Applied Algebra, Algebraic Algorithms and ErrorCorrecting Codes
Volume 1719 of the series Lecture Notes in Computer Science pp 410419
New Lower Bounds on the Periodic Crosscorrelation of QAM Codes with Arbitrary Energy
 Serdar BoztaşAffiliated withDepartment of Mathematics, RMIT University
Abstract
In this paper, we consider a recent technique of Levenshtein [9] which was introduced to prove improved lower bounds on aperiodic correlation of sequence families over the complex roots of unity. We first give a new proof of the Welch [12] lower bound on the periodic correlation of complex roots of unity sequences using a modification of Levenshtein’s technique. This improves the Welch lower bound in the case that the family size is “large enough” compared to sequence length. Our main result is an improved lower bound on the periodic complex valued sequences with QAMtype alphabets. This result improves an earlier result by Boztaş [2]. To achieve this result, we extend the Levenshtein technique in a new direction.
Here, we assume that sequences are drawn from energy “shells” which are no more than PSK signal sets with the scaling determining the signal energy. It turns out that, if the weights are associated with the energy of the sequence in question, the Levenshtein technique can be modified to obtain lower bounds.
The new bound is a nonconvex function of a set of suitably chosen “weights.” We demonstrate that our results improve those of [2] with a concrete example.
 Title
 New Lower Bounds on the Periodic Crosscorrelation of QAM Codes with Arbitrary Energy
 Book Title
 Applied Algebra, Algebraic Algorithms and ErrorCorrecting Codes
 Book Subtitle
 13th International Symposium, AAECC13 Honolulu, Hawaii, USA, November 15–19, 1999 Proceedings
 Pages
 pp 410419
 Copyright
 1999
 DOI
 10.1007/3540467963_39
 Print ISBN
 9783540667230
 Online ISBN
 9783540467960
 Series Title
 Lecture Notes in Computer Science
 Series Volume
 1719
 Series ISSN
 03029743
 Publisher
 Springer Berlin Heidelberg
 Copyright Holder
 SpringerVerlag Berlin Heidelberg
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 Editors

 Marc Fossorier ^{(4)}
 Hideki Imai ^{(5)}
 Shu Lin ^{(4)}
 Alain Poli ^{(6)}
 Editor Affiliations

 4. Department of Electrical Engineering, University of Hawaii
 5. Institute of Industrial Science, University of Tokyo
 6. AAECC/IRIT, Université Paul Sabatier
 Authors

 Serdar Boztaş ^{(7)}
 Author Affiliations

 7. Department of Mathematics, RMIT University, GPO Box 2476V, Melbourne, 3001, Australia
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