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Statistical Properties of Modulo-2 Added Binary Sequences
Akio TSUNEDA Takuro SUGAHARA Takahiro INOUE
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences
Publication Date: 2004/09/01
Print ISSN: 0916-8508
Type of Manuscript: Special Section PAPER (Special Section on Nonlinear Theory and its Applications)
modulo-2 addition, binary sequence, random number, correlation, chaos,
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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.