Statistical Properties of Modulo-2 Added Binary Sequences

Akio TSUNEDA; Takuro SUGAHARA; Takahiro INOUE

Statistical Properties of Modulo-2 Added Binary Sequences

Akio TSUNEDA, Takuro SUGAHARA, Takahiro INOUE

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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.

Publication: IEICE TRANSACTIONS on Fundamentals Vol.E87-A No.9 pp.2267-2273

Publication Date: 2004/09/01

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Type of Manuscript: Special Section PAPER (Special Section on Nonlinear Theory and its Applications)

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Akio TSUNEDA, Takuro SUGAHARA, Takahiro INOUE, "Statistical Properties of Modulo-2 Added Binary Sequences" in IEICE TRANSACTIONS on Fundamentals, vol. E87-A, no. 9, pp. 2267-2273, September 2004, doi: .
Abstract: 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.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/e87-a_9_2267/_p

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@ARTICLE{e87-a_9_2267,
author={Akio TSUNEDA, Takuro SUGAHARA, Takahiro INOUE, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Statistical Properties of Modulo-2 Added Binary Sequences},
year={2004},
volume={E87-A},
number={9},
pages={2267-2273},
abstract={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.},
keywords={},
doi={},
ISSN={},
month={September},}

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TY - JOUR
TI - Statistical Properties of Modulo-2 Added Binary Sequences
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 2267
EP - 2273
AU - Akio TSUNEDA
AU - Takuro SUGAHARA
AU - Takahiro INOUE
PY - 2004
DO -
JO - IEICE TRANSACTIONS on Fundamentals
SN -
VL - E87-A
IS - 9
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - September 2004
AB - 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.
ER -