Optical orthogonal codes with unequal auto- and cross-correlation constraints

An optical orthogonal code (OOC) is a collection of binary sequences with good auto- and cross-correlation properties; they were defined by Salehi and others as a means of obtaining code-division multiple access on optical networks. Up to now, all work on OOCs have assumed that the constraint placed on the autocorrelation and that placed on the cross-correlation are the same. We consider-codes for which the two constraints are not equal. Specifically we develop bounds on the size of such OOCs and demonstrate constriction techniques for building them. The results demonstrate that a significant increase in the code size is possible by letting the autocorrelation constraint exceed the cross-correlation constraint. These results suggest that for a given performance requirement the optimal OOC may be one with unequal constraints. This paper also views OOCs with unequal auto- and cross-correlation constraints as constant-weight unequal error protection (UEP) codes with two levels of protection. The bounds derived are interpreted from this viewpoint.<>     

Code-division multiple-access techniques in optical fiber networks - part III: optical AND logic gate receiver structure with generalized optical orthogonal codes

In this paper, we present a deep insight into the behavior of optical code-division multiple-access (OCDMA) systems based on an incoherent, intensity encoding/decoding technique using a well-known class of codes, namely, optical orthogonal codes (OOCs). As opposed to parts I and II of this paper, where OOCs with cross-correlation /spl lambda/=1 were considered, we consider generalized OOCs with 1/spl les//spl lambda//spl les/w, where w is the weight of the corresponding codes. To enhance the performance of such systems, we propose the use of an optical and logic gate receiver, which, in an ideal case, e.g., in the absence of any noise source, except the optical multiple-access interference, is optimum. Using some basic laws on probability, we present direct and exact solutions for OOCs with /spl lambda/=1,2,3,...,w, with the optical and logic gate as receiver. Using the exact solution, we obtain empirical solutions that can be easily used in optimizing the design criteria of such systems. From our optimization scheme, we obtain some fresh insight into the performance of OOCs with /spl lambda//spl ges/1. In particular, we can obtain some simple relations between P/sub emin/ (minimum error rate), L/sub min/ (minimum required OOC length), and N/sub max/ (maximum number of interfering users to be supported), which are the most desired parameters for any OCDMA system design. Furthermore, we show that in most practical cases, OOCs with /spl lambda/=2,3 perform better than OOCs with /spl lambda/=1, while having a much bigger cardinality. Finally, we show that an upper bound on the maximum weight of OOCs are on the order of /spl radic/2/spl lambda/L where L is the length of the OOCs.     

Design of a special family of optical CDMA address codes for fullyasynchronous data communications

A special family of optical address codes, called strict optical orthogonal codes (OOCs), is proposed for fiber-optic code-division multiple access (FO-CDMA) networks. Such codes can strictly guarantee both crosscorrelation and autocorrelation constraints (i.e., λ _c and λ_a) to be one in fully asynchronous data communications and ultrafast switching. Theory of strict OOCs is presented and the code design is described by using the concepts of slot distances. Moreover, the use of strict OOCs can support variable-rate and multirate data communications in an FO-CDMA network with no violation of λ_c=λ_a=1 and no increase of system complexity compared to using conventional OOCs     

Optical orthogonal codes with large crosscorrelation and their performance bound for asynchronous optical CDMA systems

Optical orthogonal codes (OOCs) are commonly used as signature codes for optical code-division multiple-access (OCDMA) communication systems. Many OOCs have been proposed and investigated. Asynchronous OCDMA systems using conventional OOCs have a very limited number of subscribers and few simultaneous users. Recently, we reported a new code family with large code size by relaxing the crosscorrelation constraint to 2. In this paper, by further loosening the crosscorrelation constraint, we adopt the random greedy algorithm to construct a code family which has larger code size and more simultaneous users. We also derive an upper bound of the number of simultaneous users for a given code length, code weight, and bit error rate. The study shows that it is possible to have codes approaching this bound.     

Linear Size Optimal $q$-ary Constant-Weight Codes and Constant-Composition Codes

An optimal constant-composition or constant-weight code of weight w has linear size if and only if its distance d is at least 2w-1. When d ? 2w, the determination of the exact size of such a constant-composition or constant-weight code is trivial, but the case of d=2w-1 has been solved previously only for binary and ternary constant-composition and constant-weight codes, and for some sporadic instances. This paper provides a construction for quasicyclic optimal constant-composition and constant-weight codes of weight w and distance 2w-1 based on a new generalization of difference triangle sets. As a result, the sizes of optimal constant-composition codes and optimal constant-weight codes of weight w and distance 2w-1 are determined for all such codes of sufficiently large lengths. This solves an open problem of Etzion. The sizes of optimal constant-composition codes of weight w and distance 2w-1 are also determined for all w ? 6, except in two cases.     

