Symbolic dynamics and coding applications

The purpose of the article is twofold: to give an elementary and concrete introduction to symbolic dynamics and to discuss two applications to coding problems. It begins with a brief discussion of the origins of symbolic dynamics going back to the work of Radamard in 1898. The rough idea is that symbolic dynamics provides a model for the orbits of a classical dynamical system via a space of sequences. Next it introduces the basic concepts of symbolic dynamics, emphasizing sliding block codes. Some of the fundamental problems, solved and unsolved, in the subject, are surveyed. Then it shows how work on these problems has led to coding applications