BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//Talks.cam//talks.cam.ac.uk//
X-WR-CALNAME:Talks.cam
BEGIN:VEVENT
SUMMARY:On privacy amplification\, lossy compression\, and their duality t
o channel coding - Joe Renes (ETH Zürich)
DTSTART:20180723T104500Z
DTEND:20180723T113000Z
UID:TALK108253@talks.cam.ac.uk
CONTACT:INI IT
DESCRIPTION:We examine the task of privacy amplification from information-
theoretic and coding-theoretic points of view. In the former\, we give a o
ne-shot characterization of the optimal rate of privacy amplification agai
nst classical adversaries in terms of the optimal type-II error in asymmet
ric hypothesis testing. This formulation can be easily computed to give fi
nite-blocklength bounds and turns out to be equivalent to smooth min-entro
py bounds by Renner and Wolf [Asiacrypt 2005] and Watanabe and Hayashi [IS
IT 2013]\, as well as a bound in terms of the E divergence by Yang\, Schae
fer\, and Poor [arXiv:1706.03866 [cs.IT]]. In the latter\, we show that pr
otocols for privacy amplification based on linear codes can be easily repu
rposed for channel simulation. Combined with known relations between chann
el simulation and lossy source coding\, this implies that privacy amplific
ation can be understood as a basic primitive for both channel simulation a
nd lossy compression. Applied to symmetric channels or lossy compression s
ettings\, our construction leads to protocols of optimal rate in the asymp
totic i.i.d. limit. Finally\, appealing to the notion of channel duality r
ecently detailed by us in [IEEE Trans. Info. Theory 64\, 577 (2018)]\, we
show that linear error-correcting codes for symmetric channels with quantu
m output can be transformed into linear lossy source coding schemes for cl
assical variables arising from the dual channel. This explains a &ldquo\;c
urious duality&rdquo\; in these problems for the (self-dual) erasure chann
el observed by Martinian and Yedidia [Allerton 2003\; arXiv:cs/0408008] an
d partly anticipates recent results on optimal lossy compression by polar
and low-density generator matrix codes.
LOCATION:Seminar Room 1\, Newton Institute
END:VEVENT
END:VCALENDAR