Rüdiger Urbanke, EPFL (École polytechnique fédérale de Lausanne)
Amir Dembo, Stanford University
Antonia Tulino, UNINA (Università degli Studi di Napoli Federico II) & Nokia Bell Labs
Maryna Viazovska, EPFL (École polytechnique fédérale de Lausanne)
(Technion – Israel Institute of Technology, Israel)
My Little Hammers and Screwdrivers for Analyzing Code Ensemble Performance
FRIDAY, 30 JUNE, 08:30-09:30
In this talk, I will give an overview of several new analytical tools, that I have gradually developed during the last decade, for assessing the performance of code ensembles in a variety of scenarios of coded communication configurations. By bypassing the traditional use certain well-known inequalities, such as Jensen's inequality and others, these analytical tools often enable exponentially tight evaluations of the average error probability, the excess distortion probability, and other types of large deviations probabilities. These tools were inspired by models and methods of statistical physics. In particular, the first tool that I will describe, which I will refer to as "type-class enumeration method", was inspired by the so-called random energy model (REM) of spin glasses in statistical mechanics, as there is a remarkable degree of similarity and parallelism between the REM and the paradigm of random coding. The second tool is a continuous-alphabet analogue of the method of types, without recourse to quantization arguments that convert the problem back to the realm of finite alphabets. In this context, one of the powerful techniques is saddle-point integration. The results obtained from these tools will be demonstrated in a variety of examples. Finally, time permits, I will also discuss additional techniques, like integral representations of the logarithmic function and non-integer power functions, with applications to information theory, as well as methods for reversing Jensen's inequality and manipulating it in various ways.
Neri Merhav has received the B.Sc., M.Sc., and D.Sc. degrees from the Technion, Israel Institute of Technology, in 1982, 1985, and 1988, respectively, all in electrical engineering. From 1988 to 1990 he was with AT&T Bell Laboratories, Murray Hill, NJ, USA. Since 1990 he has been with the Electrical Engineering Department (now, the Viterbi ECE Department) of the Technion, where he is the Irving Shepard Professor. During 1994-2000 he was also serving as a consultant to the Hewlett--Packard Laboratories - Israel (HPL-I). His research interests include information theory, statistical communications, and statistical signal processing. He is especially interested in the areas of lossless/lossy source coding and prediction/filtering, relationships between information theory and statistics, detection, estimation, as well as in the area of Shannon Theory, including topics in joint source--channel coding, source/channel simulation, and coding with side information with applications to information hiding and watermarking systems. Another recent research interest concerns the relationships between Information Theory and statistical physics. Dr. Merhav was a co-recipient of the 1993 Paper Award of the IEEE Information Theory Society and he is a Fellow of the IEEE since 1999 and a Life Fellow since 2023. He also received the 1994 American Technion Society Award for Academic Excellence and the 2002 Technion Henry Taub Prize for Excellence in Research. More recently, he was a co-recipient of the Best Paper Award of the 2015 IEEE Workshop on Information Forensics and Security (WIFS 2015).During 1996-1999 he served as an Associate Editor for Source Coding to the IEEE Transactions on Information Theory, and during 2017-2020 - as an Associate Editor for Shannon Theory in the same journal. He also served as a co-chairperson of the Program Committee of the 2001 IEEE International Symposium on Information Theory. He is currently on the Editorial Board of Foundations and Trends in Communications and Information Theory.