A Parametric Study of Binary Sequence

Abstract

We study, in this paper, several properties of the binary sequence defined by the values (0,1), we present a review of the high order statistics as function of the average value known as the density. Different entropy functions, applied in information theory and statistical mechanics, are presented where their expressions are derived as function of the density. In the second part, we partially study the randomness characteristic of the binary sequence, based on a recently proposed metric inspired from diffraction theory, we present a new function whose expression is based on a principal equation in the field of antennas and propagation, based on the array factor which gives the interference pattern of uniform linear array of antennas in the far field region, we propose a real valued function in order to characterize the geometric repartition of the binary values of the sequence. Numerical simulations show its consistency with Shannon entropy. For binary sequence generated from logarithmic logistic map, the obtained results indicate the equivalency between this function and the diffraction based metric.