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Optimal Two‐Dimensional Optical Orthogonal Codes with the Best Cross‐Correlation Constraint
Author(s) -
Feng Tao,
Wang Lidong,
Wang Xiaomiao,
Zhao Yancai
Publication year - 2017
Publication title -
journal of combinatorial designs
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.618
H-Index - 34
eISSN - 1520-6610
pISSN - 1063-8539
DOI - 10.1002/jcd.21554
Subject(s) - mathematics , combinatorial design , orthogonal array , code (set theory) , correlation , combinatorics , discrete mathematics , algorithm , computer science , geometry , statistics , set (abstract data type) , taguchi methods , programming language
The study of optical orthogonal codes has been motivated by an application in an optical code‐division multiple access system. From a practical point of view, compared to one‐dimensional optical orthogonal codes, two‐dimensional optical orthogonal codes tend to require smaller code length. On the other hand, in some circumstances only with good cross‐correlation one can deal with both synchronization and user identification. These motivate the study of two‐dimensional optical orthogonal codes with better cross‐correlation than auto‐correlation. This paper focuses on optimal two‐dimensional optical orthogonal codes with the auto‐correlation λ a and the best cross‐correlation 1. By examining the structures of w ‐cyclic group divisible designs and semi‐cyclic incomplete holey group divisible designs, we present new combinatorial constructions for two‐dimensional ( n × m , k , λ a , 1 ) ‐optical orthogonal codes. When k = 3 andλ a = 2 , the exact number of codewords of an optimal two‐dimensional ( n × m , 3 , 2 , 1 ) ‐optical orthogonal code is determined for any positive integers n and m ≡ 2( mod 4 ) .