Nine new two-dimensional Optical Orthogonal Codes (2-D OOCs) are presented here, all sharing the common feature of a code size that is much larger in relation to the number of time slots than those of constructions appearing previously in the literature. Each of these constructions is either optimal or asymptotically optimal with respect to either the original Johnson bound or else a nonbinary version of the Johnson bound introduced in this paper. The first five codes are constructed using polynomials over finite fields—the first construction is optimal while the remaining four are asymptotically optimal. The next two codes are constructed using rational functions in place of polynomials and these are asymptotically optimal. The last two codes, also asymptotically optimal, are constructed by composing two of the above codes with a constant weight binary code. Also presented is a three-dimensional Optical Orthogonal Code (3-D OOC) that exploits the polarization dimension. Finally, phase-encoded optical CDMA is considered and construction of two efficient codes are provided.

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$n=q^a-1,$$\omega=q,$and$\lambda=1$.

Recently there has been some interest in optical CDMA (OCDMA) for optical networks. A major drawback of OCDMA systems is their low spectral efficiency. This paper explores a novel modulation scheme for OCDMA systems which increases the spectral efficiency called code-cycle modulation (CCM) which uses different cyclic shifts of the spreading sequence assigned to each user to transmit an M-ary information. While the idea of using M-ary OCDMA modulation has been proposed using other means, most of these modulation schemes need M different receiver units to recover the data which causes complexity and power issues in the receiver. The advantage of our scheme is that we propose a supporting receiver architecture which doesn't suffer from complexity and power issues as mentioned above. In the rest of the paper we analyze the performance of this modulation scheme.

The cyclic difference sets constructed by Singer are also examples of perfect distinct difference sets (DDS). The Bose construction of distinct difference sets, leads to a relative difference set. In this paper we introduce the concept of partial relative DDS and prove that an optical orthogonal code (OOC) construction due to Moreno et. al., is a partial relative DDS. We generalize the concept of ideal matrices previously introduced by Kumar and relate it to the concepts of this paper. Another variation of ideal matrices is introduced in this paper: Welch ideal matrices of dimension n by (n - 1). We prove that Welch ideal matrices exist only for n prime. Finally, we recast an old conjecture of Golomb on the Welch construction of Costas arrays using the concepts of this paper. This connection suggests that our construction of partial relative difference sets is in a sense, unique

There are only a few multiple target families of Costas and sonar arrays with perfect correlation property. In this paper using the Welch Costas array and some results from design theory we construct perfect auto and cross-correlation families of sonar and extended Costas arrays

In phase encoding optical CDMA (OCDMA) the spreading is achieved by encoding the phase of signal spectrum. In this paper we first derive a mathematical model for the output of phase encoding OCDMA systems. Based on this model we introduce a metric to design spreading sequences for asynchronous transmission. Then we connect the phase encoding sequence design problem to OFDM PMEPR (peak to mean envelope power ratio) problem. Using this connection we conclude that designing sequences with good properties for samples of timing delay guarantees that the same sequence to be good for all timing delays. Finally using generalized bent function we manage to construct a family of sequences which are good for asynchronous phase encoding OCDMA systems and using these sequences we introduce an M-ary modulation scheme for phase encoding OCDMA

Some bounds and efficient constructions for 2-D optical orthogonal codes (OOC) in which spreading is carried out over both wavelength and time are provided. Such codes are of current practical interest as they enable fiber-optic communication at lower chip rates. The bounds provided include 2-D versions of the Johnson bound as well as a novel bound based on an extension of the Johnson bound to non-binary alphabets. The Singleton bound is recovered as a special instance of this bound. Several constructions of 2-D OOC are presented in the paper and almost all of these are either optimal or else asymptotically optimum in the sense of having code size that equals or approaches the maximum possible as the size of the code matrix (along the dimension associated to time) approaches infinity. Our principal construction views each wavelength-time OOC as the plot of a function and the functions employed in the constructions belonging to this class are either polynomials or rational functions. Other constructions include a technique for deriving 2-D OOCs from 1-D OOCs using the Chinese remainder theorem, a means of making use of MDS codes to construct 2-D OOCs satisfying the one-pulse-per-wavelength constraint and a method of concatenating a constant-weight code with a one-pulse-per-wavelength 2-D OOC to generate OOCs with at most one pulse per wavelength

Optical orthogonal codes (OOC) are used as spreading sequences for optical CDMA networks. An OOC is a family of constant weight binary codes with a pre-specified maximum correlation parameter (MCP). Johnson in his 1962 paper introduced three bounds for constant weight codes, that we call bounds A, B, and hybrid. Subsequently Chung et al. adapted Johnson bound A to generate a bound for OOCs, which has been widely used to prove the optimality of OOCs. Johnson bound B has been used in a prior work of this paper's authors to prove the optimality of some OOCs. In this paper we give an improvement of this bound, and based on that prove the optimality of some other constructions which were not known to be optimal. Using the results from Agrell et al., 2000 paper we also give an improvement of Johnson hybrid bound for constant weight codes, and then use it to generate a bound for OOCs. Finally, we introduce a new family of OOCs, based on flats in an affine geometry. While OOCs based on lines and hyperplanes are optimal, we can't say much about other OOCs resulting from this construction. We show that the hybrid bound gives tighter bound than the other two bounds in some regions for this construction. Recently lot of interest has been shown to find all optimal OOCs with weight 4 and 5 and MCP 1 and 2. Using affine geometry construction, a new family of optimal OOCs with weight 4 and MCP 2 is introduced

Two new optimal constructions of optical orthogonal codes with lambdages2 are introduced. The first is based on a previous construction for the case lambda=1. The second is based on difference sets. A new bound for optical orthogonal codes based on a known bound for constant weight codes is introduced. This bound is used to prove the optimality of our constructions

In this paper, we show that the direct transmission scheme of low-density parity-check (LDPC) codes can achieve the upper bound of rate-diversity tradeoff with probability one for multiple-input multiple-output (MIMO) systems with BPSK modulation. We then present an algorithm to construct the LDPC space-time codes through a 2-dimensional array whose doubly-periodic correlation is bounded by 1.