Functional Representation of Random variables and Applications

Tuesday, November 13, 2018 - 4:00pm to Wednesday, November 14, 2018 - 4:55pm

Event Calendar Category

LIDS Seminar Series

Speaker Name

Abbas El Gamal


Stanford University

Building and Room Number



The functional representation lemma says that given random variables X and Y, there exists a random variable Z, independent of X, and a function g(x,z) such that Y=g(X,Z). This lemma has had several applications in information theory aimed at simplifying computations of certain information functional. I will present a strengthened version of this lemma and applications to several one shot coding problems. The first application is to channel simulation with common randomness, where we obtain an improved bound on the achievable rate by Harsha et al. that applies to arbitrary (not just discrete) random variables. More interestingly, the Poisson construction used in the proof of the strengthened lemma leads to new and simple achievability results for one-shot coding theorems, including lossy source coding, multiple description coding, and the Gray--Wyner system. I will end with an application of the Poisson construction to minimax learning for remote inference.


The new results presented in this talk are joint with Cheuk Ting Li, Xiugang Wu, and Ayfer Ozgur.


Abbas El Gamal is the Hitachi America Professor in the School of Engineering at Stanford University. He received his B.Sc. Honors degree from Cairo University in 1972, and his M.S. in Statistics and Ph.D. in Electrical Engineering both from Stanford University in 1977 and 1978, respectively. From 1978 to 1980, he was an Assistant Professor of Electrical Engineering at USC. From 2003 to 2012, he was Director of the Information Systems Laboratory at Stanford University. From 2012-2017 he was the Fortinet Founders Chair of the Department of Electrical Engineering at Stanford University. His research contributions have been in network information theory, FPGAs, digital imaging devices and systems, and smart grid modeling and control. He has authored or coauthored over 230 papers and holds 35 patents in these areas. He is coauthor of the book Network Information Theory (Cambridge Press 2011). He is a member of the US National Academy of Engineering and a Fellow of the IEEE. He received several awards for his research contributions, including the 2016 IEEE Richard Hamming Medal and the 2012 Claude E. Shannon Award. He served on the Board of Governors of the Information Theory Society from 2009 to 2016 and was its President in 2014. He has been involved in several Silicon Valley startups as cofounder, board of director member, advisor and in several key technical and management positions.