Families of perfect polyphase sequences from the array structure of Fermat-Quotient sequences and Frank-Zadoff sequences

Ki Hyeon Park; Hong Yeop Song; Dae San Kim

doi:10.1109/ISIT.2015.7282713

Families of perfect polyphase sequences from the array structure of Fermat-Quotient sequences and Frank-Zadoff sequences

Ki Hyeon Park, Hong Yeop Song, Dae San Kim

Department of Electrical and Electronic Engineering

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

1 Citation (Scopus)

Abstract

We show that a p-ary polyphase sequence of period p² from the Fermat quotients is 'perfect.' That is, its periodic autocorrelation is zero for all non-trivial shifts. We call this Fermat-Quotient sequences. Using this and the fact that the Frank-Zadoff sequences (which is known to be also perfect), we propose a collection of 'optimum' families of perfect polyphase sequences in the sense of Sarwate Bound. That is, the cross-correlation of two members in a family is upper bounded by p. We may say these families are 'completely optimum' since the cross-correlation of any two members in a family is exactly p for all phase-shifts.

Original language	English
Title of host publication	Proceedings - 2015 IEEE International Symposium on Information Theory, ISIT 2015
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	1537-1540
Number of pages	4
ISBN (Electronic)	9781467377041
DOIs	https://doi.org/10.1109/ISIT.2015.7282713
Publication status	Published - 2015 Sep 28
Event	IEEE International Symposium on Information Theory, ISIT 2015 - Hong Kong, Hong Kong Duration: 2015 Jun 14 → 2015 Jun 19

Publication series

Name	IEEE International Symposium on Information Theory - Proceedings
Volume	2015-June
ISSN (Print)	2157-8095

Other

Other	IEEE International Symposium on Information Theory, ISIT 2015
Country	Hong Kong
City	Hong Kong
Period	15/6/14 → 15/6/19

All Science Journal Classification (ASJC) codes

Theoretical Computer Science
Information Systems
Modelling and Simulation
Applied Mathematics

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Park, K. H., Song, H. Y., & Kim, D. S. (2015). Families of perfect polyphase sequences from the array structure of Fermat-Quotient sequences and Frank-Zadoff sequences. In Proceedings - 2015 IEEE International Symposium on Information Theory, ISIT 2015 (pp. 1537-1540). [7282713] (IEEE International Symposium on Information Theory - Proceedings; Vol. 2015-June). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/ISIT.2015.7282713

Park, Ki Hyeon ; Song, Hong Yeop ; Kim, Dae San. / Families of perfect polyphase sequences from the array structure of Fermat-Quotient sequences and Frank-Zadoff sequences. Proceedings - 2015 IEEE International Symposium on Information Theory, ISIT 2015. Institute of Electrical and Electronics Engineers Inc., 2015. pp. 1537-1540 (IEEE International Symposium on Information Theory - Proceedings).

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title = "Families of perfect polyphase sequences from the array structure of Fermat-Quotient sequences and Frank-Zadoff sequences",

abstract = "We show that a p-ary polyphase sequence of period p2 from the Fermat quotients is 'perfect.' That is, its periodic autocorrelation is zero for all non-trivial shifts. We call this Fermat-Quotient sequences. Using this and the fact that the Frank-Zadoff sequences (which is known to be also perfect), we propose a collection of 'optimum' families of perfect polyphase sequences in the sense of Sarwate Bound. That is, the cross-correlation of two members in a family is upper bounded by p. We may say these families are 'completely optimum' since the cross-correlation of any two members in a family is exactly p for all phase-shifts.",

author = "Park, {Ki Hyeon} and Song, {Hong Yeop} and Kim, {Dae San}",

year = "2015",

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language = "English",

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publisher = "Institute of Electrical and Electronics Engineers Inc.",

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Park, KH, Song, HY & Kim, DS 2015, Families of perfect polyphase sequences from the array structure of Fermat-Quotient sequences and Frank-Zadoff sequences. in Proceedings - 2015 IEEE International Symposium on Information Theory, ISIT 2015., 7282713, IEEE International Symposium on Information Theory - Proceedings, vol. 2015-June, Institute of Electrical and Electronics Engineers Inc., pp. 1537-1540, IEEE International Symposium on Information Theory, ISIT 2015, Hong Kong, Hong Kong, 15/6/14. https://doi.org/10.1109/ISIT.2015.7282713

Families of perfect polyphase sequences from the array structure of Fermat-Quotient sequences and Frank-Zadoff sequences. / Park, Ki Hyeon; Song, Hong Yeop; Kim, Dae San.

Proceedings - 2015 IEEE International Symposium on Information Theory, ISIT 2015. Institute of Electrical and Electronics Engineers Inc., 2015. p. 1537-1540 7282713 (IEEE International Symposium on Information Theory - Proceedings; Vol. 2015-June).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

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N2 - We show that a p-ary polyphase sequence of period p2 from the Fermat quotients is 'perfect.' That is, its periodic autocorrelation is zero for all non-trivial shifts. We call this Fermat-Quotient sequences. Using this and the fact that the Frank-Zadoff sequences (which is known to be also perfect), we propose a collection of 'optimum' families of perfect polyphase sequences in the sense of Sarwate Bound. That is, the cross-correlation of two members in a family is upper bounded by p. We may say these families are 'completely optimum' since the cross-correlation of any two members in a family is exactly p for all phase-shifts.

AB - We show that a p-ary polyphase sequence of period p2 from the Fermat quotients is 'perfect.' That is, its periodic autocorrelation is zero for all non-trivial shifts. We call this Fermat-Quotient sequences. Using this and the fact that the Frank-Zadoff sequences (which is known to be also perfect), we propose a collection of 'optimum' families of perfect polyphase sequences in the sense of Sarwate Bound. That is, the cross-correlation of two members in a family is upper bounded by p. We may say these families are 'completely optimum' since the cross-correlation of any two members in a family is exactly p for all phase-shifts.

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Park KH, Song HY, Kim DS. Families of perfect polyphase sequences from the array structure of Fermat-Quotient sequences and Frank-Zadoff sequences. In Proceedings - 2015 IEEE International Symposium on Information Theory, ISIT 2015. Institute of Electrical and Electronics Engineers Inc. 2015. p. 1537-1540. 7282713. (IEEE International Symposium on Information Theory - Proceedings). https://doi.org/10.1109/ISIT.2015.7282713