"IEEE Transactions on Information Theory"},{"issue":"1","key":"2026032712181594700_ref023","doi-asserted-by":"crossref","first-page":"270","DOI":"10.1214\/18-AOP1261","article-title":"R\u00e9nyi divergence and the central limit theorem","volume":"47","author":"Bobkov","year":"2019","journal-title":"Annals of Probability"},{"issue":"10","key":"2026032712181594700_ref024","doi-asserted-by":"crossref","first-page":"6351","DOI":"10.1109\/TIT.2011.2134067","article-title":"On extracting common random bits from correlated sources","volume":"57","author":"Bogdanov","year":"2011","journal-title":"IEEE Transactions on Information Theory"},{"key":"2026032712181594700_ref025","doi-asserted-by":"crossref","first-page":"193","DOI":"10.5802\/aif.297","article-title":"Ensembles \u039b(p) dans le dual de D\u221e","volume":"18","author":"Bonami","year":"1968","journal-title":"Annales de l\u2019institut Fourier"},{"key":"2026032712181594700_ref026","doi-asserted-by":"crossref","first-page":"335","DOI":"10.5802\/aif.357","article-title":"\u00c9tude des coefficients de Fourier des fonctions de Lp(G)","volume":"20","author":"Bonami","year":"1970","journal-title":"Annales de l\u2019institut Fourier"},{"issue":"3","key":"2026032712181594700_ref027","doi-asserted-by":"crossref","first-page":"225","DOI":"10.1007\/BF01318906","article-title":"Positivity improving operators and hypercontractiv- ity","volume":"180","author":"Borell","year":"1982","journal-title":"Mathematische Zeitschrift"},{"issue":"1","key":"2026032712181594700_ref028","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/BF00532234","article-title":"Geometric bounds on the Ornstein\u2013Uhlenbeck velocity process","volume":"70","author":"Borell","year":"1985","journal-title":"Probability Theory and Related Fields"},{"issue":"2","key":"2026032712181594700_ref029","doi-asserted-by":"crossref","first-page":"151","DOI":"10.1016\/0001-8708(76)90184-5","article-title":"Best constants in Young\u2019s inequality, its converse, and its generalization to more than three functions","volume":"20","author":"Brascamp","year":"1976","journal-title":"Advances in Mathematics"},{"key":"2026032712181594700_ref030","doi-asserted-by":"crossref","first-page":"147","DOI":"10.1007\/s00037-016-0125-z","article-title":"Information-theoretic approximations of the nonnegative rank","volume":"26","author":"Braun","year":"2017","journal-title":"Computational Complexity"},{"key":"2026032712181594700_ref031","first-page":"688","article-title":"Common information and unique disjointness","author":"Braun","year":"2013"},{"issue":"961","key":"2026032712181594700_ref032","article-title":"Conditional R\u00e9nyi divergence saddlepoint and the maximization of \u03b1-mutual information","volume":"21","author":"Cai","year":"2019","journal-title":"Entropy"},{"issue":"2","key":"2026032712181594700_ref033","doi-asserted-by":"crossref","first-page":"373","DOI":"10.1007\/s00039-009-0001-y","article-title":"Subadditivity of the entropy and its relation to Brascamp\u2013Lieb type inequalities","volume":"19","author":"Carlen","year":"2009","journal-title":"Geometric and Functional Analysis"},{"issue":"5","key":"2026032712181594700_ref034","doi-asserted-by":"crossref","first-page":"1299","DOI":"10.1137\/120861072","article-title":"An optimal lower bound on the communication complexity of gap-Hamming-distance","volume":"41","author":"Chakrabarti","year":"2012","journal-title":"SIAM Journal on Computing"},{"issue":"3","key":"2026032712181594700_ref035","doi-asserted-by":"crossref","first-page":"399","DOI":"10.1215\/S0012-7094-02-11331-3","article-title":"A polynomial bound in Freiman\u2019s theorem","volume":"113","author":"Chang","year":"2002","journal-title":"Duke Mathematical Journal"},{"key":"2026032712181594700_ref036","doi-asserted-by":"crossref","DOI":"10.1002\/9780470747278","volume-title":"Nonnegative Matrix and Tensor Factorizations: Applications to Exploratory Multi-way Data Analysis and Blind Source Separation","author":"Cichocki","year":"2009"},{"key":"2026032712181594700_ref037","doi-asserted-by":"crossref","DOI":"10.1007\/978-0-387-87859-1","volume":"261","author":"\u00c7\u0131nlar","year":"2011","journal-title":"Probability and Stochastics"},{"issue":"1","key":"2026032712181594700_ref038","doi-asserted-by":"crossref","first-page":"149","DOI":"10.1016\/0024-3795(93)90224-C","article-title":"Nonnegative ranks, decompositions, and factorizations of nonnegative matrices","volume":"190","author":"Cohen","year":"1993","journal-title":"Linear Algebra and its Applications"},{"key":"2026032712181594700_ref039","volume-title":"Introduction to Algorithms","author":"Cormen","year":"2003","edition":"2"},{"issue":"8","key":"2026032712181594700_ref040","doi-asserted-by":"crossref","first-page":"4515","DOI":"10.1109\/TIT.2014.2326877","article-title":"Which Boolean functions maximize mutual information on noisy inputs?","volume":"60","author":"Courtade","year":"2014","journal-title":"IEEE Transactions on Information Theory"},{"issue":"3","key":"2026032712181594700_ref041","doi-asserted-by":"crossref","first-page":"226","DOI":"10.1109\/TIT.1975.1055356","article-title":"A proof of the data compression theorem of Slepian and Wolf for ergodic sources","volume":"21","author":"Cover","year":"1975","journal-title":"IEEE Transactions on Information Theory"},{"key":"2026032712181594700_ref042","volume-title":"Elements of Information Theory","author":"Cover","year":"2006","edition":"2"},{"issue":"1","key":"2026032712181594700_ref043","doi-asserted-by":"crossref","first-page":"26","DOI":"10.1109\/18.370121","article-title":"Generalized cutoff rates and R\u00e9nyi\u2019s information measures","volume":"41","author":"Csisz\u00e1r","year":"1995","journal-title":"IEEE Transactions on Information Theory"},{"issue":"3","key":"2026032712181594700_ref044","doi-asserted-by":"crossref","first-page":"339","DOI":"10.1109\/TIT.1978.1055892","article-title":"Broadcast channels with confidential messages","volume":"24","author":"Csisz\u00e1r","year":"1978","journal-title":"IEEE