Facets of Entropy

2009 ISIT Plenary Lecture
Facets of Entropy
Professor Raymond W. Yeung
Chinese University of Hong Kong


Constraints on the entropy function are sometimes referred to as the laws of information theory. For a long time, the submodular inequalities, or equivalently the nonnegativity of the Shannon information measures, are the only known constraints. Inequalities that are implied by the submodular inequality are categorically referred to as Shannon-type inequalities. If the number of random variables is fixed, a Shannon-type inequality can in principle be verified by a linear program known as ITIP.
A non-Shannon-type inequality is a constraint on the entropy function which is not implied by the submodular inequality. In the late 1990’s, the discovery of a few such inequalities revealed that Shannon-type inequalities alone do not constitute a complete set of constraints on the entropy function.
In the past decade, connections between the entropy function and a number of fields in information science, mathematics, and physics have been established. These fields include probability theory, network coding, combinatorics, group theory, Kolmogorov complexity, matrix theory, and quantum mechanics. This talk is an attempt to present a picture for the many facets of the entropy function.

Raymond W. Yeung received the BS, MEng and PhD degrees in electrical engineering from Cornell University in 1984, 1985, and 1988, respectively. He joined AT&T Bell Laboratories in 1988. He came to CUHK in 1991 and has been with the Department since then, where he is currently a chair professor. He is the author of the book entitled A First Course in Information Theory (Kluwer Academic/Plenum Publishers, 2002). His research interest is in information theory and network coding. He was a consultant in a project of Jet Propulsion Laboratory for salvaging the malfunctioning Galileo Spacecraft. He is a member of the Board of Governors of the IEEE Information Theory Societyfrom 1999 to 2001. He has served on the committees of a number of information theory symposiums and workshops.  He was the General Chair of the First Workshop on Network, Coding, and Applications (NetCod 2005), a Technical Co-Chair of the 2006 IEEE International Symposium on Information Theory, and a Technical Co-Chair of the 2006 IEEE Information Theory Workshop, Chengdu. He also has served on the editorial board of a number of academic journals. He was an Associate Editor for Shannon Theory of the IEEE Transactions on Information Theory from 2002 to 2005. He currently serves as an Editor-at-Large of Communications in Information and Systems, an Editor of Foundation and Trends in Communications and Information Theory and an Editor of Foundation and Trends in Networking. He was a recipient of the Croucher Senior Research Fellowship for 2000/01, the Best Paper Award (Communication Theory) of the 2004 International Conference on Communications, Circuits and System, the 2005 IEEE Information Theory Society Paper Award, and the Friedrich Wilhelm Bessel Research Award from the Alexander von Humboldt Foundation in 2007. He is a Fellow of the IEEE and the Hong Kong Institution of Engineers.