The original paper is in English. Non-English content has been machine-translated and may contain typographical errors or mistranslations. ex. Some numerals are expressed as "XNUMX".
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The original paper is in English. Non-English content has been machine-translated and may contain typographical errors or mistranslations. Copyrights notice
Um conjunto composto por K subconjuntos de Msequências de comprimento L é chamado de conjunto de sequências complementares expresso por A(L, K, M), se a soma das funções de autocorrelação aperiódica fora de fase das sequências dentro de um subconjunto e a soma das funções de correlação cruzada entre as sequências correspondentes em quaisquer dois subconjuntos forem zero em qualquer mudança de fase. Suehiro et al. primeiro conjunto complementar proposto A(Nn, N, N) Onde N e n são inteiros positivos maiores ou iguais a 2. Recentemente, vários conjuntos complementares relacionados à construção de Suehiro, como N sendo uma potência de um número primo, foram propostas. No entanto, não há discussão sobre sua relação de inclusão e propriedades das sequências. Este artigo formula e investiga rigorosamente as funções lógicas (generalizadas) dos conjuntos complementares de Suehiro et al. para compreender seu método de construção e as propriedades das sequências. Como resultado, mostra-se que existe um caso em que a função lógica é dobrada quando n é par. Isso significa que pode-se garantir que cada série tenha propriedades pseudo-aleatórias até certo ponto. Em outras palavras, significa que o conjunto complementar pode ser aplicado com sucesso à comunicação em canais flutuantes. As funções lógicas também permitem a simplificação dos geradores de sequência e seus filtros correspondentes.
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
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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},}
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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 -