An old coding theorem (and two new ones, too)
Mon., May 5, 2014
3:00 - 4:00 PM
521 Cory Hall
Abstract:
In 1965, L.L. Campbell discovered a beautiful connection between Renyi entropy and the exponential moments of codeword lengths in lossless compression. While Campbell's theorem is unfamiliar to most, it has a natural place in the now-fashionable 'one-shot' approach that has proved central to non-asymptotic analyses of the three major Shannon-theoretic settings: lossless compression, lossy compression, and data transmission. In this talk, I will show that Campbell's result was a precursor to the one-shot paradigm. Indeed, it contains all the information-theoretic ingredients necessary to prove non-asymptotic lossless compression theorems in full generality by only invoking standard limiting arguments. I will also discuss analogs of Campbell's coding theorem for lossy compression and data transmission in terms of the d-tilted Renyi entropy and the Renyi mutual information, respectively. Joint work with Sergio Verdu
Bio:
Thomas Courtade is an Assistant Professor in the Department of Electrical Engineering and Computer Sciences. Before joining Berkeley in 2014, Thomas was at Stanford University, where he was supported by a postdoctoral fellowship through the NSF Center for Science of Information. He graduated summa cum laude with a B.Sc. in Electrical Engineering from Michigan Technological University in 2007, and received his M.Sc. and Ph.D. degrees in Electrical Engineering from UCLA in 2008 and 2012, respectively.
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