Design of multilength optical orthogonal codes for optical CDMA multimedia networks

To simultaneously support multimedia services with different signaling rates and quality-of-service requirements in optical code division multiple access (CDMA) networks, a new class of multilength, constant-weight optical orthogonal codes (OOCs) with good correlation properties is constructed algebraically in this paper. The performance of these new OOCs in an optical CDMA system with double-media services is analyzed. In contrast to conventional CDMA, our study shows that the performance of these multilength OOCs worsens as the code length increases, allowing prioritization in optical CDMA. Finally, an application of these multilength OOCs to integrate different types of multimedia services is briefly discussed.     

Novel optical fiber code-division multiple access networkssupporting real-time multichannel variable-bit-rate (VBR) videodistributions

we design novel code-division multiple access (CDMA) networks which use strict optical orthogonal codes (OOCs) and incoherent optical processing for multichannel variable-bit-rate (VBR) video broadcasting. The proposed techniques possess the characteristics of fast access tunability and bit-rate flexibility. This in turn can facilitate real-time VBR video distributions for entertainment HDTV applications. Compared with conventional OOCs, the use of strict OOCs can ensure both auto- and cross-correlation constraints to be minimum (i.e., “1”) for multichannel VBR video broadcasting and high-speed photonic switching applications. A parallel-serial hybrid architecture for all-optical tunable decoders (or encoders) is also presented to strict OOCs, which has a fast reconfiguration time to support real-time video applications in high-speed optical fiber CDMA networks     

Upper bounds for constant-weight codes

Let A(n,d,w) denote the maximum possible number of codewords in an (n,d,w) constant-weight binary code. We improve upon the best known upper bounds on A(n,d,w) in numerous instances for n⩽24 and d⩽12, which is the parameter range of existing tables. Most improvements occur for d=8, 10, where we reduce the upper bounds in more than half of the unresolved cases. We also extend the existing tables up to n⩽28 and d⩽14. To obtain these results, we develop new techniques and introduce new classes of codes. We derive a number of general bounds on A(n,d,w) by means of mapping constant-weight codes into Euclidean space. This approach produces, among other results, a bound on A(n,d,w) that is tighter than the Johnson bound. A similar improvement over the best known bounds for doubly-constant-weight codes, studied by Johnson and Levenshtein, is obtained in the same way. Furthermore, we introduce the concept of doubly-bounded-weight codes, which may be thought of as a generalization of the doubly-constant-weight codes. Subsequently, a class of Euclidean-space codes, called zonal codes, is introduced, and a bound on the size of such codes is established. This is used to derive bounds for doubly-bounded-weight codes, which are in turn used to derive bounds on A(n,d,w). We also develop a universal method to establish constraints that augment the Delsarte inequalities for constant-weight codes, used in the linear programming bound. In addition, we present a detailed survey of known upper bounds for constant-weight codes, and sharpen these bounds in several cases. All these bounds, along with all known dependencies among them, are then combined in a coherent framework that is amenable to analysis by computer. This improves the bounds on A(n,d,w) even further for a large number of instances of n, d, and w     

Flexible optical fiber CDMA networks using strict opticalorthogonal codes for multimedia broadcasting and distributionapplications

Flexible optical fiber code-division multiple-access (CDMA) networks are proposed to support real-time multimedia communication services of constant bit rate (CBR) and variable bit rate (VBR)/multiple bit rate (MBR). Since strict optical orthogonal codes (OOCs) are employed in incoherent optical fiber CDMA networks, their use can strictly guarantee the correlation constraint λ to be the minimum value (i.e., an unit “1”) for multimedia applications. This is achieved without increasing any system complexity compared with the use of conventional OOCs. Moreover, optimal strict OOCs can have the same length as optimal conventional OOCs or a slightly longer length than the latter. It is shown that the proposed optical fiber CDMA networks have a distinguishing feature of high bit-rate flexibility and fast access tunability. Consequently, this can effectively support both VBR and CBR video communications as well as multimedia broadcasting/distributions in a given network without any violation of the minimum correlation constraint λ=1. The proposed network can be also used as a backbone to interconnect various local-area networks with different data bit rates. However, conventional OOC-based optical CDMA networks do not possess such characteristics because of violation of λ=1 for VBR or MBR communications     

Novel combinatorial constructions of optical orthogonal codes for incoherent optical CDMA systems

Three novel classes of optical orthogonal codes (OOCs) based on combinatorial designs are proposed. They are applicable to both synchronous and asynchronous incoherent optical code-division multiple access (OCDMA) and compatible with spectral-amplitude-coding (SAC), fast frequency hopping, and time-spreading schemes. Simplicity of construction, larger codeword families, and larger flexibility in cross-correlation control make the proposed OOC families interesting candidates for future OCDMA applications. A novel balanced SAC receiver for multiuser interference cancellation that can handle unequal in-phase cross correlation of OOC is also proposed. The upper bound on the bit-error rate as a function of the number of users in SAC schemes is given for all proposed OOC classes.     

