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Optical orthogonal codes: their bounds and new optimal constructions

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2 Author(s)
Fuji-Hara, R. ; Inst. of Policy & Planning Sci., Tsukuba Univ., Japan ; Ying Miao

A (v, k, λa, λc) optical orthogonal code (OOC) C is a family of (0, 1)-sequences of length v and weight k satisfying the following two correlation properties: (1) Σ0⩽t⩽v-1xtxt+i ⩽λa for any x=(x0,x1,···,xv-1 )∈C and any integer i not equivalent 0 mod v; and (2) Σ 0⩽t⩽v-1xtyt+i⩽λ b for any x=(x0,x1,···, xv-1) ∈ C, y=(y0,y1,···,yv-1) ∈C with x≠y, and any integer i, where the subscripts are taken modulo v. The study of optical orthogonal codes is motivated by an application in optical code-division multiple-access communication systems. In this paper, upper bounds on the size of an optical orthogonal code are discussed. Several new constructions for optimal optical orthogonal codes with weight k⩾4 and correlation constraints λac=1 are described by means of optimal cyclic packings. Many new infinite series of such optimal optical orthogonal codes are thus produced

Published in:

Information Theory, IEEE Transactions on  (Volume:46 ,  Issue: 7 )

Date of Publication:

Nov 2000

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