Transactions on Information Theory"},{"key":"2026032712181594700_ref045","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9780511921889","volume-title":"Information Theory: Coding Theorems for Discrete Memoryless Systems","author":"Csisz\u00e1r","year":"2011"},{"issue":"2","key":"2026032712181594700_ref046","doi-asserted-by":"crossref","first-page":"344","DOI":"10.1109\/18.825796","article-title":"Common randomness and secret key generation with a helper","volume":"46","author":"Csisz\u00e1r","year":"2000","journal-title":"IEEE Transactions on Information Theory"},{"issue":"8","key":"2026032712181594700_ref047","doi-asserted-by":"crossref","first-page":"5509","DOI":"10.1109\/TIT.2011.2159047","article-title":"Zero-error channel capacity and simulation assisted by non-local correlations","volume":"57","author":"Cubitt","year":"2011","journal-title":"IEEE Transactions on Information Theory"},{"key":"2026032712181594700_ref048","doi-asserted-by":"crossref","unstructured":"P.\n              Cuff\n            \n          , \u201cDistributed channel synthesis,\u201d IEEE Transactions on Information Theory, vol. 59, no. 11, 2013, pp. 7071\u20137096.","DOI":"10.1109\/TIT.2013.2279330"},{"key":"2026032712181594700_ref049","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4612-5320-4","volume-title":"Large Deviations Techniques and Applications","author":"Dembo","year":"1998","edition":"2"},{"key":"2026032712181594700_ref050","first-page":"1","volume-title":"Theory of Cryptography","author":"Dodis","year":"2013"},{"key":"2026032712181594700_ref051","volume-title":"Network Information Theory","author":"El Gamal","year":"2012"},{"issue":"2","key":"2026032712181594700_ref052","doi-asserted-by":"crossref","first-page":"561","DOI":"10.1007\/s00222-014-0556-6","article-title":"A two-sided estimate for the Gaussian noise stability deficit","volume":"201","author":"Eldan","year":"2015","journal-title":"Inventiones Mathematicae"},{"key":"2026032712181594700_ref053","author":"Erkip","year":"1996"},{"issue":"1","key":"2026032712181594700_ref054","first-page":"1","article-title":"On the Liapunoff limit of error in the theory of probability,","volume":"A28","author":"Esseen","year":"1942","journal-title":"Arkiv F\u00f6r Matematik, Astronomi och Fysik"},{"issue":"1","key":"2026032712181594700_ref055","doi-asserted-by":"crossref","first-page":"133","DOI":"10.1007\/s10107-015-0922-1","article-title":"On the nonnegative rank of distance matrices","volume":"153","author":"Fawzi","year":"2015","journal-title":"Mathematical Programming"},{"issue":"1","key":"2026032712181594700_ref056","doi-asserted-by":"crossref","first-page":"41","DOI":"10.1007\/s10107-014-0837-2","article-title":"Lower bounds on nonnegative rank via nonnegative nuclear norms","volume":"153","author":"Fawzi","year":"2015","journal-title":"Mathematical Programming Series B"},{"issue":"1","key":"2026032712181594700_ref057","doi-asserted-by":"crossref","first-page":"228","DOI":"10.1007\/BF01504345","article-title":"\u00dcber die verteilung der wurzeln bei gewissen alge- braischen gleichungen mit ganzzahligen koeffizienten","volume":"17","author":"Fekete","year":"1923","journal-title":"Mathe- matische Zeitschrift"},{"key":"2026032712181594700_ref058","article-title":"Real analysis in computer science: A collection of open problems","author":"Filmus","year":"2014","journal-title":"Preprint"},{"issue":"3","key":"2026032712181594700_ref059","doi-asserted-by":"crossref","first-page":"263","DOI":"10.1016\/S0166-218X(00)00284-5","article-title":"On the minimum average distance of binary codes: Linear programming approach","volume":"111","author":"Fu","year":"2001","journal-title":"Discrete Applied Mathematics"},{"issue":"2","key":"2026032712181594700_ref060","first-page":"149","article-title":"Common information is far less than mutual information","volume":"2","author":"G\u00e1cs","year":"1973","journal-title":"Problems of Control and Information Theory"},{"key":"2026032712181594700_ref061","volume-title":"Stochastic Processes: Theory for Applications","author":"Gallager","year":"2014"},{"key":"2026032712181594700_ref062","first-page":"1","article-title":"Relaxed Wyner\u2019s common information","author":"Gastpar","year":"2019"},{"issue":"6","key":"2026032712181594700_ref063","doi-asserted-by":"crossref","first-page":"364","DOI":"10.1002\/zamm.19410210604","article-title":"Das statistische problem der korrelation als varia- tions-und eigenwertproblem und sein zusammenhang mit der ausgleichsrechnung,","volume":"21","author":"Gebelein","year":"1941","journal-title":"ZAMM-Journal of Applied Mathematics and Mechanics\/Zeitschrift f\u00fcr Angewandte Mathematik und Mechanik"},{"issue":"11","key":"2026032712181594700_ref064","doi-asserted-by":"crossref","first-page":"5377","DOI":"10.1109\/TIT.2010.2068710","article-title":"On Pinsker\u2019s and Vajda\u2019s type inequalities for Csisz\u00e1r\u2019s f -divergences","volume":"56","author":"Gilardoni","year":"2010","journal-title":"IEEE Transactions on Information Theory"},{"key":"2026032712181594700_ref065","doi-asserted-by":"crossref","DOI":"10.1137\/1.9781611976410","author":"Gillis","year":"2020","journal-title":"Nonnegative Matrix Factorization"},{"key":"2026032712181594700_ref066","first-page":"2207","article-title":"Gray\u2013Wyner and Slepian\u2013Wolf guessing","author":"Graczyk","year":"2020"},{"key":"2026032712181594700_ref067","article-title":"Conditional and relevant common information","volume":"iaab021","author":"Graczyk","year":"2022","journal-title":"Information and Inference: A Journal of the IMA"},{"key":"2026032712181594700_ref068","doi-asserted-by":"crossref","first-page":"1681","DOI":"10.1002\/j.1538-7305.1974.tb02812.x","article-title":"Source coding for a simple network","volume":"53","author":"Gray","year":"1974","journal-title":"The Bell Systems Technical Journal"},{"issue":"4","key":"2026032712181594700_ref069","doi-asserted-by":"crossref","first-page":"1061","DOI":"10.2307\/2373688","article-title":"Logarithmic