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Delay independence of mutual-information rate of two symbolic sequences
Jean-Luc Blanc1, Laurent Pezard, Annick Lesne
1Laboratoire de Neurosciences Intégratives et Adaptatives UMR 6149 CNRS Aix-Marseille Université, 3 Place Victor Hugo, F-13331 Marseille Cedex 03, France.
Abstract:
Introduced by Shannon as a "rate of actual transmission," mutual information rate (MIR) is an extension of mutual information to a pair of dynamical processes. We show a delay-independence theorem, according to which MIR is not sensitive to a time shift between the two processes. Numerical studies of several benchmark situations confirm that this theoretical asymptotic property remains valid for realistic finite sequences. Estimations based on block entropies and a causal state machine algorithm perform better than an estimation based on a Lempel-Ziv compression algorithm provided that block length and maximum history length, respectively, can be chosen larger than the delay. MIR is thus a relevant index for measuring nonlinear correlations between two experimental or simulated sequences when the transmission delay (in input-output devices) or dephasing (in coupled systems) is variable or unknown.
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