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SUMMARY:On maps between Hamming spaces that expand pairwise distances
DTSTART:20170501T110000
DTEND:20170501T120000
DTSTAMP:20260407T105720Z
UID:fd77273f614d778d4a506f0cd791763b30644a9f1c1481948b8c9159
CATEGORIES:Conferences - Seminars
DESCRIPTION:Prof. Yury Polyanskiy Associate Professor of Electrical Engine
 ering and Computer Science and a member of LIDS at MIT. Yury received M.S.
  degree in applied mathematics and physics from the Moscow Institute of Ph
 ysics and Technology\, Moscow\, Russia in 2005 and Ph.D. degree in electri
 cal engineering from Princeton University\, Princeton\, NJ in 2010. Curren
 tly\, his research focuses on basic questions in information theory\, erro
 r-correcting codes\, wireless communication and fault-tolerant and defect-
 tolerant circuits. Dr. Polyanskiy won the 2013 NSF CAREER award and 2011 I
 EEE Information Theory Society Paper Award.\nWe discuss interaction betwee
 n metric and linear structures on a Hamming space (i.e. finite-dimensional
  vector space over field $GF(2)$ with Hamming metric). Namely\, we conside
 r linear maps between these spaces possessing the property that image of a
 ny heavy Hamming weight vector has itself a heavy weight. We prove an asym
 ptotic upper-bound on the ratio of the dimensions of domain and co-domain.
  Our method builds upon an elegant idea of Tillich and Zemor (which we wil
 l review)\, as well as new results on harmonic analysis for the hypercube.
  More concretely\, we show that a function whose energy is concentrated on
  a set of small size\, and whose Fourier energy is concentrated on a small
  Hamming ball must be zero. This is a form of uncertainty principle for wh
 ich we derive an asymptotically optimal tradeoff. In the course of the pro
 of we establish a new log-Sobolev inequality and a new hypercontractivity 
 result for functions on the hypercube with (exponentially) small support. 
 Joint work with Alex Samorodnitsky (HUJI).
LOCATION:BC 229 https://plan.epfl.ch/?room==BC%20229
STATUS:CONFIRMED
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