TY - GEN
T1 - Meeting the Levenshtein bound with equality by weighted-correlation complementary set
AU - Liu, Zi Long
AU - Guan, Yong Liang
PY - 2012
Y1 - 2012
N2 - Levenshtein improved the Welch bound on aperiodic correlation by weighting the cyclic shifts of the sequences over complex roots-of-unity. Although many works have been concerned on meeting the Welch bound with equality, no such effort has been reported for the Levenshtein bound. We show that the Levenshtein bound with equality is met if and only if the non-trivial aperiodic correlations have identical amplitude for all time-shifts, and the sequences form a novel class of complementary set whose aperiodic correlation is defined as the conventional aperiodic correlation modulated by a simplex weighting vector.
AB - Levenshtein improved the Welch bound on aperiodic correlation by weighting the cyclic shifts of the sequences over complex roots-of-unity. Although many works have been concerned on meeting the Welch bound with equality, no such effort has been reported for the Levenshtein bound. We show that the Levenshtein bound with equality is met if and only if the non-trivial aperiodic correlations have identical amplitude for all time-shifts, and the sequences form a novel class of complementary set whose aperiodic correlation is defined as the conventional aperiodic correlation modulated by a simplex weighting vector.
UR - http://www.scopus.com/inward/record.url?scp=84867522794&partnerID=8YFLogxK
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U2 - 10.1109/ISIT.2012.6282286
DO - 10.1109/ISIT.2012.6282286
M3 - Conference contribution
AN - SCOPUS:84867522794
SN - 9781467325790
T3 - IEEE International Symposium on Information Theory - Proceedings
SP - 1010
EP - 1013
BT - 2012 IEEE International Symposium on Information Theory Proceedings, ISIT 2012
T2 - 2012 IEEE International Symposium on Information Theory, ISIT 2012
Y2 - 1 July 2012 through 6 July 2012
ER -