TY - GEN
T1 - Brascamp-Lieb inequality and its reverse
T2 - 2016 IEEE International Symposium on Information Theory, ISIT 2016
AU - Liu, Jingbo
AU - Courtade, Thomas A.
AU - Cuff, Paul
AU - Verdu, Sergio
N1 - Publisher Copyright:
© 2016 IEEE.
PY - 2016/8/10
Y1 - 2016/8/10
N2 - We generalize a result by Carlen and Cordero-Erausquin on the equivalence between the Brascamp-Lieb inequality and the subadditivity of relative entropy by allowing for random transformations (a broadcast channel). This leads to a unified perspective on several functional inequalities that have been gaining popularity in the context of proving impossibility results. We demonstrate that the information theoretic dual of the Brascamp-Lieb inequality is a convenient setting for proving properties such as data processing, tensorization, convexity and Gaussian optimality. Consequences of the latter include an extension of the Brascamp-Lieb inequality allowing for Gaussian random transformations, the determination of the multivariate Wyner common information for Gaussian sources, and a multivariate version of Nelson's hypercontractivity theorem. Finally we present an information theoretic characterization of a reverse Brascamp-Lieb inequality involving a random transformation (a multiple access channel).
AB - We generalize a result by Carlen and Cordero-Erausquin on the equivalence between the Brascamp-Lieb inequality and the subadditivity of relative entropy by allowing for random transformations (a broadcast channel). This leads to a unified perspective on several functional inequalities that have been gaining popularity in the context of proving impossibility results. We demonstrate that the information theoretic dual of the Brascamp-Lieb inequality is a convenient setting for proving properties such as data processing, tensorization, convexity and Gaussian optimality. Consequences of the latter include an extension of the Brascamp-Lieb inequality allowing for Gaussian random transformations, the determination of the multivariate Wyner common information for Gaussian sources, and a multivariate version of Nelson's hypercontractivity theorem. Finally we present an information theoretic characterization of a reverse Brascamp-Lieb inequality involving a random transformation (a multiple access channel).
UR - http://www.scopus.com/inward/record.url?scp=84985905012&partnerID=8YFLogxK
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U2 - 10.1109/ISIT.2016.7541459
DO - 10.1109/ISIT.2016.7541459
M3 - Conference contribution
AN - SCOPUS:84985905012
T3 - IEEE International Symposium on Information Theory - Proceedings
SP - 1048
EP - 1052
BT - Proceedings - ISIT 2016; 2016 IEEE International Symposium on Information Theory
PB - Institute of Electrical and Electronics Engineers Inc.
Y2 - 10 July 2016 through 15 July 2016
ER -