EE Seminar: The SNR-Evolution of the MMSE of Codes
~~(The talk will be given in English)
Speaker: Dr. Ronit Bustin
EE, TAU
Sunday, January 17th, 2016
15:00 - 16:00
Room 011, Kitot Bldg., Faculty of Engineering
The SNR-Evolution of the MMSE of Codes
Abstract:
In this talk we present the concept of the SNR-evolution of the minimum mean-square error (MMSE) of code sequences. This concept leads us to a new approach in the investigation of the long standing open problem of the two-user Gaussian interference Channel.
We begin by examining the I-MMSE trade-off problem, where the goal is to maximize the rate to one receiver, while at the same time limiting the disturbance on some unintended receiver. The disturbance is measured in term of the MMSE at that additional (unintended) receiver. The optimization problem is a simplification of the intereference channel problem, in the sense that here we consider only a single transmitter. Nonetheless, its analysis provides strong support for the best known achievability scheme - the Han-Kobayashi scheme. Motivated by this result, we turned to examine the two-user Gaussian interference channel problem, where simultaneous transmissions from two users interfere with each other. Using the SNR-evolution approach, we were able to resolve the Costa Conjecture for bounded variance inputs, a.k.a the missing corner points conjecture.
We've demonstrated the usefulness of SNR-evolution in capacity problems, where blocklength goes to infinity. As such our goal is to extend the approach to the finite blocklength regime.
Recently we have been exploring the SNR-evolution of the MMSE of finite inputs in the maximization of the MMSE at one SNR point, given an MMSE constraint at a different SNR point. Our result recover the known limiting expressions for the I-MMSE trade-off problem.
The key technical novelty used here is a new upper bound on the MMSE. This new bound allows to bound the MMSE for all SNR values below a certain SNR at which the MMSE is known (which corresponds to the disturbance constraint). This new bound complements the “single-crossing property” of the MMSE that upper bounds the MMSE for all SNR values above a certain value at which the MMSE value is known. The new MMSE upper bound provides a refined characterization of the phase-transition phenomenon which manifests, in the limit as the block-length goes to infinity, as a discontinuity of the MMSE for the problem at hand. Finally, a matching lower bound to within an additive gap of the order of O( log log( SNR ) ), achieved by “mixed inputs”, gives new insights to the properties required form the optimal inputs.
Bio:
Ronit Bustin received a B.Sc. degree in electrical engineering and computer science and a M.Sc. degree in electrical engineering in 2004 and 2006, respectively, from Tel-Aviv university, Israel. She received a Ph.D. in electrical engineering in 2013 from the the Technion - Israel Institute of Technology, Haifa. From 2013 to 2015 she was a postdoctoral research associate in the department of electrical engineering at Princeton University. She is currently a postdoctoral research associate in the department of electrical engineering at Tel Aviv University. Her research interests include multi-user information theory, secrecy constraints, Gaussian MIMO channels, estimation theory, channel coding, interactive communication and communication complexity. Ronit Bustin received the Irwin and Joan Jacobs scholarship for excellence in graduate studies and research, in January 2010. She is a recipient of the Adams fellowship from the Israel Academy of Sciences and Humanities, April 2010, and an Andrew and Erna Finci Viterbi graduate fellow in the faculty of electrical engineering at the Technion for the fall semester 2010-2011. Ronit received the Rothschild fellowship in 2013 and the women postdoctoral scholarship of Israel’s Council for Higher Education (VATAT) for her post-doctoral studies at Princeton.