Sobolev inequalities","volume":"97","author":"Gross","year":"1975","journal-title":"American Journal of Mathematics"},{"issue":"5","key":"2026032712181594700_ref070","first-page":"2659","article-title":"Channel simulation via interactive communications","volume":"63","author":"Haddadpour","year":"2017","journal-title":"IEEE Transactions on Information Theory"},{"key":"2026032712181594700_ref071","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-662-12066-8","volume-title":"Information-Spectrum Methods in Information Theory","author":"Han","year":"2003"},{"issue":"4","key":"2026032712181594700_ref072","first-page":"1217","article-title":"Weak variable-length source coding","volume":"46","author":"Han","year":"2006","journal-title":"IEEE Transactions on Information Theory"},{"issue":"3","key":"2026032712181594700_ref073","doi-asserted-by":"crossref","first-page":"752","DOI":"10.1109\/18.256486","article-title":"Approximation theory of output statistics","volume":"39","author":"Han","year":"1993","journal-title":"IEEE Transactions on Information Theory"},{"issue":"1","key":"2026032712181594700_ref074","doi-asserted-by":"crossref","first-page":"131","DOI":"10.1137\/0112012","article-title":"Optimal assignments of numbers to vertices","volume":"12","author":"Harper","year":"1964","journal-title":"Journal of the Society for Industrial and Applied Mathematics"},{"issue":"1","key":"2026032712181594700_ref075","doi-asserted-by":"crossref","first-page":"438","DOI":"10.1109\/TIT.2009.2034824","article-title":"The communication complexity of correlation","volume":"56","author":"Harsha","year":"2010","journal-title":"IEEE Transactions on Information Theory"},{"issue":"4","key":"2026032712181594700_ref076","doi-asserted-by":"crossref","first-page":"1562","DOI":"10.1109\/TIT.2006.871040","article-title":"General nonasymptotic and asymptotic formulas in channel resolvability and identification capacity and their application to the wiretap channel","volume":"52","author":"Hayashi","year":"2006","journal-title":"IEEE Transactions on Information Theory"},{"issue":"10","key":"2026032712181594700_ref077","doi-asserted-by":"crossref","first-page":"4619","DOI":"10.1109\/TIT.2008.928985","article-title":"Second-order asymptotics in fixed-length source coding and intrinsic randomness","volume":"54","author":"Hayashi","year":"2008","journal-title":"IEEE Transactions on Information Theory"},{"issue":"11","key":"2026032712181594700_ref078","doi-asserted-by":"crossref","first-page":"4947","DOI":"10.1109\/TIT.2009.2030478","article-title":"Information spectrum approach to second-order coding rate in channel coding","volume":"55","author":"Hayashi","year":"2009","journal-title":"IEEE Transactions on Information Theory"},{"issue":"6","key":"2026032712181594700_ref079","doi-asserted-by":"crossref","first-page":"3989","DOI":"10.1109\/TIT.2011.2110950","article-title":"Exponential decreasing rate of leaked information in universal random privacy amplification","volume":"57","author":"Hayashi","year":"2011","journal-title":"IEEE Transactions on Information Theory"},{"issue":"7","key":"2026032712181594700_ref080","doi-asserted-by":"crossref","first-page":"1753","DOI":"10.1109\/TIT.2003.813556","article-title":"General formulas for capacity of classical-quantum channels","volume":"49","author":"Hayashi","year":"2003","journal-title":"IEEE Transactions on Information Theory"},{"issue":"2","key":"2026032712181594700_ref081","doi-asserted-by":"crossref","first-page":"975","DOI":"10.1109\/TIT.2016.2636154","article-title":"Equivocations, exponents and second-order coding rates under various R\u00e9nyi information measures","volume":"63","author":"Hayashi","year":"2017","journal-title":"IEEE Transactions on Information Theory"},{"issue":"71","key":"2026032712181594700_ref082","first-page":"1","article-title":"Euclidean partitions optimizing noise stability","volume":"19","author":"Heilman","year":"2014","journal-title":"Electronic Journal of Probability"},{"issue":"4","key":"2026032712181594700_ref083","doi-asserted-by":"crossref","first-page":"2192","DOI":"10.1007\/s10959-020-01031-y","article-title":"Low correlation noise stability of symmetric sets","volume":"34","author":"Heilman","year":"2021","journal-title":"Journal of Theoretical Probability"},{"key":"2026032712181594700_ref084","doi-asserted-by":"crossref","first-page":"520","DOI":"10.1017\/S0305004100013517","article-title":"A connection between correlation and contingency","volume":"31","author":"Hirschfeld","year":"1935","journal-title":"Mathematical Proceedings of the Cambridge Philosophical Society"},{"key":"2026032712181594700_ref085","doi-asserted-by":"crossref","first-page":"457","DOI":"10.1016\/j.ipl.2012.02.009","article-title":"On the nonnegative rank of distance matrices","volume":"112","author":"Hrube\u0161","year":"2012","journal-title":"Information Processing Letters"},{"key":"2026032712181594700_ref086","first-page":"1098","article-title":"A method for the construction of minimumredundancy codes","author":"Huffman","year":"1952"},{"issue":"1","key":"2026032712181594700_ref087","doi-asserted-by":"crossref","first-page":"347","DOI":"10.1007\/s11856-011-0181-7","article-title":"Maximally stable Gaussian partitions with discrete applications","volume":"189","author":"Isaksson","year":"2012","journal-title":"Israel Journal of Mathematics"},{"key":"2026032712181594700_ref088","first-page":"103","article-title":"Information theoretic security for encryption based on conditional R\u00e9nyi entropies","author":"Iwamoto","year":"2013"},{"issue":"8","key":"2026032712181594700_ref089","doi-asserted-by":"crossref","first-page":"5171","DOI":"10.1109\/TIT.2013.2258372","article-title":"Efficient protocols for generating bipartite classical distributions and quantum states","volume":"59","author":"Jain","year":"2013","journal-title":"IEEE Transactions on Information Theory"},{"key":"2026032712181594700_ref090","first-page":"68","article-title":"The influence