A Generalized Bose-Chowla Family of Optical Orthogonal Codes and Distinct Difference Sets

Chen

et al. 2015

J. Lightwave Technol.

Optical codes with large cardinality and tree structure of multiple levels of subsets of codewords for adjustable performance and cardinality have recently been studied. These codes support contemporary applications, such as a scalable, multihop, multilevel network architecture with rapid codeswitching/dropping and multicode-keying encryption for improving physical-layer confidentiality in optical code-division multiple-access systems and networks. In this paper, to further enlarge such code collection, two new families of optical codes are constructed from the rich families of cyclic maximal-distanceseparable (MDS) codes. The code performances are algebraically analyzed using both the distance and weight distributions of the MDS codes and validated with computer simulation.

Section: B Mds-based Optical Codes Of Lengthmentioning

confidence: 99%

New Tree-Structured Optical Codes for Incoherent Optical-CDMA Applications

Liu

Chen

et al. 2015

J. Lightwave Technol.

“…Another new optimal class of VW-OOCs can be constructed from the optimal u k − 1, u, 1, 1 CW-OOC of size u k−2 + u k−3 + · · · + 1 in [23], where u is a prime power and k ≥ 2.…”

Section: Corollarymentioning

confidence: 99%

New Families of Optimal Variable-Weight Optical Orthogonal Codes With High Weights

Chung

IEEE Trans. Inform. Theory

2015

The optical orthogonal codes (OOCs) have been widely used as spreading codes in communication systems employing the unipolar transmission. They are classified into constant-weight OOCs (CW-OOCs) and variable-weight OOCs (VW-OOCs) according to the number of distinct Hamming weights which their codewords have. In this paper, we present a new generic construction of VW-OOCs of length (q − 1)N from a CW-OOC of length N, where q is a prime power and gcd(q − 1, N) = 1. As a result, three new families of optimal VW-OOCs with a maximum correlation value 1 are obtained. In particular, these families can have the codewords of high weights, while most of the previously known optimal VW-OOCs have only codewords of weight less than 8.

“…In [3], Chung, Salehi, and Wei presented a guideline for design of OOCs, and gave some constructions of optimal OOCs. Since then, several constructions for (asymptotically) optimal OOCs with small λ have been reported in the literature (see [6]- [15]). Moreover, Omrani and Kumar proposed two-dimensional OOCs which spread both time and wavelength domain [17].…”

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

confidence: 99%

“…optimal or asymptotically optimal [15] (q a − 1, q, 1, 1) q a−2 + q a−3 + · · · + 1 a ≥ 2 optimal Theorem 7 ((p − 1)p 2 , p − 1, 1, 1) p + 1 − asymptotically optimal Theorem 11 (Mp 1 p 2 , M, 1, 1) Then…”

Section: Referencementioning

confidence: 99%

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

Chung

2012 IEEE International Symposium on Information Theory Proceedings

2012

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).