Statistical Properties of Modulo-2 Added Binary Sequences

Akio TSUNEDA  Takuro SUGAHARA  Takahiro INOUE  

Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E87-A   No.9   pp.2267-2273
Publication Date: 2004/09/01
Online ISSN: 
DOI: 
Print ISSN: 0916-8508
Type of Manuscript: Special Section PAPER (Special Section on Nonlinear Theory and its Applications)
Category: 
Keyword: 
modulo-2 addition,  binary sequence,  random number,  correlation,  chaos,  

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Summary: 
Modulo-2 addition (or exclusive-OR) is one of fundamental operations for binary variables. In this paper, we discuss statistical properties of sequences obtained by modulo-2 addition of two binary sequences. Firstly, we theoretically evaluate statistics of sequences obtained by modulo-2 addition of two general binary random variables. Secondly, we consider statistics of modulo-2 added chaotic binary sequences generated by a class of one-dimensional chaotic maps. Furthermore, we consider synthesis of an aperiodic binary sequence and a periodic one by modulo-2 addition with the purpose of generating aperiodic sequences with good statistical properties. We also perform computer experiments about such sequences.