of variables on Boolean functions","author":"Kahn","year":"1988"},{"issue":"5","key":"2026032712181594700_ref091","doi-asserted-by":"crossref","first-page":"1467","DOI":"10.1109\/18.412711","article-title":"On the distance distribution of codes","volume":"41","author":"Kalai","year":"1995","journal-title":"IEEE Transactions on Information Theory"},{"key":"2026032712181594700_ref092","first-page":"627","article-title":"Reverse hypercontractivity using information measures","author":"Kamath","year":"2015"},{"key":"2026032712181594700_ref093","first-page":"1340","article-title":"A new dual to the G\u00e1cs-K\u00f6rner common information defined via the Gray-Wyner system","author":"Kamath","year":"2010"},{"issue":"6","key":"2026032712181594700_ref094","doi-asserted-by":"crossref","first-page":"3419","DOI":"10.1109\/TIT.2016.2553672","article-title":"On non-interactive simulation of joint distributions","volume":"62","author":"Kamath","year":"2016","journal-title":"IEEE Transactions on Information Theory"},{"key":"2026032712181594700_ref095","author":"Kiener","year":"1969"},{"key":"2026032712181594700_ref096","volume-title":"Remarks on the most informative function conjecture at fixed mean","author":"Kindler","year":"2015"},{"issue":"6","key":"2026032712181594700_ref097","doi-asserted-by":"crossref","first-page":"3509","DOI":"10.1109\/TIT.2021.3071597","article-title":"A moment ratio bound for polynomials and some extremal properties of Krawchouk polynomials and Hamming spheres","volume":"67","author":"Kirshner","year":"2021","journal-title":"IEEE Transactions on Information Theory"},{"issue":"4","key":"2026032712181594700_ref098","doi-asserted-by":"crossref","first-page":"1546","DOI":"10.1109\/TIT.2005.844098","article-title":"Asymptotic properties on codeword lengths of an optimal FV code for general sources","volume":"51","author":"Koga","year":"2005","journal-title":"IEEE Transactions on Information Theory"},{"key":"2026032712181594700_ref099","first-page":"411","article-title":"Coding of an information source having ambiguous alphabet and the entropy of graphs","author":"K\u00f6rner","year":"1973"},{"issue":"9","key":"2026032712181594700_ref100","doi-asserted-by":"crossref","first-page":"4316","DOI":"10.1109\/TIT.2015.2438831","article-title":"Variable-length compression allowing errors","volume":"61","author":"Kostina","year":"2015","journal-title":"IEEE Transactions on Information Theory"},{"key":"2026032712181594700_ref101","unstructured":"L. G.\n              Kraft\n            \n          , \u201cA device for quantizing, grouping, and coding amplitude modulated pulses,\u201d M.S. thesis, Department of Electrical Engineering, Massachusetts Institute of Technology, Cambridge, MA, 1949."},{"key":"2026032712181594700_ref102","first-page":"226","article-title":"Which Boolean functions are most informative?","author":"Kumar","year":"2013"},{"key":"2026032712181594700_ref103","first-page":"161","article-title":"Exact common information","author":"Kumar","year":"2014"},{"key":"2026032712181594700_ref104","volume-title":"Th\u00e9orie des \u00c9quations Num\u00e9riques","author":"Laguerre","year":"1884"},{"key":"2026032712181594700_ref105","volume":"1709","author":"Ledoux","year":"2006","journal-title":"Concentration of Measure and Logarithmic Sobolev Inequalities"},{"key":"2026032712181594700_ref106","doi-asserted-by":"crossref","first-page":"788","DOI":"10.1038\/44565","article-title":"Learning the parts of objects with nonnegative matrix factorization","volume":"401","author":"Lee","year":"1999","journal-title":"Nature"},{"issue":"10","key":"2026032712181594700_ref107","doi-asserted-by":"crossref","first-page":"6329","DOI":"10.1109\/TIT.2017.2735438","article-title":"Distributed simulation of continuous random variables","volume":"63","author":"Li","year":"2017","journal-title":"IEEE Transactions on Information Theory"},{"issue":"8","key":"2026032712181594700_ref108","doi-asserted-by":"crossref","first-page":"5862","DOI":"10.1109\/TIT.2017.2787182","article-title":"Extended Gray\u2013Wyner system with complementary causal side information","volume":"64","author":"Li","year":"2017","journal-title":"IEEE Transactions on Information Theory"},{"issue":"11","key":"2026032712181594700_ref109","doi-asserted-by":"crossref","first-page":"6967","DOI":"10.1109\/TIT.2018.2865570","article-title":"Strong functional representation lemma and applications to coding theorems","volume":"64","author":"Li","year":"2018","journal-title":"IEEE Transactions on Information Theory"},{"issue":"2","key":"2026032712181594700_ref110","doi-asserted-by":"crossref","first-page":"778","DOI":"10.1109\/TIT.2020.3041028","article-title":"Boolean functions: Noise stability, noninteractive correlation distillation, and mutual information","volume":"67","author":"Li","year":"2021","journal-title":"IEEE Transactions on Information Theory"},{"issue":"4-5","key":"2026032712181594700_ref111","doi-asserted-by":"publisher","first-page":"355","DOI":"10.1561\/0100000036","article-title":"Information theoretic security","volume":"5","author":"Liang","year":"2019","journal-title":"Foundations and Trends\u00ae in Communications and Information Theory"},{"key":"2026032712181594700_ref112","author":"Liu","year":"2018"},{"key":"2026032712181594700_ref113","first-page":"1048","article-title":"Brascamp\u2013Lieb inequality and its reverse: An information theoretic view","author":"Liu","year":"2016"},{"key":"2026032712181594700_ref114","first-page":"836","article-title":"The common information of N dependent random variables,","author":"Liu","year":"2010"},{"issue":"5","key":"2026032712181594700_ref115","doi-asserted-by":"crossref","first-page":"2856","DOI":"10.1109\/TIT.2014.2306938","article-title":"Fundamental limits of caching","volume":"60","author":"Maddah-Ali","year":"2014","journal-title":"IEEE Transactions on Information Theory"},{"key":"2026032712181594700_ref116","first-page":"501","article-title":"From the information bottleneck to the privacy