Classification, construction and search of general quasi-orthogonal binary signal sets

Ki Hyeon Park, Hong Yeop Song

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

In this paper, we derive a kind of classification of binary signal set by adopting Hadamard equivalence of binary matrices. To do this, we study various properties of this equivalence relation and its classes. We propose to use a concept named "HR-minimal" as a representative of each equivalence class, and some properties and constructions of HR-minimals are investigated. Especially, careful observation about the weight on an HR-minimal's second row are performed since it is highly related with orthogonality of a matrix. We give a construction ensuring sufficiently large m at some condition. We also give an exhaustive search algorithm to find the maximum m at given n and second row weight. Moreover, HR-minimals with the largest weight on its second row, defined as Quasi-Hadamard matrices (QH matrices), are studied. They include Hadamard matrices as a special case and generalize the property of Hadamard matrices in the sense that the row vectors of m × n QH matrices form a set of m binary vectors of length n with minimum pairwise absolute correlation. Some properties and existence of QH matrices are also discussed, including the examples of 16 × (6, 10, 17) QH matrices found by computer.

Original languageEnglish
Title of host publicationProceedings of the 5th International Workshop on Signal Design and Its Applications in Communications, IWSDA'11
Pages60-63
Number of pages4
DOIs
Publication statusPublished - 2011 Dec 1
Event5th International Workshop on Signal Design and Its Applications in Communications, IWSDA'11 - Guilin, China
Duration: 2011 Oct 102011 Oct 14

Other

Other5th International Workshop on Signal Design and Its Applications in Communications, IWSDA'11
CountryChina
CityGuilin
Period11/10/1011/10/14

Fingerprint

Hadamard matrices
Equivalence classes

All Science Journal Classification (ASJC) codes

  • Computer Networks and Communications
  • Computer Science Applications
  • Signal Processing

Cite this

Park, K. H., & Song, H. Y. (2011). Classification, construction and search of general quasi-orthogonal binary signal sets. In Proceedings of the 5th International Workshop on Signal Design and Its Applications in Communications, IWSDA'11 (pp. 60-63). [6159441] https://doi.org/10.1109/IWSDA.2011.6159441
Park, Ki Hyeon ; Song, Hong Yeop. / Classification, construction and search of general quasi-orthogonal binary signal sets. Proceedings of the 5th International Workshop on Signal Design and Its Applications in Communications, IWSDA'11. 2011. pp. 60-63
@inproceedings{847623080c7b4d6182322ab644be3a78,
title = "Classification, construction and search of general quasi-orthogonal binary signal sets",
abstract = "In this paper, we derive a kind of classification of binary signal set by adopting Hadamard equivalence of binary matrices. To do this, we study various properties of this equivalence relation and its classes. We propose to use a concept named {"}HR-minimal{"} as a representative of each equivalence class, and some properties and constructions of HR-minimals are investigated. Especially, careful observation about the weight on an HR-minimal's second row are performed since it is highly related with orthogonality of a matrix. We give a construction ensuring sufficiently large m at some condition. We also give an exhaustive search algorithm to find the maximum m at given n and second row weight. Moreover, HR-minimals with the largest weight on its second row, defined as Quasi-Hadamard matrices (QH matrices), are studied. They include Hadamard matrices as a special case and generalize the property of Hadamard matrices in the sense that the row vectors of m × n QH matrices form a set of m binary vectors of length n with minimum pairwise absolute correlation. Some properties and existence of QH matrices are also discussed, including the examples of 16 × (6, 10, 17) QH matrices found by computer.",
author = "Park, {Ki Hyeon} and Song, {Hong Yeop}",
year = "2011",
month = "12",
day = "1",
doi = "10.1109/IWSDA.2011.6159441",
language = "English",
isbn = "9781612840468",
pages = "60--63",
booktitle = "Proceedings of the 5th International Workshop on Signal Design and Its Applications in Communications, IWSDA'11",

}

Park, KH & Song, HY 2011, Classification, construction and search of general quasi-orthogonal binary signal sets. in Proceedings of the 5th International Workshop on Signal Design and Its Applications in Communications, IWSDA'11., 6159441, pp. 60-63, 5th International Workshop on Signal Design and Its Applications in Communications, IWSDA'11, Guilin, China, 11/10/10. https://doi.org/10.1109/IWSDA.2011.6159441

Classification, construction and search of general quasi-orthogonal binary signal sets. / Park, Ki Hyeon; Song, Hong Yeop.

Proceedings of the 5th International Workshop on Signal Design and Its Applications in Communications, IWSDA'11. 2011. p. 60-63 6159441.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

TY - GEN

T1 - Classification, construction and search of general quasi-orthogonal binary signal sets

AU - Park, Ki Hyeon

AU - Song, Hong Yeop

PY - 2011/12/1

Y1 - 2011/12/1

N2 - In this paper, we derive a kind of classification of binary signal set by adopting Hadamard equivalence of binary matrices. To do this, we study various properties of this equivalence relation and its classes. We propose to use a concept named "HR-minimal" as a representative of each equivalence class, and some properties and constructions of HR-minimals are investigated. Especially, careful observation about the weight on an HR-minimal's second row are performed since it is highly related with orthogonality of a matrix. We give a construction ensuring sufficiently large m at some condition. We also give an exhaustive search algorithm to find the maximum m at given n and second row weight. Moreover, HR-minimals with the largest weight on its second row, defined as Quasi-Hadamard matrices (QH matrices), are studied. They include Hadamard matrices as a special case and generalize the property of Hadamard matrices in the sense that the row vectors of m × n QH matrices form a set of m binary vectors of length n with minimum pairwise absolute correlation. Some properties and existence of QH matrices are also discussed, including the examples of 16 × (6, 10, 17) QH matrices found by computer.

AB - In this paper, we derive a kind of classification of binary signal set by adopting Hadamard equivalence of binary matrices. To do this, we study various properties of this equivalence relation and its classes. We propose to use a concept named "HR-minimal" as a representative of each equivalence class, and some properties and constructions of HR-minimals are investigated. Especially, careful observation about the weight on an HR-minimal's second row are performed since it is highly related with orthogonality of a matrix. We give a construction ensuring sufficiently large m at some condition. We also give an exhaustive search algorithm to find the maximum m at given n and second row weight. Moreover, HR-minimals with the largest weight on its second row, defined as Quasi-Hadamard matrices (QH matrices), are studied. They include Hadamard matrices as a special case and generalize the property of Hadamard matrices in the sense that the row vectors of m × n QH matrices form a set of m binary vectors of length n with minimum pairwise absolute correlation. Some properties and existence of QH matrices are also discussed, including the examples of 16 × (6, 10, 17) QH matrices found by computer.

UR - http://www.scopus.com/inward/record.url?scp=84858379753&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84858379753&partnerID=8YFLogxK

U2 - 10.1109/IWSDA.2011.6159441

DO - 10.1109/IWSDA.2011.6159441

M3 - Conference contribution

AN - SCOPUS:84858379753

SN - 9781612840468

SP - 60

EP - 63

BT - Proceedings of the 5th International Workshop on Signal Design and Its Applications in Communications, IWSDA'11

ER -

Park KH, Song HY. Classification, construction and search of general quasi-orthogonal binary signal sets. In Proceedings of the 5th International Workshop on Signal Design and Its Applications in Communications, IWSDA'11. 2011. p. 60-63. 6159441 https://doi.org/10.1109/IWSDA.2011.6159441