Estimating the information content of symbol sequences and efficient codes

Several variants of an algorithm for estimating Shannon entropies of symbol sequences are presented. They are all related to the Lempel-Ziv algorithm (1976, 1977) and to recent algorithms for estimating Hausdorff dimensions. The average storage and running times increase as N and Nlog N, respectively, with the sequence length N. These algorithms proceed basically by constructing efficient codes. They seem to be the optimal algorithms for sequences with strong long-range correlations, e.g. natural languages. An application to written English illustrates their use