funnel","author":"Makhdoumi","year":"2014"},{"key":"2026032712181594700_ref117","first-page":"351","article-title":"Information-theoretic key agreement: From weak to strong secrecy for free","author":"Maurer","year":"2000","journal-title":"Advances in Cryptology (EUROCRYPT)"},{"issue":"1","key":"2026032712181594700_ref118","doi-asserted-by":"crossref","first-page":"156","DOI":"10.1137\/140990139","article-title":"An almost optimal algorithm for computing nonnegative rank","volume":"45","author":"Moitra","year":"2016","journal-title":"SIAM Journal of Computing"},{"key":"2026032712181594700_ref119","volume-title":"Mixing in product spaces","author":"Mossel","year":"2017"},{"key":"2026032712181594700_ref120","doi-asserted-by":"crossref","DOI":"10.1090\/bull\/1751","article-title":"Probabilistic view of voting, paradoxes, and manipulation,","author":"Mossel","year":"2021","journal-title":"Bul l. Amer. Math. Soc."},{"issue":"2","key":"2026032712181594700_ref121","doi-asserted-by":"crossref","first-page":"433","DOI":"10.4171\/jems\/507","article-title":"Robust optimality of Gaussian noise stability","volume":"17","author":"Mossel","year":"2015","journal-title":"Journal of the European Mathematical Society"},{"issue":"4","key":"2026032712181594700_ref122","doi-asserted-by":"crossref","first-page":"418","DOI":"10.1002\/rsa.20062","article-title":"Coin flipping from a cosmic source: On error correction of truly random bits","volume":"26","author":"Mossel","year":"2005","journal-title":"Random Structures & Algorithms"},{"issue":"1","key":"2026032712181594700_ref123","doi-asserted-by":"crossref","first-page":"295","DOI":"10.4007\/annals.2010.171.295","article-title":"Noise stability of functions with low influences: Invariance and optimality","volume":"171","author":"Mossel","year":"2010","journal-title":"Annals of Mathematics"},{"issue":"1","key":"2026032712181594700_ref124","doi-asserted-by":"crossref","first-page":"299","DOI":"10.1007\/BF02773611","article-title":"Non-interactive correlation distillation, inhomogeneous Markov chains, and the reverse Bonami-Beckner inequality","volume":"154","author":"Mossel","year":"2006","journal-title":"Israel Journal of Mathematics"},{"issue":"3","key":"2026032712181594700_ref125","doi-asserted-by":"crossref","first-page":"1062","DOI":"10.1007\/s00039-013-0229-4","article-title":"On reverse hypercon- tractivity","volume":"23","author":"Mossel","year":"2013","journal-title":"Geometric and Functional Analysis"},{"key":"2026032712181594700_ref126","article-title":"Equivalent formulations of hypercontractivity using information measures","author":"Nair","year":"2014"},{"key":"2026032712181594700_ref127","first-page":"570","article-title":"Evaluating hypercontractivity parameters using information measures","author":"Nair","year":"2016"},{"key":"2026032712181594700_ref128","first-page":"938","article-title":"Reverse hypercontractivity region for the binary erasure channel","author":"Nair","year":"2017"},{"key":"2026032712181594700_ref129","author":"Neeman","year":""},{"key":"2026032712181594700_ref130","volume-title":"Open problems in analysis of Boolean functions","author":"O\u2019Donnell","year":"2012"},{"key":"2026032712181594700_ref131","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9781139814782","volume-title":"Analysis of Boolean Functions","author":"O\u2019Donnell","year":"2014"},{"issue":"5","key":"2026032712181594700_ref132","doi-asserted-by":"crossref","first-page":"352","DOI":"10.3390\/e20050352","article-title":"Exponential strong converse for source coding with side information at the decoder","volume":"20","author":"Oohama","year":"2018","journal-title":"Entropy"},{"issue":"11","key":"2026032712181594700_ref133","doi-asserted-by":"crossref","first-page":"7878","DOI":"10.1109\/TIT.2020.3018232","article-title":"A note on the probability of rectangles for correlated binary strings","volume":"66","author":"Ordentlich","year":"2020","journal-title":"IEEE Transactions on Information Theory"},{"key":"2026032712181594700_ref134","first-page":"500","article-title":"An improved upper bound for the most informative Boolean function conjecture","author":"Ordentlich","year":"2016"},{"issue":"3","key":"2026032712181594700_ref135","doi-asserted-by":"crossref","first-page":"903","DOI":"10.1109\/18.915643","article-title":"Coding for computing","volume":"47","author":"Orlitsky","year":"2001","journal-title":"IEEE Transactions on Information Theory"},{"issue":"5","key":"2026032712181594700_ref136","doi-asserted-by":"crossref","first-page":"3094","DOI":"10.1214\/18-AAP1384","article-title":"Dictator functions maximize mutual information","volume":"28","author":"Pichler","year":"2018","journal-title":"The Annals of Applied Probability"},{"key":"2026032712181594700_ref137","article-title":"Hypercontractivity for sparse functions on the discrete hypercube,","author":"Polyanskiy","year":"2019","journal-title":"Manuscript"},{"issue":"5","key":"2026032712181594700_ref138","doi-asserted-by":"crossref","first-page":"2307","DOI":"10.1109\/TIT.2010.2043769","article-title":"Channel coding rate in the finite blocklength regime","volume":"56","author":"Polyanskiy","year":"2010","journal-title":"IEEE Transactions on Information Theory"},{"issue":"11","key":"2026032712181594700_ref139","doi-asserted-by":"crossref","DOI":"10.1016\/j.jfa.2019.108280","article-title":"Improved log-Sobolev inequalities, hypercontractivity and uncertainty principle on the hypercube","volume":"277","author":"Polyanskiy","year":"2019","journal-title":"Journal of Functional Analysis"},{"key":"2026032712181594700_ref140","first-page":"1334","article-title":"Channel dispersion and moderate deviations limits for memoryless channels","author":"Polyanskiy","year":"2010"},{"key":"2026032712181594700_ref141","volume-title":"Mass Transportation Problems: Theory","author":"Rachev","year":"1998"},{"issue":"6","key":"2026032712181594700_ref142","doi-asserted-by":"crossref","first-page":"3355","DOI":"10.1109\/TIT.2016.2549542","article-title":"Strong