Open AccessSumming modulo 2 of stationary binary stochastic processes
Author(s) -
Mieczyslaw Jessa,
Jakub Nikonowicz
Publication year - 2025
Publication title -
ieee access
Language(s) - English
Resource type - Magazines
SCImago Journal Rank - 0.587
H-Index - 127
eISSN - 2169-3536
DOI - 10.1109/access.2025.3615472
Subject(s) - aerospace , bioengineering , communication, networking and broadcast technologies , components, circuits, devices and systems , computing and processing , engineered materials, dielectrics and plasmas , engineering profession , fields, waves and electromagnetics , general topics for engineers , geoscience , nuclear engineering , photonics and electrooptics , power, energy and industry applications , robotics and control systems , signal processing and analysis , transportation
In the paper, we analyze the properties of the stochastic process obtained as the result of summing modulo 2 without carry of a finite number of stationary binary stochastic processes, some of which do not satisfy the independence condition. The primary goal of the mathematical analysis is to determine the formula for the minimum number of independent stochastic processes that will ensure the mean and the covariance values between adjacent elements of the output process are acceptable to the user, regardless of the number of dependent stochastic processes at the input. We assume that we do not know which of the summed processes are dependent and which are independent. To the authors’ knowledge, this problem has not been addressed in the literature so far, and it may be helpful when using the modulo 2 summation of binary stationary independent random processes with binary dependent processes. Possible applications include random sequence generation, cryptography, simulations, coding theory, etc.
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