title: Delay independence of mutual-information rate of two symbolic sequences.
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.
authors: Laboratoire de Neurosciences Intégratives et Adaptatives UMR 6149 CNRS Aix-Marseille Université, 3 Place Victor Hugo, F-13331 Marseille Cedex 03, France.
authors: Jean-Luc
authors: JL
authors: Blanc
authors: Laurent
authors: L
authors: Pezard
authors: Annick
authors: A
authors: Lesne
mesh_terms: D008390:Markov Chains; D008962:Models, Theoretical; D013269:Stochastic Processes; D013997:Time Factors