data processing inequalities and \u03a6-Sobolev inequalities for discrete channels","volume":"62","author":"Raginsky","year":"2016","journal-title":"IEEE Transactions on Information Theory"},{"issue":"1-2","key":"2026032712181594700_ref143","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1561\/0100000064","article-title":"Concentration of measure inequalities in information theory, communications and coding","volume":"10","author":"Raginsky","year":"2013","journal-title":"Foundations and Trends\u00ae in Communications and Information Theory"},{"issue":"3-4","key":"2026032712181594700_ref144","first-page":"441","article-title":"On measures of dependence","volume":"10","author":"R\u00e9nyi","year":"1959","journal-title":"Acta Mathematica Hungarica"},{"key":"2026032712181594700_ref145","volume":"597","author":"Rudnicki","year":"2002","journal-title":"Markov Semigroups and Their Applications"},{"issue":"12","key":"2026032712181594700_ref146","doi-asserted-by":"crossref","first-page":"7708","DOI":"10.1109\/TIT.2021.3117591","article-title":"Third-order asymptotics of variable-length compression allowing errors","volume":"67","author":"Sakai","year":"2021","journal-title":"IEEE Transactions on Information Theory"},{"key":"2026032712181594700_ref147","first-page":"2234","article-title":"Approximate G\u00e1cs- K\u00f6rner common information","author":"Salamatian","year":"2020"},{"key":"2026032712181594700_ref148","volume-title":"A modified logarithmic Sobolev inequality for the Hamming cube and some applications","author":"Samorodnitsky","year":"2008"},{"issue":"10","key":"2026032712181594700_ref149","doi-asserted-by":"crossref","first-page":"5446","DOI":"10.1109\/TIT.2016.2584625","article-title":"On the entropy of a noisy function","volume":"62","author":"Samorodnitsky","year":"2016","journal-title":"IEEE Transactions on Information Theory"},{"issue":"1","key":"2026032712181594700_ref150","first-page":"11","article-title":"On the probability of large deviations of random variables,","author":"Sanov","year":"1961","journal-title":"Mat. Sbornik"},{"issue":"1","key":"2026032712181594700_ref151","doi-asserted-by":"crossref","first-page":"23","DOI":"10.1109\/TIT.2015.2504100","article-title":"On the R\u00e9nyi divergence, joint range of relative entropies, and a channel coding theorem","volume":"62","author":"Sason","year":"2016","journal-title":"IEEE Transactions on Information Theory"},{"issue":"1","key":"2026032712181594700_ref152","doi-asserted-by":"crossref","first-page":"36","DOI":"10.1007\/BF00534116","article-title":"Fermeture en probabilit\u00e9 de certains sous-espaces d\u2019un espace L2 ,","volume":"14","author":"Schreiber","year":"1969","journal-title":"Zeitschrift f\u00fcr Wahrscheinlichkeitstheorie und Verwandte Gebiete"},{"key":"2026032712181594700_ref153","doi-asserted-by":"crossref","first-page":"379","DOI":"10.1002\/j.1538-7305.1948.tb01338.x","article-title":"A Mathematical Theory of Communication","volume":"27","author":"Shannon","year":"1948","journal-title":"The Bell Systems Technical Journal"},{"key":"2026032712181594700_ref154","first-page":"894","article-title":"On R\u00e9nyi measures and hypothesis testing","author":"Shayevitz","year":"2011"},{"key":"2026032712181594700_ref155","doi-asserted-by":"crossref","first-page":"149","DOI":"10.1007\/BF00537520","article-title":"Information radius","volume":"14","author":"Sibson","year":"1969","journal-title":"Z. Wahrscheinlichkeitstheorie verw. Geb"},{"issue":"4","key":"2026032712181594700_ref156","doi-asserted-by":"crossref","first-page":"471","DOI":"10.1109\/TIT.1973.1055037","article-title":"Noiseless coding of correlated information sources","volume":"19","author":"Slepian","year":"1973","journal-title":"IEEE Transactions on Information Theory"},{"issue":"1","key":"2026032712181594700_ref157","doi-asserted-by":"crossref","first-page":"63","DOI":"10.1109\/18.481779","article-title":"Simulation of random processes and rate-distortion theory","volume":"42","author":"Steinberg","year":"1996","journal-title":"IEEE Transactions on Information Theory"},{"issue":"1","key":"2026032712181594700_ref158","doi-asserted-by":"crossref","first-page":"5","DOI":"10.1109\/TIT.2019.2946364","article-title":"Communication for generating correlation: A unifying survey","volume":"66","author":"Sudan","year":"2020","journal-title":"IEEE Transactions on Information Theory"},{"key":"2026032712181594700_ref159","first-page":"920","article-title":"Moderate-deviations of lossy source coding for discrete and Gaussian sources","author":"Tan","year":"2012"},{"issue":"1-2","key":"2026032712181594700_ref160","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1561\/0100000086","article-title":"Asymptotic estimates in information theory with non-vanishing error probabilities,","volume":"11","author":"Tan","year":"2014","journal-title":"Foundations and Trends\u00ae in Communications and Information Theory"},{"issue":"5","key":"2026032712181594700_ref161","doi-asserted-by":"crossref","first-page":"3734","DOI":"10.1109\/TIT.2018.2792495","article-title":"Analysis of remaining uncertainties and exponents under various conditional R\u00e9nyi entropies","volume":"64","author":"Tan","year":"2018","journal-title":"IEEE Transactions on Information Theory"},{"issue":"7","key":"2026032712181594700_ref162","doi-asserted-by":"crossref","first-page":"1592","DOI":"10.1109\/TPAMI.2012.240","article-title":"Automatic relevance determination in nonnegative matrix factorization with the \u03b2-divergence","volume":"35","author":"Tan","year":"2013","journal-title":"IEEE Transactions on Pattern Analysis and Machine Intel li- gence"},{"key":"2026032712181594700_ref163","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4612-1236-2","volume":"14","author":"Thorisson","year":"2000","journal-title":"Coupling, Stationarity, and Regeneration"},{"issue":"6","key":"2026032712181594700_ref164","first-page":"468","article-title":"What are the numbers that experiments