Information Inequalities

                 	Asaf Cohen
   Center for the Mathematics of Information
       California Institute of Technology

Abstract: Information inequalities can be seen as the basic laws of
information theory. Governing the fundamental relations between the Shannon
entropies of random variables, information inequalities are used in
virtually any basic result in information theory: source coding, channel
coding and the various applications of information theory in other fields.

In this tutorial talk, we formally define information inequalities, give the
inequalities laid out by Shannon and their canonical form, and describe some
of their applications. We then describe some of the non-Shannon information
inequalities discovered in the last decade and their applications in
specific network coding problems as well as in understanding the fundamental
restrictions on the tools we use - random variables and their Shannon
entropies.