Mutual Information Functions Versus Correlation Functions

This paper studies one application of mutual information to symbolic sequence: the mutual information function M(d). This function is compared with the more frequently used correlation function (d). An exact relation between M(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 to M(d) = 0. This linear, but not general, independence between symbols separated by a distance is studied for ternary sequences. Also included in this paper is the estimation of the nite-size e ect on calculating mutual information. Finally, the concept of \symbolic noise" is discussed.