Open AccessSets of frequency hopping sequences under aperiodic Hamming correlation: Upper bound and optimal constructions
Author(s) -
Xing Liu,
Daiyuan Peng
Publication year - 2014
Publication title -
advances in mathematics of communications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.601
H-Index - 26
eISSN - 1930-5346
pISSN - 1930-5338
DOI - 10.3934/amc.2014.8.359
Subject(s) - aperiodic graph , mathematics , hamming distance , sequence (biology) , hamming code , upper and lower bounds , combinatorics , hamming bound , hamming(7,4) , hamming weight , frequency hopping spread spectrum , hamming graph , discrete mathematics , complementary sequences , algorithm , mathematical analysis , block code , telecommunications , computer science , decoding methods , genetics , biology
In order to evaluate the goodness of frequency hopping (FH) sequence design, the periodic Hamming correlation function is used as an important measure. Aperiodic Hamming correlation of FH sequences matters in real applications, while it received little attraction in the literature compared with periodic Hamming correlation. In this paper, an upper bound on the family size of FH sequences, with respect to the size of the frequency slot set, the sequence length, the maximum aperiodic Hamming correlation is established. Further, a construction of optimal FH sequence sets under aperiodic Hamming correlation from Reed-Solomon codes is presented, whose parameters meet the upper bound with equality. From generalized $m$ sequences (GM sequences) and generalized Gordon-Mills-Welch sequences (GGMW sequences), two classes of optimal FH sequence sets under aperiodic Hamming correlation are also presented, whose parameters meet the upper bound with equality.
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