@article{ae343c30919a4f718ba7dbcc1328d806,
title = "Capacity Upper Bounds for the Relay Channel via Reverse Hypercontractivity",
abstract = "We revisit the primitive relay channel, introduced by Cover in 1987. Recent work derived upper bounds on the capacity of this channel that are tighter than the classical cutset bound using the concentration of measure. In this paper, we recover, generalize, and improve upon some of these upper bounds with simpler proofs using reverse hypercontractivity. To our knowledge, this is the first application of reverse hypercontractivity in proving first-order converses in network information theory.",
keywords = "Markov semigroups, Shannon theory, concentration of measure, converses, relay channel, reverse hypercontractivity",
author = "Jingbo Liu and Ayfer Ozgur",
note = "Funding Information: Manuscript received November 27, 2018; revised May 24, 2020; accepted June 8, 2020. Date of publication July 13, 2020; date of current version August 18, 2020. This work was supported in part by the National Science Foundation (NSF) under Grant CCF-1350595, Grant CCF-1016625, Grant CCF-0939370, Grant CCF-1514538, and Grant DMS-1148711; in part by the Army Research Office (ARO) under Grant W911NF-15-1-0479 and Grant W911NF-14-1-0094; and in part by the Center for Science of Information (CSoI), an NSF Science and Technology Center, under Agreement CCF-0939370. This article was presented in part at the 2019 IEEE International Symposium on Information Theory (ISIT). (Corresponding author: Jingbo Liu.) Jingbo Liu is with the Institute for Data, Systems, and Society, Massachusetts Institute of Technology, Cambridge, MA 02142 USA, and also with the Department of Statistics, University of Illinois at Urbana-Champaign, Champaign, IL 61820 USA (e-mail: jingbol@illinois.edu). Publisher Copyright: {\textcopyright} 1963-2012 IEEE.",
year = "2020",
month = sep,
doi = "10.1109/TIT.2020.3008599",
language = "English (US)",
volume = "66",
pages = "5448--5455",
journal = "IRE Professional Group on Information Theory",
issn = "0018-9448",
publisher = "Institute of Electrical and Electronics Engineers Inc.",
number = "9",
}