Measuring correlations in symbol sequences

The paper is devoted to relations between correlation functions and mutual information. It is shown that, in sequences over an alphabet of λ symbols, statistical dependences are measured by (λ − 1)2 independent parameters. However, not all of them can be determined by autocorrelation functions. Appropriate sets of correlation functions (including crosscorrelations) are introduced, which allow the detection of all dependences. The results are exemplified for binary, ternary, and quaternary symbol sequences. As an application, it is discussed that a nonuniform codon usage in protein-coding DNA sequences introduces periodic correlations even at distances in the order of 1000 base pairs