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Generalization and Improvement of the Levenshtein Lower Bound for Aperiodic Correlation

Arlery, Fabien and Tan, Uly Hour and Rabaste, Olivier Generalization and Improvement of the Levenshtein Lower Bound for Aperiodic Correlation. (2019) IEEE Transactions on Information Theory, 65 (2). 1258-1266. ISSN 0018-9448

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Official URL: http://doi.org/10.1109/TIT.2018.2844189

Abstract

This paper deals with lower bounds on aperiodic correlation of sequences. It intends to solve two open questions. The first one is on the validity of the Levenshtein bound for a set of sequences other than binary sequences or those over the roots of unity. Although this result could be a priori extended to polyphase sequences, a formal demonstration is presented here, proving that it does actually hold for these sequences. The second open question is on the possibility to find a bound tighter than Welch’s, in the case of a set consisting of two sequences M = 2. By including the specific structure of correlation sequences, a tighter lower bound is introduced for this case. Besides, this method also provides in the cases M = 3 and M = 4 a tighter bound than the up-to-now tightest bound provided by Liu et al.

Item Type:Article
Additional Information:Thanks to the IEEE (Institute of Electrical and Electronics Engineers). This paper is available at : https://ieeexplore.ieee.org/document/8372628 “© 2019 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.
Audience (journal):International peer-reviewed journal
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Institution:French research institutions > Centre National de la Recherche Scientifique - CNRS (FRANCE)
Other partners > Institut Mines-Télécom (FRANCE)
French research institutions > Office National d'Etudes et Recherches Aérospatiales - ONERA (FRANCE)
Other partners > Ecole Supérieure d'Electricité - SUPELEC (FRANCE)
Other partners > Thales (FRANCE)
Other partners > CentraleSupélec (FRANCE)
Other partners > DSO National Laboratories - DSO (SINGAPORE)
Other partners > National University of Singapore - NUS (REPUBLIC OF SINGAPORE)
Other partners > Télécom SudParis - TSP (FRANCE)
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Deposited On:04 Mar 2019 17:29

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