Autocorrelation versus entropy-based autoinformation for measuring dependence in random signal

This paper studies in conjunction correlation and entropy-based information measures for the characterization of statistical dependence in a random signal. Several simple reference models of random signal are presented, for which both the autocorrelation and autoinformation functions are calculated explicitly in analytical form. Conditions are investigated where a general relation is shown to exist between these two functions in asymptotic regime, and which especially apply to stationary signals. Another, recent, model of nonstationary random signal with long-range dependence, is also presented and analyzed. For this model, the autocorrelation and autoinformation functions are calculated and compared for the first time, and exhibit more complex asymptotic behavior. This paper is intended to provide essentially theoretical models and results useful for better appreciation of the potentialities of the autoinformation function, in complement to the more common autocorrelation function, for the study of structures, informational contents and properties of complex random signals.