Connection Between Common Information and Algebraic Structure

Common information (CI) has played a major role in communication theory and control theory. It is a measure of degeneracy in the joint PMF of a pair of random variables and is characterized using a pair of univariate functions. Constructing the pair of random variables, that characterize messages recovered by two receiver terminals, with non-trivial CI enlarges the achievable rate region of interference channels and broadcast channels. We present a generalization of CI to three random variables based on both univariate and bivariate functions of the triple, and is characterized as a seven-dimensional vector. We connect these bivariate functions with algebraic structures such as a finite fields and develop a unified framework for a class of multi-terminal communication problems.
S. Sandeep Pradhan obtained his M.E. degree from the Indian Institute of Science (IIS), India in 1996 and Ph.D. from the University of California at Berkeley in 2001. From 2002 to 2008 he was an assistant professor in the Department of Electrical Engineering and Computer Science at the University of Michigan at Ann Arbor. Currently he is an associate professor. He is the recipient of 2001 Eliahu Jury award given by the University of California at Berkeley for outstanding research in the areas of systems, signal processing, communications and control, the CAREER award given by the National Science Foundation (NSF), and the Outstanding achievement award for the year 2009 from the University of Michigan. His research interests include sensor networks, multi-terminal communication systems, coding theory, quantization, information theory.