Estimation of Entropy from Subword Complexity

Subword complexity is a function that describes how many different substrings of a given length are contained in a given string. In this paper, two estimators of block entropy are proposed, based on the profile of subword complexity. The first estimator works well only for IID processes with uniform probabilities. The second estimator provides a lower bound of block entropy for any strictly stationary process with the distributions of blocks skewed towards less probable values. Using this estimator, some estimates of block entropy for natural language are obtained, confirming earlier hypotheses.