Quadratic Congruence Code Research Articles

Modified quadratic congruence codes for fiber Bragg-grating-based spectral-amplitude-coding optical CDMA systems

We have constructed a series of new code families for the spectral-amplitude-coding optical code-division multiple-access (CDMA) system, and proposed new transmitter and receiver structures based on tunable chirped fiber Bragg gratings (FBGs). The proposed system has been analyzed by taking into account the effects of phase-induced intensity noise, shot noise, and thermal noise. We have also compared the performance of this system with that of a former system where a Hadamard code is used. It has been shown that the new code families can suppress the intensity noise effectively and improve the system performance significantly. When the effective power is large (i.e., >-10 dBm), the intensity noise is the main factor that limits the system performance. When the effective power is not sufficiently large, thermal and shot noise sources become the main limiting factors and the effect of thermal noise is much larger than that of shot noise.

Letter: Cyclical coincidence arrays and exact pdfs representing interference for some CDMA systems

AbstractA new class of coincidence (hit) arrays called cyclical hit arrays is defined. Cyclical hit arrays give insight into previously unknown properties of several sets of number theoretic frequency‐hop patterns, based on Welch‐Costas and Quadratic Congruence codes. Three theorems related to cyclical hit arrays are proved. The theorems are used to determine exact probability distribution functions of random variables which represent the number of coincidences between two arbitrary patterns from the same set of codes. The number of coincidences expresses interference levels between two users of code‐division multiple‐access (CDMA) systems which utilize the considered patterns. The obtained results can be used for computing the exact expressions for the total interference and for error probabilities in several CDMA systems.

Massive optical LANs using wavelength hopping/time spreading with increased security

A hybrid wavelength hopping/time spreading all-optical code division multiple access (CDMA) system using extended quadratic congruence codes for spreading and prime codes and their cyclic shifts for hopping is examined. The codes feature excellent correlation properties even in the case of an asymmetric system with random wavelength selection and the number of codes in the family is substantially increased making them attractive for massive, asynchronous LAN's with increased security demands.

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.

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.

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. >