Large Families of Asymptotically Optimal Two-Dimensional Optical Orthogonal Codes

Omrani, Reza; Garg, Gagan; Kumar, P. Vijay; Elia, Petros; Bhambhani, Pankaj

doi:10.1109/tit.2011.2169299

Cited by 36 publications

(21 citation statements)

References 69 publications

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“…Note that in the particular case where

m = 1

and

n = v

, the 2D

(m \times n, k, λ)

‐OOC is nothing else than a 1D

(v, k, λ)

‐OOC. Many constructions for 2D

(m \times n, k, λ)

‐OOCs have been given, see .…”

Section: M‐cyclic H(mn43)′s Applicationmentioning

confidence: 99%

Constructions of Strictlym-Cyclic and Semi-Cyclic H(m,n,4,3)

Bao

Ji²

2015

J. Combin. Designs

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An H(m, n, 4, 3) is a triple (X, T , B), where X is a set of mn points, T is a partition of X into m disjoint sets of size n and B is a set of 4-element transverses of T , such that each 3-element transverse of T is contained in exactly one of them. If the full automorphism group of an H(m, n, 4, 3) admits an automorphism α consisting of n cycles of length m (resp. m cycles of length n), then this H(m, n, 4, 3) is called m-cyclic (resp. semi-cyclic). Further, if all blockorbits of an m-cyclic (resp. semi-cyclic) H(m, n, 4, 3) are full, then it is called strictly cyclic. In this paper, we construct some infinite classes of strictly m-cyclic and semi-cyclic H(m, n, 4, 3), and use them to give new infinite classes of perfect two-dimensional optical orthogonal codes with maximum collision parameter λ = 2 and AM-OPPTS/AM-OPPW property.

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“…Note that in the particular case where

m = 1

and

n = v

, the 2D

(m \times n, k, λ)

‐OOC is nothing else than a 1D

(v, k, λ)

‐OOC. Many constructions for 2D

(m \times n, k, λ)

‐OOCs have been given, see .…”

Section: M‐cyclic H(mn43)′s Applicationmentioning

confidence: 99%

Constructions of Strictlym-Cyclic and Semi-Cyclic H(m,n,4,3)

Bao

Ji²

2015

J. Combin. Designs

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“…Moreover, Omrani and Kumar proposed two-dimensional OOCs which spread both time and wavelength domain [17]. For a survey of two-dimensional OOCs, we refer to [18].…”

Section: Theorem 2 ([5] Johnson Bound) Anmentioning

confidence: 99%

New constructions of asymptotically optimal optical orthogonal codes with λ = 1

Chung

Yang

2012

2012 IEEE International Symposium on Information Theory Proceedings

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Optical orthogonal codes (OOCs) are widely used as spreading codes in optical fiber networks. For reliable and efficient data transmission in these systems, it is required to design OOCs with low correlation and large size. In this paper, we present two new constructions for asymptotically optimal OOCs with respect to the Johnson bound, whose maximum nontrivial correlation value is 1. We first construct an asymptotically optimal OOC of length (p − 1)p 2 for an odd prime p by using the structure of the ring of integers modulo p 2 . We then present an asymptotically optimal OOC of length Mp1p2 from a product of two finite fields, where p1 and p2 are odd primes, and M is an integer such that M | pi − 1 for i = 1, 2.Index Terms-Correlation, optical fiber networks, finite fields, ring of integers modulo n, optical orthogonal codes (OOCs).

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“…When

λ_{a} = λ_{c} = λ

, much work has been done by many authors to determine the exact value of

Φ (n \times m, k, λ, λ)

. The reader may refer to for more information.…”

Section: Introductionmentioning

confidence: 99%

Optimal Two‐Dimensional Optical Orthogonal Codes with the Best Cross‐Correlation Constraint

Feng

Wang

et al. 2016

J of Combinatorial Designs

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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 λa 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,λa,1)‐optical orthogonal codes. When k=3 and λa=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(mod4).

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Large Families of Asymptotically Optimal Two-Dimensional Optical Orthogonal Codes

Cited by 36 publications

References 69 publications

Constructions of Strictlym-Cyclic and Semi-Cyclic H(m,n,4,3)

Constructions of Strictlym-Cyclic and Semi-Cyclic H(m,n,4,3)

New constructions of asymptotically optimal optical orthogonal codes with λ = 1

Optimal Two‐Dimensional Optical Orthogonal Codes with the Best Cross‐Correlation Constraint

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Large Families of Asymptotically Optimal Two-Dimensional Optical Orthogonal Codes

Cited by 36 publications

References 69 publications

Constructions of Strictlym-Cyclic and Semi-Cyclic H(m,n,4,3)

Constructions of Strictlym-Cyclic and Semi-Cyclic H(m,n,4,3)

New constructions of asymptotically optimal optical orthogonal codes with &#x03BB; &#x003D; 1

Optimal Two‐Dimensional Optical Orthogonal Codes with the Best Cross‐Correlation Constraint

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New constructions of asymptotically optimal optical orthogonal codes with λ = 1