Mutual information functions versus correlation functions

This paper studies one application of mutual information to symbolic sequences: the mutual information functionM(d). This function is compared with the more frequently used correlation function(d). An exact relation betweenM(d) and(d) is derived for binary sequences. For sequences with more than two symbols, no such general relation exists; in particular,(d)=0 may or may not lead toM(d)=0. This linear, but not general, independence between symbols separated by a distance is studied for ternary sequences. Also included is the estimation of the finite-size effect on calculating mutual information. Finally, the concept of symbolic noise is discussed.