Family Of Optical Orthogonal Codes Research Articles

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

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> A new construction of optical orthogonal codes is provided in this correspondence which is a generalization of the well-known construction of distinct difference set (DDS) by Bose and Chowla. This construction is optimal with respect to the Johnson bound and has parameters <emphasis><formula formulatype="inline"> <tex>$n=q^a-1,$</tex></formula></emphasis> <emphasis><formula formulatype="inline"> <tex>$\omega=q,$</tex></formula></emphasis> and <emphasis><formula formulatype="inline"> <tex>$\lambda=1$</tex></formula></emphasis>. </para>

Classes of optical orthogonal codes from arcs in root subspaces

We present new constructions for ( n , w , λ ) optical orthogonal codes (OOC) using techniques from finite projective geometry. In one case codewords correspond to ( q - 1 ) -arcs contained in Baer subspaces (and, in general, k th-root subspaces) of a projective space. In the other construction, we use sublines isomorphic to PG ( 2 , q ) lying in a projective plane isomorphic to PG ( 2 , q k ) , k > 1 . Our construction yields for each λ > 1 an infinite family of OOCs which, in many cases, are asymptotically optimal with respect to the Johnson bound.

Outer-Product Matrix Representation of Optical Orthogonal Codes

In this letter, we introduce a whole new approach in defining and representing optical orthogonal codes (OOCs), namely, outer-product matrix representation. Instead of applying commonly used approaches based on inner product to construct OOC codes, we use the newly defined approach to obtain a more efficient algorithm in constructing and generating OOC codes. The outer-product matrix approach can obtain a family of OOC codes with a cardinality closer to the Johnson upper bound, when compared with the previously defined accelerated greedy algorithm using the inner-product approach. We believe the new look introduced in this letter on OOCs could help to devise new approaches in designing and generating OOC codes, using the rich literature in matrix algebra

Optical orthogonal codes and arcs in [formula omitted

We present a new construction for ( n , w , λ ) -optical orthogonal codes (OOCs). The construction is pleasingly simple, where codewords correspond to arcs, specifically normal rational curves. Moreover, our construction yields for each λ > 1 an infinite family of OOCs which are asymptotically optimal (with respect to the Johnson bound).

New optical orthogonal codes by using diophantine equations

Two families of optical orthogonal codes (OOC's) are algebraically designed by using the parametric binary quartic and quadratic forms. The first family of codes has ideal auto and cross-correlation properties and the second family has nonideal cross-correlation properties. The performance of these codes is presented as function of the number of simultaneous OCDMA system users. We present examples of the constructed codes for illustration purposes. The algebraic OOC's being proposed in this paper find applications in asynchronous optical code division multiple access (OCDMA) systems.

Performance analysis of optical orthogonal codes in CDMA LANs

The adoption of optical signal processing in CDMA LANs requires the design of new families of spreading codes called optical orthogonal codes (OOCs), due to the absence of negative elements in the system. Previously, performance analysis used in electrical signal-processing systems has been applied in optical systems without taking into account the differences between the two systems. The probabilities of data bit errors for systems with OOCs as spreading codes are derived and evaluated by taking into account these differences. The analysis presents a more realistic picture of the performance of OOCs in optical CDMA LANs, and hence provides a reliable way of comparing the performances of different families of OOCs.

Multimedia transmission in fiber-optic LANs using optical CDMA

In this paper, we address the problem of multimedia transmission in fiber-optic networks. We apply the code-division multiple-access (CDMA) technique for such a network. The necessary conditions for successful operation of the network are given. It is shown that for successful operation, new families of optical orthogonal codes (OOCs) are needed which will have not only good correlation properties within one code family, but also between families of different code lengths. Some possible constructions of multimedia OOCs and the corresponding basic structure of the receiver for the multimedia network are given. Specific examples of OOCs for the case of users with two different data rates are given, and the probability of error (using the Gaussian approximation) as a function of the number of low and high rate users is calculated.

Construction and performance analysis of a new family of optical orthogonal codes for CDMA fiber-optic networks

A construction of a new family of optical orthogonal codes (OOCs) for use in code division multiple access (CDMA) fiber-optic networks is given. Previous families of OOCs are reviewed and basic requirements for successful implementation of the fiber-optic CDMA system given. The new code construction is based on Costas (1970) arrays and the codes are proved to be (/spl omega/(2p-3), /spl omega/, 1, 1), p a prime and /spl omega/*Q/spl les/p-1, where Q is the maximum number of users, OOCs. The probability of error (using the Gaussian approximation) in the multiuser system as a performance measure is calculated and compared with that of existing OOCs. The size of the code family is compared against the Johnson bound. >

Some new families of optical orthogonal codes for code-division multiple-access fibre-optic networks

An optical orthogonal code (OOC) is a collection of binary sequences with good auto- and cross-correlation properties; they were defined by Chung and others as a means of obtaining code division multiple access on optical networks. In the paper three new families of OOCs are constructed from the balanced incompleted block design techniques. The first family of the codes is with ideal auto- and cross-correlation properties and they have optimal cardinalities. The other two families of the codes are with ideal auto-correlation and nearly ideal cross-correlation properties. The second family of the codes is demonstrated to have twice as many codewords as the optimal codes. The third family of the codes is demonstrated to have more codewords than the quadratic congruence codes when the weight of the codeword is less than eight.

A new family of optical code sequences for use in spread-spectrum fiber-optic local area networks

The problem of the algebraic construction of a particular family of optical codes for use in code-division multiple-access (CDMA) fiber-optic local area networks (LANs) is treated. The conditions that the code families have to satisfy when used in such systems are reviewed. The new codes are called quadratic congruence codes, and the construction of the corresponding sequences is based on the number-theoretic concept of quadratic congruences. It is shown that p-1 codes exist for every odd prime p and can serve as many as p-1 different users in the CDMA fiber-optic system. The codes belong to the family of optical orthogonal codes, their auto- and cross-correlation properties are established, and their performance is compared to that of the previous optical codes. Examples of the codes and examples of their auto- and cross-correlation functions are given. >

New family of algebraically designed optical orthogonal codes for use in CDMA fibre-optic networks

The construction of a new family of optical orthogonal codes (OOC) with nearly ideal auto- and crosscorrelation properties for use in fibre-optic networks is presented. The codes are proved to be [(p * (2p − 1)] OOC codes and their construction is based on properties of quadratic congruences. The codes are named extended quadratic congruence (EQC) codes.