IEICE TRANSACTIONS on Fundamentals
Logic Functions of Polyphase Complementary Sets
Summary :
A set consisting of K subsets of Msequences of length L is called a complementary sequence set expressed by A(L, K, M), if the sum of the out-of-phase aperiodic autocorrelation functions of the sequences within a subset and the sum of the cross-correlation functions between the corresponding sequences in any two subsets are zero at any phase shift. Suehiro et al. first proposed complementary set A(Nn, N, N) where N and n are positive integers greater than or equal to 2. Recently, several complementary sets related to Suehiro's construction, such as N being a power of a prime number, have been proposed. However, there is no discussion about their inclusion relation and properties of sequences. This paper rigorously formulates and investigates the (generalized) logic functions of the complementary sets by Suehiro et al. in order to understand its construction method and the properties of sequences. As a result, it is shown that there exists a case where the logic function is bent when n is even. This means that each series can be guaranteed to have pseudo-random properties to some extent. In other words, it means that the complementary set can be successfully applied to communication on fluctuating channels. The logic functions also allow simplification of sequence generators and their matched filters.
- Publication
- IEICE TRANSACTIONS on Fundamentals Vol.E106-A No.12 pp.1475-1483
- Publication Date
- 2023/12/01
- Publicized
- 2023/09/05
- Online ISSN
- 1745-1337
- DOI
- 10.1587/transfun.2023SDP0003
- Type of Manuscript
- Special Section PAPER (Special Section on Signal Design and Its Applications in Communications)
- Category
- Information Theory
Authors
Shinya MATSUFUJI
Yamaguchi University
Sho KURODA
FX Systems Corporation, GrandFront Osaka North
Yuta IDA
Yamaguchi University
Takahiro MATSUMOTO
Kagoshima University
Naoki SUEHIRO
Signal Design Co., Ltd
Keyword
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Shinya MATSUFUJI, Sho KURODA, Yuta IDA, Takahiro MATSUMOTO, Naoki SUEHIRO, "Logic Functions of Polyphase Complementary Sets" in IEICE TRANSACTIONS on Fundamentals,
vol. E106-A, no. 12, pp. 1475-1483, December 2023, doi: 10.1587/transfun.2023SDP0003.
Abstract: A set consisting of K subsets of Msequences of length L is called a complementary sequence set expressed by A(L, K, M), if the sum of the out-of-phase aperiodic autocorrelation functions of the sequences within a subset and the sum of the cross-correlation functions between the corresponding sequences in any two subsets are zero at any phase shift. Suehiro et al. first proposed complementary set A(Nn, N, N) where N and n are positive integers greater than or equal to 2. Recently, several complementary sets related to Suehiro's construction, such as N being a power of a prime number, have been proposed. However, there is no discussion about their inclusion relation and properties of sequences. This paper rigorously formulates and investigates the (generalized) logic functions of the complementary sets by Suehiro et al. in order to understand its construction method and the properties of sequences. As a result, it is shown that there exists a case where the logic function is bent when n is even. This means that each series can be guaranteed to have pseudo-random properties to some extent. In other words, it means that the complementary set can be successfully applied to communication on fluctuating channels. The logic functions also allow simplification of sequence generators and their matched filters.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/transfun.2023SDP0003/_p
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@ARTICLE{e106-a_12_1475,
author={Shinya MATSUFUJI, Sho KURODA, Yuta IDA, Takahiro MATSUMOTO, Naoki SUEHIRO, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Logic Functions of Polyphase Complementary Sets},
year={2023},
volume={E106-A},
number={12},
pages={1475-1483},
abstract={A set consisting of K subsets of Msequences of length L is called a complementary sequence set expressed by A(L, K, M), if the sum of the out-of-phase aperiodic autocorrelation functions of the sequences within a subset and the sum of the cross-correlation functions between the corresponding sequences in any two subsets are zero at any phase shift. Suehiro et al. first proposed complementary set A(Nn, N, N) where N and n are positive integers greater than or equal to 2. Recently, several complementary sets related to Suehiro's construction, such as N being a power of a prime number, have been proposed. However, there is no discussion about their inclusion relation and properties of sequences. This paper rigorously formulates and investigates the (generalized) logic functions of the complementary sets by Suehiro et al. in order to understand its construction method and the properties of sequences. As a result, it is shown that there exists a case where the logic function is bent when n is even. This means that each series can be guaranteed to have pseudo-random properties to some extent. In other words, it means that the complementary set can be successfully applied to communication on fluctuating channels. The logic functions also allow simplification of sequence generators and their matched filters.},
keywords={},
doi={10.1587/transfun.2023SDP0003},
ISSN={1745-1337},
month={December},}
Copy
TY - JOUR
TI - Logic Functions of Polyphase Complementary Sets
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 1475
EP - 1483
AU - Shinya MATSUFUJI
AU - Sho KURODA
AU - Yuta IDA
AU - Takahiro MATSUMOTO
AU - Naoki SUEHIRO
PY - 2023
DO - 10.1587/transfun.2023SDP0003
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E106-A
IS - 12
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - December 2023
AB - A set consisting of K subsets of Msequences of length L is called a complementary sequence set expressed by A(L, K, M), if the sum of the out-of-phase aperiodic autocorrelation functions of the sequences within a subset and the sum of the cross-correlation functions between the corresponding sequences in any two subsets are zero at any phase shift. Suehiro et al. first proposed complementary set A(Nn, N, N) where N and n are positive integers greater than or equal to 2. Recently, several complementary sets related to Suehiro's construction, such as N being a power of a prime number, have been proposed. However, there is no discussion about their inclusion relation and properties of sequences. This paper rigorously formulates and investigates the (generalized) logic functions of the complementary sets by Suehiro et al. in order to understand its construction method and the properties of sequences. As a result, it is shown that there exists a case where the logic function is bent when n is even. This means that each series can be guaranteed to have pseudo-random properties to some extent. In other words, it means that the complementary set can be successfully applied to communication on fluctuating channels. The logic functions also allow simplification of sequence generators and their matched filters.
ER -
English
