Generalization and Improvement of the Levenshtein Lower Bound for Aperiodic Correlation

Fabien Arlery (1, 2, 3, 4) , Uy Hour Tan (1, 5) , Olivier Rabaste (6)

1 Thales Air Systems
2 TIPIC-SAMOVAR - Traitement de l'Information Pour Images et Communications
3 TSP - CITI - Communications, Images et Traitement de l'Information
4 CNRS - Centre National de la Recherche Scientifique
5 SONDRA - Sondra, CentraleSupélec, Université Paris-Saclay (COmUE)
6 DEMR, ONERA, Université Paris Saclay (COmUE) [Palaiseau]

This article 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.

Domaines: Electromagnétisme

Fabien Arlery, Uy Hour Tan, Olivier Rabaste. Generalization and Improvement of the Levenshtein Lower Bound for Aperiodic Correlation. IEEE Transactions on Information Theory, 2019, 65 (2), pp.1258-1266. ⟨10.1109/TIT.2018.2844189⟩. ⟨hal-02053343⟩