provide","volume":"17","author":"Tsallis","year":"1994","journal-title":"Quimica Nova"},{"issue":"9","key":"2026032712181594700_ref165","doi-asserted-by":"crossref","first-page":"5627","DOI":"10.1109\/TIT.2013.2264355","article-title":"Common information and secret key capacity","volume":"59","author":"Tyagi","year":"2013","journal-title":"IEEE Transactions on Information Theory"},{"issue":"7","key":"2026032712181594700_ref166","doi-asserted-by":"crossref","first-page":"3797","DOI":"10.1109\/TIT.2014.2320500","article-title":"R\u00e9nyi divergence and Kullback- Leibler divergence","volume":"60","author":"van Erven","year":"2014","journal-title":"IEEE Transactions on Information Theory"},{"key":"2026032712181594700_ref167","doi-asserted-by":"crossref","first-page":"369","DOI":"10.1007\/s10898-015-0350-z","article-title":"Heuristics for exact nonnegative matrix factorization","volume":"65","author":"Vandaele","year":"2016","journal-title":"Journal of Global Optimization"},{"issue":"3","key":"2026032712181594700_ref168","doi-asserted-by":"crossref","first-page":"1364","DOI":"10.1137\/070709967","article-title":"On the complexity of nonnegative matrix factorization","volume":"20","author":"Vavasis","year":"2009","journal-title":"SIAM Journal of Optimization"},{"key":"2026032712181594700_ref169","first-page":"370","article-title":"Sufficient conditions for the equality of exact and Wyner common information","author":"Vellambi","year":"2016"},{"key":"2026032712181594700_ref170","first-page":"151","article-title":"New results on the equality of exact and Wyner common information rates","author":"Vellambi","year":"2018"},{"issue":"5","key":"2026032712181594700_ref171","doi-asserted-by":"crossref","first-page":"1322","DOI":"10.1109\/18.412679","article-title":"Generating random bits from an arbitrary source: Fundamental limits","volume":"41","author":"Vembu","year":"1995","journal-title":"IEEE Transactions on Information Theory"},{"issue":"4","key":"2026032712181594700_ref172","doi-asserted-by":"crossref","first-page":"1147","DOI":"10.1109\/18.335960","article-title":"A general formula for channel capacity","volume":"40","author":"Verd\u00fa","year":"1994","journal-title":"IEEE Transactions on Information Theory"},{"issue":"6","key":"2026032712181594700_ref173","doi-asserted-by":"crossref","first-page":"3238","DOI":"10.1109\/TIT.2014.2315805","article-title":"The lossy common information of correlated sources","volume":"60","author":"Viswanatha","year":"2014","journal-title":"IEEE Transactions on Information Theory"},{"issue":"11","key":"2026032712181594700_ref174","doi-asserted-by":"crossref","first-page":"6393","DOI":"10.1109\/TIT.2016.2604851","article-title":"Information-theoretic caching: Sequential coding for computing","volume":"62","author":"Wang","year":"2016","journal-title":"IEEE Transactions on Information Theory"},{"key":"2026032712181594700_ref175","volume-title":"Compression of sources of probability distributions and density operators","author":"Winter","year":"2002"},{"issue":"5","key":"2026032712181594700_ref176","doi-asserted-by":"crossref","first-page":"493","DOI":"10.1109\/TIT.1975.1055437","article-title":"A conditional entropy bound for a pair of discrete random variables","volume":"21","author":"Witsenhausen","year":"1975","journal-title":"IEEE Transactions on Information Theory"},{"issue":"2","key":"2026032712181594700_ref177","doi-asserted-by":"crossref","first-page":"313","DOI":"10.1137\/0131026","article-title":"Values and bounds for the common information of two discrete random variables","volume":"31","author":"Witsenhausen","year":"1976","journal-title":"SIAM Journal on Applied Mathematics"},{"issue":"1","key":"2026032712181594700_ref178","doi-asserted-by":"crossref","first-page":"100","DOI":"10.1137\/0128010","article-title":"On sequences of pairs of dependent random variables","volume":"28","author":"Witsenhausen","year":"1975","journal-title":"SIAM Journal on Applied Mathematics"},{"issue":"4","key":"2026032712181594700_ref179","first-page":"591","article-title":"The coding of messages subject to chance errors","volume":"1","author":"Wolfowitz","year":"1957","journal-title":"Il linois Journal of Mathematics"},{"key":"2026032712181594700_ref180","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-642-66822-7","volume-title":"Coding Theorems of Information Theory","author":"Wolfowitz","year":"1978","edition":"3"},{"key":"2026032712181594700_ref181","first-page":"17","article-title":"Large deviations, moderate deviations and LIL for empirical processes,","author":"Wu","year":"1994","journal-title":"Annals of Probability"},{"issue":"2","key":"2026032712181594700_ref182","doi-asserted-by":"crossref","first-page":"163","DOI":"10.1109\/TIT.1975.1055346","article-title":"The common information of two dependent random variables","volume":"21","author":"Wyner","year":"1975","journal-title":"IEEE Transactions on Information Theory"},{"key":"2026032712181594700_ref183","doi-asserted-by":"crossref","first-page":"1355","DOI":"10.1002\/j.1538-7305.1975.tb02040.x","article-title":"The wire-tap channel","volume":"54","author":"Wyner","year":"1975","journal-title":"The Bell Systems Technical Journal"},{"issue":"6","key":"2026032712181594700_ref184","doi-asserted-by":"crossref","first-page":"769","DOI":"10.1109\/TIT.1973.1055107","article-title":"A theorem on the entropy of certain binary sequences and applications: Part I","volume":"19","author":"Wyner","year":"1973","journal-title":"IEEE Transactions on Information Theory"},{"issue":"1","key":"2026032712181594700_ref185","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1109\/TIT.1976.1055508","article-title":"The rate-distortion function for source coding with side information at the decoder","volume":"22","author":"Wyner","year":"1976","journal-title":"IEEE Transactions on Information Theory"},{"issue":"2","key":"2026032712181594700_ref186","doi-asserted-by":"crossref","first-page":"754","DOI":"10.1109\/TIT.2015.2506560","article-title":"A lossy source coding interpretation of Wyner\u2019s