Improved constructions and bounds for 2-D optical orthogonal codes

Omrani, Reza; Kumar, P. Vijay

doi:10.1109/isit.2005.1523307

Cited by 16 publications

(19 citation statements)

References 13 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Afterwards, we compare the value of K p,C1 satisfying (5) and (7) and the value of K p,C2 satisfying (6) and (8). The larger of them will be the minimum number of padding zeros, K p , required for both codewords in order to preserve λ c = 1 after folding.…”

Section: Zero-padding Folding Methodsmentioning

confidence: 99%

“…For example, Yang and Kwong [4] proposed a direct code-mapping method, which constructed various 2-D carrier-hopping prime codes from 1-D prime sequences. Omrani and Kumar [8] used the Chinese remainder theorem [10] to perform a one-to-one mapping from n-tuples of 1-D optical orthogonal codes (OOCs) into M × N matrices of 2-D OOCs, where n is the code length of the 1-D OOCs, M is the number of wavelengths used in the 2-D OOCs, and N is the code length of the 2-D OOCs, n = MN, and M and N are relatively prime. (Note: the term OOCs refer to those optical codes with λ c = 1.)…”

Section: Introductionmentioning

confidence: 99%

“…(Note: the term OOCs refer to those optical codes with λ c = 1.) Omrani and Kumar [8] further stated that 2-D OOCs with optimal cardinality could be obtained if the original 1-D OOCs were optimal (in cardinality). However, optimal 1-D OOCs usually require the use of a prime n [2], thus rendering their method with limited applications.…”

Section: Introductionmentioning

confidence: 99%

“…To match the code length n of the Golomb rulers with the M ×N matrices of the folded 2-D optical codes, Mendez et al padded MN −n zeros to the end of the Golomb rulers before folding. This "zeropadding" method did not have the limitation of n = MN and, thus, was more flexible in the choice of M and N than the Chinese remainer theorem in [8]. By selectively rotating the Golomb rulers before folding, Mendez et al improved the cardinality of the folded 2-D optical codes.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Three Code-Mapping Methods for Optical CDMA

Chang

Yang

et al. 2010

2010 Symposium on Photonics and Optoelectronics

View full text Add to dashboard Cite

In this paper, we propose three code-mapping methods, which make use of existing optical codes of one dimension to construct optical codes of a different dimension. A reverse codemapping method is first introduced, which allows the generation of 1-D prime codes from their 2-D counterparts. Afterwards, the one-to-one correspondence between 1-D and 2-D optical codes is established with the use of the Chinese remainder theorem. This theorem is then used for the first time to generate rare, difficultto-construct 1-D optical codes of cross-correlation values of at most two. Finally, an improved zero-padding folding method for mapping 1-D to 2-D optical codes with more flexible selection of code parameters than previous methods is detailed.

show abstract

Section: Zero-padding Folding Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Three Code-Mapping Methods for Optical CDMA

Chang

Yang

et al. 2010

2010 Symposium on Photonics and Optoelectronics

View full text Add to dashboard Cite

show abstract

“…Using the bound for non-binary constant weight codes introduced in [12] we can bound size our construction by:…”

mentioning

confidence: 99%

A new method to construct double periodic arrays with optimal correlation

Moreno¹,

Ortiz-Ubarri

2009

2009 IEEE Information Theory Workshop

View full text Add to dashboard Cite

Double-periodic arrays with good correlation are useful for applications in multiple target Costas and sonar, optical communications, and more recently digital watermarking. There are only a few double-periodic constructions with perfect correlation. In previous work we presented a method to construct families of double-periodic arrays with perfect correlation from the Welch Costas construction using the Chinese Remainder. In this work we introduce a similar method to construct new families of double-periodic arrays without using the Chinese Remainder. We apply this new method to the Quadratic sonar and the Welch Costas arrays to produce new families of doubleperiodic arrays with perfect correlation properties. We also apply the method to the family of Quadratic sonars to produce new families of double-periodic arrays with close to perfect correlation. Finally we discuss the family size optimality of the constructions.

show abstract

n-dimensional optical orthogonal codes, bounds and optimal constructions

Alderson

2019

AAECC

View full text Add to dashboard Cite

We generalized to higher dimensions the notions of optical orthogonal codes. We establish uper bounds on the capacity of general n-dimensional OOCs, and on specific types of ideal codes (codes with zero off-peak autocorrelation). The bounds are based on the Johnson bound, and subsume many of the bounds that are typically applied to codes of dimension three or less. We also present two new constructions of ideal codes; one furnishes an infinite family of optimal codes for each dimension n ≥ 2, and another which provides an asymptotically optimal family for each dimension n ≥ 2. The constructions presented are based on certain point-sets in finite projective spaces of dimension k over GF (q) denoted P G(k, q).

show abstract

Improved constructions and bounds for 2-D optical orthogonal codes

Cited by 16 publications

References 13 publications

Three Code-Mapping Methods for Optical CDMA

Three Code-Mapping Methods for Optical CDMA

A new method to construct double periodic arrays with optimal correlation

n-dimensional optical orthogonal codes, bounds and optimal constructions

Contact Info

Product

Resources

About