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Spectral classification and multiplicative partitioning of constant-weight sequences based on circulant matrix representation of optical orthogonal codes

Alem Karladani, M. M ; Sharif University of Technology

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  1. Type of Document: Article
  2. DOI: 10.1109/TIT.2010.2054570
  3. Abstract:
  4. Considering the space of constant-weight sequences as the reference set for every optical orthogonal code (OOC) design algorithm, we propose a classification method that preserves the correlation properties of sequences. First, we introduce the circulant matrix representation of optical orthogonal codes and, based on the spectrum of circulant matrices, we define the spectral classification of the set Sn,w of all (0, 1)-sequences with length n, weight w, and the first chip 1. Then, as a method for spectrally classifying the set Sn,w, we discuss an algebraic structure called multiplicative group action. Using the above multiplicative group action, we define an equivalence relation on Sn,w in order to classify it into equivalence classes called multiplicative partitions which are the same as the spectral classes. The algebraic properties of the proposed partitioning such as the number of classes and the size of each class are investigated and in the case of prime n, a novel formula for the number of classes is derived. Finally, we present and prove the autocorrelation, intraclass and interclass cross-correlation properties of our proposed classification of the space S n,w that decrease the computational complexity of search algorithms in designing and constructing (n,w,λa,λc)- OOC
  5. Keywords:
  6. Cross correlation ; Group action ; Optical orthogonal code (OOC) ; Circulant matrix ; Cross correlations ; Group actions ; Multiplicative partitioning ; Optical orthogonal codes ; Spectral classification ; Algebra ; Autocorrelation ; Codes (symbols) ; Computational complexity ; Data communication systems ; Equivalence classes ; Image classification ; Optical correlation ; Set theory ; Matrix algebra
  7. Source: IEEE Transactions on Information Theory ; Volume 56, Issue 9 , 2010 , Pages 4659-4667 ; 00189448 (ISSN)
  8. URL: http://ieeexplore.ieee.org/document/5550470