Perfect Sequences of Odd Prime Length

A sequence is said to be perfect if it has an ideal periodic autocorrelation function. In addition, the degree of a sequence is defined as the number of distinct nonzero elements within each period of the sequence. This study presents a systematic method for constructing perfect sequences (PSs) of o...

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Bibliographic Details
Published in:IEEE signal processing letters 2018-07, Vol.25 (7), p.966-969
Main Authors: Li, Chih-Peng, Chang, Kuo-Jen, Chang, Ho-Hsuan, Chen, Yen-Ming
Format: Article
Language:English
Subjects:
Channel estimation
Correlation
Cyclic group
finite field
Indexes
perfect sequence (PS)
periodic autocorrelation function (PACF)
Solids
Spread spectrum communication
Synchronization
Systematics
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Summary:A sequence is said to be perfect if it has an ideal periodic autocorrelation function. In addition, the degree of a sequence is defined as the number of distinct nonzero elements within each period of the sequence. This study presents a systematic method for constructing perfect sequences (PSs) of odd prime periods, where the general constraint equations for the sequence coefficients are derived, providing a solid theoretical foundation to the construction of PSs. The proposed scheme commences by partitioning a cyclic group Z P = {1, 2, ⋯ , P - 1} into K cosets of cardinality M, where P = K · M + 1 is an odd prime. Based on this partition, the degree-(K + 1) PSs are then constructed. Finally, case studies are presented to illustrate the proposed construction.
ISSN:1070-9908
1558-2361
DOI:10.1109/LSP.2018.2832719