A Unified Construction for Yielding Quaternary Sequences with Optimal Periodic Autocorrelation

Fanxin ZENG; Xiaoping ZENG; Zhenyu ZHANG; Guixin XUAN

doi:10.1587/transfun.E96.A.1593

A Unified Construction for Yielding Quaternary Sequences with Optimal Periodic Autocorrelation

Fanxin ZENG, Xiaoping ZENG, Zhenyu ZHANG, Guixin XUAN

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A unified construction for transforming binary sequences of balance or unbalance into quaternary sequences is presented. On the one hand, when optimal and balanced binary sequences with even period are employed, our construction is exactly the same Jang, et al.'s and Chung, et al.'s ones, which result in balanced quaternary sequences with optimal autocorrelation magnitude. On the other hand, when ideal and balanced binary sequences with odd period N are made use of, our construction produces new balanced quaternary sequences with optimal autocorrelation value (OAV), in which there are N distinct sequences in terms of cyclic shift equivalence, and includes Tang, et al.'s and Jang, et al.'s ones as special cases. In addition, when binary sequences without period 2ⁿ-1 or balance are employed, the transformation of Jang, et al.'s method is invalid, however, the proposed construction works very good. As a consequence, this unified construction allows us to construct optimal and balanced quaternary sequences from ideal/optimal balanced binary sequences with arbitrary period.

Publication: IEICE TRANSACTIONS on Fundamentals Vol.E96-A No.7 pp.1593-1601

Publication Date: 2013/07/01

Publicized

Online ISSN: 1745-1337

DOI: 10.1587/transfun.E96.A.1593

Type of Manuscript: PAPER

Category: Information Theory

Authors

Fanxin ZENG
  Chongqing University,Chongqing Communication Institute
Xiaoping ZENG
  Chongqing University
Zhenyu ZHANG
  Chongqing Communication Institute
Guixin XUAN
  Chongqing Communication Institute

Keyword

quaternary sequence, balanced property, autocorrelation, interleaved sequence, Gray mapping

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Fanxin ZENG, Xiaoping ZENG, Zhenyu ZHANG, Guixin XUAN, "A Unified Construction for Yielding Quaternary Sequences with Optimal Periodic Autocorrelation" in IEICE TRANSACTIONS on Fundamentals, vol. E96-A, no. 7, pp. 1593-1601, July 2013, doi: 10.1587/transfun.E96.A.1593.
Abstract: A unified construction for transforming binary sequences of balance or unbalance into quaternary sequences is presented. On the one hand, when optimal and balanced binary sequences with even period are employed, our construction is exactly the same Jang, et al.'s and Chung, et al.'s ones, which result in balanced quaternary sequences with optimal autocorrelation magnitude. On the other hand, when ideal and balanced binary sequences with odd period N are made use of, our construction produces new balanced quaternary sequences with optimal autocorrelation value (OAV), in which there are N distinct sequences in terms of cyclic shift equivalence, and includes Tang, et al.'s and Jang, et al.'s ones as special cases. In addition, when binary sequences without period 2ⁿ-1 or balance are employed, the transformation of Jang, et al.'s method is invalid, however, the proposed construction works very good. As a consequence, this unified construction allows us to construct optimal and balanced quaternary sequences from ideal/optimal balanced binary sequences with arbitrary period.
URL: https://globals.ieice.org/en_transactions/fundamentals/10.1587/transfun.E96.A.1593/_p

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@ARTICLE{e96-a_7_1593,
author={Fanxin ZENG, Xiaoping ZENG, Zhenyu ZHANG, Guixin XUAN, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={A Unified Construction for Yielding Quaternary Sequences with Optimal Periodic Autocorrelation},
year={2013},
volume={E96-A},
number={7},
pages={1593-1601},
abstract={A unified construction for transforming binary sequences of balance or unbalance into quaternary sequences is presented. On the one hand, when optimal and balanced binary sequences with even period are employed, our construction is exactly the same Jang, et al.'s and Chung, et al.'s ones, which result in balanced quaternary sequences with optimal autocorrelation magnitude. On the other hand, when ideal and balanced binary sequences with odd period N are made use of, our construction produces new balanced quaternary sequences with optimal autocorrelation value (OAV), in which there are N distinct sequences in terms of cyclic shift equivalence, and includes Tang, et al.'s and Jang, et al.'s ones as special cases. In addition, when binary sequences without period 2ⁿ-1 or balance are employed, the transformation of Jang, et al.'s method is invalid, however, the proposed construction works very good. As a consequence, this unified construction allows us to construct optimal and balanced quaternary sequences from ideal/optimal balanced binary sequences with arbitrary period.},
keywords={},
doi={10.1587/transfun.E96.A.1593},
ISSN={1745-1337},
month={July},}

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TY - JOUR
TI - A Unified Construction for Yielding Quaternary Sequences with Optimal Periodic Autocorrelation
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 1593
EP - 1601
AU - Fanxin ZENG
AU - Xiaoping ZENG
AU - Zhenyu ZHANG
AU - Guixin XUAN
PY - 2013
DO - 10.1587/transfun.E96.A.1593
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E96-A
IS - 7
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - July 2013
AB - A unified construction for transforming binary sequences of balance or unbalance into quaternary sequences is presented. On the one hand, when optimal and balanced binary sequences with even period are employed, our construction is exactly the same Jang, et al.'s and Chung, et al.'s ones, which result in balanced quaternary sequences with optimal autocorrelation magnitude. On the other hand, when ideal and balanced binary sequences with odd period N are made use of, our construction produces new balanced quaternary sequences with optimal autocorrelation value (OAV), in which there are N distinct sequences in terms of cyclic shift equivalence, and includes Tang, et al.'s and Jang, et al.'s ones as special cases. In addition, when binary sequences without period 2ⁿ-1 or balance are employed, the transformation of Jang, et al.'s method is invalid, however, the proposed construction works very good. As a consequence, this unified construction allows us to construct optimal and balanced quaternary sequences from ideal/optimal balanced binary sequences with arbitrary period.
ER -