Grant: Discovery Grants Program - Individual

Sequences of symbols or strings drawn from some (finite or infinite) alphabet appear in many applications where objects can be encoded into strings in natural ways. Such sequences are often viewed as realizations of stochastic processes also known as ``information sources''. In many applications, when dealing with information sources, one naturally faces the following two tasks: analyzing/estimating sources properties and changing them in certain desirable ways. An important quantity characterizing an information source is its entropy (entropy rate). Entropy appears in many applications in digital and analog communications, biology, chemistry, physics, etc. For example, in studying chaotic dynamical systems, measuring the entropy of a (symbolic) dynamical system is important for deciding whether the system is chaotic. The long-term objectives of this research program are to develop methods and design efficient algorithms for measuring and estimating information-theoretic properties/quantities of information sources such as entropy, relative entropy and conditional entropy; and to design efficient algorithms for source transformation.