common information","volume":"62","author":"Xu","year":"2016","journal-title":"IEEE Transactions on Information Theory"},{"key":"2026032712181594700_ref187","first-page":"1202","article-title":"On the most informative Boolean functions of the very noisy channel","author":"Yang","year":"2019"},{"issue":"2","key":"2026032712181594700_ref188","doi-asserted-by":"crossref","first-page":"157","DOI":"10.1016\/j.tcs.2007.03.007","article-title":"On the (im)possibility of non-interactive correlation distillation","volume":"382","author":"Yang","year":"2007","journal-title":"Theoretical Computer Science"},{"issue":"4","key":"2026032712181594700_ref189","doi-asserted-by":"crossref","first-page":"441","DOI":"10.1016\/0022-0000(91)90024-Y","article-title":"Expressing combinatorial optimization problems by linear programs","volume":"43","author":"Yannakakis","year":"1991","journal-title":"Journal of Computer and System Sciences"},{"issue":"6","key":"2026032712181594700_ref190","doi-asserted-by":"crossref","first-page":"2964","DOI":"10.1109\/TIT.2015.2428236","article-title":"Channel simulation via interactive communications","volume":"61","author":"Yassaee","year":"2015","journal-title":"IEEE Transactions on Information Theory"},{"key":"2026032712181594700_ref191","volume-title":"\u201cOn the \u03a6-stability and related conjectures\u201d,","author":"Yu","year":"2021"},{"key":"2026032712181594700_ref192","volume-title":"Strong Brascamp\u2013Lieb inequalities","author":"Yu","year":"2021"},{"key":"2026032712181594700_ref193","volume-title":"The convexity and concavity of envelopes of the minimum- eelative-entropy region for the DSBS","author":"Yu","year":"2021"},{"issue":"105583","key":"2026032712181594700_ref194","first-page":"1","article-title":"Edge-isoperimetric inequalities and ball-noise stability: Linear programming and probabilistic approaches","volume":"188","author":"Yu","year":"2022","journal-title":"Journal of Combinatorial Theory, Series A"},{"key":"2026032712181594700_ref195","volume-title":"Graphs of joint types, noninteractive simulation, and stronger hypercontractivity","author":"Yu","year":"2021"},{"key":"2026032712181594700_ref196","volume-title":"Generalized common informations: Measuring commonness by the conditional maximal correlation","author":"Yu","year":"2016"},{"issue":"5","key":"2026032712181594700_ref197","doi-asserted-by":"crossref","first-page":"3616","DOI":"10.1109\/TIT.2018.2806569","article-title":"Wyner\u2019s common information under R\u00e9nyi divergence measures","volume":"64","author":"Yu","year":"2018","journal-title":"IEEE Transactions on Information Theory"},{"key":"2026032712181594700_ref198","volume-title":"An improved linear programming bound on the average distance of a binary code","author":"Yu","year":"2019"},{"issue":"3","key":"2026032712181594700_ref199","doi-asserted-by":"crossref","first-page":"1321","DOI":"10.1109\/TIT.2018.2857763","article-title":"Asymptotic coupling and its applications in information theory","volume":"65","author":"Yu","year":"2019","journal-title":"IEEE Transactions on Information Theory"},{"issue":"3","key":"2026032712181594700_ref200","doi-asserted-by":"crossref","first-page":"1862","DOI":"10.1109\/TIT.2018.2885318","article-title":"R\u00e9nyi resolvability and its applications to the wiretap channel","volume":"65","author":"Yu","year":"2019","journal-title":"IEEE Transactions on Information Theory"},{"issue":"6","key":"2026032712181594700_ref201","doi-asserted-by":"crossref","first-page":"3349","DOI":"10.1109\/TIT.2019.2891363","article-title":"Simulation of random variables under R\u00e9nyi divergence measures of all orders","volume":"65","author":"Yu","year":"2019","journal-title":"IEEE Transactions on Information Theory"},{"issue":"4","key":"2026032712181594700_ref202","doi-asserted-by":"crossref","first-page":"2599","DOI":"10.1109\/TIT.2020.2970404","article-title":"Corrections to \u201cWyner\u2019s common information under R\u00e9nyi divergence measures\u201d,","volume":"66","author":"Yu","year":"2020","journal-title":"IEEE Transactions on Information Theory"},{"key":"2026032712181594700_ref203","doi-asserted-by":"crossref","unstructured":"L.\n              Yu\n            \n            \n              V. Y. F.\n              Tan\n            \n          , \u201cExact channel synthesis,\u201d IEEE Transactions on Information Theory, vol. 66, no. 5, 2020, pp. 2299\u20132818.","DOI":"10.1109\/TIT.2019.2944625"},{"issue":"6","key":"2026032712181594700_ref204","doi-asserted-by":"crossref","first-page":"3366","DOI":"10.1109\/TIT.2020.2970396","article-title":"On exact and \u221e-R\u00e9nyi common information","volume":"66","author":"Yu","year":"2020","journal-title":"IEEE Transactions on Information Theory"},{"issue":"4","key":"2026032712181594700_ref205","doi-asserted-by":"crossref","first-page":"2528","DOI":"10.1109\/TIT.2021.3054659","article-title":"On non-interactive simulation of binary random variables","volume":"67","author":"Yu","year":"2021","journal-title":"IEEE Transactions on Information Theory"}],"container-title":["Foundations and Trends\u00ae in Communications and Information Theory"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.emerald.com\/ftcit\/article-pdf\/19\/2\/107\/11137409\/0100000122en.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/www.emerald.com\/ftcit\/article-pdf\/19\/2\/107\/11137409\/0100000122en.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T14:10:33Z","timestamp":1777471833000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.emerald.com\/ftcit\/article\/19\/2\/107\/1331437\/Common-Information-Noise-Stability-and-Their"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,4,28]]},"references-count":205,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2022,4,28]]}},"URL":"https:\/\/doi.org\/10.1561\/0100000122","relation":{},"ISSN":["1567-2190","1567-2328"],"issn-type":[{"value":"1567-2190","type":"print"},{"value":"1567-2328","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,4,28]]}}}