Meeting the Levenshtein bound with equality by weighted-correlation complementary set
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 Le...
| Main Authors: | , |
|---|---|
| Other Authors: | |
| Format: | Conference Paper |
| Language: | English |
| Published: |
2013
|
| Subjects: | |
| Online Access: | https://hdl.handle.net/10356/102566 http://hdl.handle.net/10220/16358 |
| _version_ | 1811694541382615040 |
|---|---|
| author | Liu, Zi Long Guan, Yong Liang |
| author2 | School of Electrical and Electronic Engineering |
| author_facet | School of Electrical and Electronic Engineering Liu, Zi Long Guan, Yong Liang |
| author_sort | Liu, Zi Long |
| collection | NTU |
| description | 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. |
| first_indexed | 2024-10-01T07:09:13Z |
| format | Conference Paper |
| id | ntu-10356/102566 |
| institution | Nanyang Technological University |
| language | English |
| last_indexed | 2024-10-01T07:09:13Z |
| publishDate | 2013 |
| record_format | dspace |
| spelling | ntu-10356/1025662020-03-07T13:24:51Z Meeting the Levenshtein bound with equality by weighted-correlation complementary set Liu, Zi Long Guan, Yong Liang School of Electrical and Electronic Engineering IEEE International Symposium on Information Theory (2012 : Cambridge, US) DRNTU::Engineering::Computer science and engineering::Data::Coding and information theory 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. 2013-10-10T03:48:10Z 2019-12-06T20:57:00Z 2013-10-10T03:48:10Z 2019-12-06T20:57:00Z 2012 2012 Conference Paper Liu, Z. L., & Guan, Y. L. (2012). Meeting the Levenshtein bound with equality by weighted-correlation complementary set. 2012 IEEE International Symposium on Information Theory (ISIT), pp.1010-1013. https://hdl.handle.net/10356/102566 http://hdl.handle.net/10220/16358 10.1109/ISIT.2012.6282286 en |
| spellingShingle | DRNTU::Engineering::Computer science and engineering::Data::Coding and information theory Liu, Zi Long Guan, Yong Liang Meeting the Levenshtein bound with equality by weighted-correlation complementary set |
| title | Meeting the Levenshtein bound with equality by weighted-correlation complementary set |
| title_full | Meeting the Levenshtein bound with equality by weighted-correlation complementary set |
| title_fullStr | Meeting the Levenshtein bound with equality by weighted-correlation complementary set |
| title_full_unstemmed | Meeting the Levenshtein bound with equality by weighted-correlation complementary set |
| title_short | Meeting the Levenshtein bound with equality by weighted-correlation complementary set |
| title_sort | meeting the levenshtein bound with equality by weighted correlation complementary set |
| topic | DRNTU::Engineering::Computer science and engineering::Data::Coding and information theory |
| url | https://hdl.handle.net/10356/102566 http://hdl.handle.net/10220/16358 |
| work_keys_str_mv | AT liuzilong meetingthelevenshteinboundwithequalitybyweightedcorrelationcomplementaryset AT guanyongliang meetingthelevenshteinboundwithequalitybyweightedcorrelationcomplementaryset |