A study of ergodicity and redundancy based on intersymbol correlation of finite range

Abstract

Some of the basic concepts of information theory are critically reviewed in the light of a generalized formulation of the theory of Markoff's chains, in which the initial and final states are sequences of symbols of different lengths, and occurrence of symbols is governed by inter-symbol correlation probability of finite range. In particular, the conditions of ergodicity and the structure of "ergodic subsets" of sequences of arbitrary length are carefully discussed. A mathematical method is developed to determine the "range" and "strength" of inter-symbol correlation. A brief summary of the content is given at the end of Section 1.