Code division multiple-access techniques in optical fiber networks.I. Fundamental principles

An examination is made of fiber-optic code-division multiple-access (FO-CDMA), a technique in which low information data rates are mapped into very-high-rate address codes (signature sequences) for the purpose of achieving random, asynchronous communications free of network control, among many users. The need for a special class of signature sequences to achieve the multiple-access capability using fiber-optic signal processing techniques is discussed. A class of signature sequences called optical orthogonal codes (OOCs) that provide the auto- and cross-correlation properties required for FO-CDMA is introduced and used in an experiment to show the principles of FO-CDMA. The experiment demonstrates the auto- and cross-correlation properties of the codes. The concept of optical disk patterns, an equivalent way of representing the OOCs, is introduced. The patterns are used to derive the probability density functions associated with any two interfering OOCs. A detailed study of different interference patterns is presented, and the strongest and the weakest interference patterns are determined     

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     

OCDMA-coded free-space optical links for wireless optical-mesh networks

We propose a wireless optical-mesh network based on optical code-division multiple-access (OCDMA)-coded free-space optical links. The performance of the proposed network under intermediate and strong turbulence channel conditions is investigated for synchronous and asynchronous OCDMA. We show that synchronous OCDMA using complementary Walsh-Hadamard codes operating at a raw bit rate of 622 Mb/s per user can achieve a bit-error rate of 10/sup -9/. This is achievable in channels with strong turbulence and high temporal correlation, or in channels with intermediate turbulence conditions; reasonable conditions based on channel characteristics inferred from the refractive index spectrum. For asynchronous OCDMA using optical orthogonal codes (OOCs), using a lower bound, we show that asynchronous OCDMA using OOCs cannot achieve acceptable performance for the same channel conditions, due to interference limitations.     

A New Family of 2-D Codes for Fiber-Optic CDMA Systems With and Without the Chip-Synchronous Assumption

In this paper, we propose a new family of wavelength-time codes, which are based on one-dimensional optical orthogonal codes (1-D OOCs) of cross-correlation functions of at most two. By relaxing the maximum cross-correlation values to two, the new 2-D codes provide larger code cardinality for accommodating more subscribers and support heavier code weight for better code performance. It is known that the traditional chip-synchronous assumption used in the analyses of optical codes gives a pessimistic performance upper bound, while the newer chip-asynchronous assumption offers a more accurate analysis. The performance of the new 2-D codes is here analyzed under both assumptions for comparison. Under certain conditions, our results show that the new wavelength-time codes outperform our recently reported multiple-wavelength OOCs and 2-D codes, which were based on 1-D OOCs of cross-correlation functions of at most one and two, respectively.      

Analytical comparison of various fiber-optic CDMA receiverstructures

We study the performance of optical code-division multiple access (CDMA) systems using various receivers structures. Two general classes of receivers based on required electronic bandwidth are studied. Optical orthogonal codes (OOCs) are utilized as signature sequences and the performance studied in this paper takes into account the effect of all major noise sources, i.e., quantum shot-noise, dark current noise, and Gaussian circuit noise. Furthermore, this paper introduces a generalized method of analyzing the performance of various optical CDMA receiver structures. Required mean number of photon count per chip time for reliable transmission of data bits for various receiver structures is investigated. Finally, the advantages and disadvantages of various receiver structures are discussed     

Multiple-length multiple-wavelength optical orthogonal codes for optical CDMA systems supporting multirate multimedia services

Multiple-wavelength optical orthogonal codes (MWOOCs) with autocorrelation sidelobes and cross-correlation values of both at most one were recently proposed for wavelength-time optical code-division multiple-access (O-CDMA) systems. The codes have cardinality as a quadratic function of the number of wavelengths and find applications in high bit-rate O-CDMA systems with broadband supercontinuum lasers, in which the number of available wavelengths is larger than the number of time slots. To support multimedia services with different bit-rate and quality-of-service requirements, a new class of multiple-length constant-weight MWOOCs with autocorrelation sidelobes of zero and cross correlations of at most one is constructed algebraically in this paper. The performance of these new codes in an O-CDMA system with double-media services is analyzed. In contrary to conventional single-length codes, our study shows that the performance of these multiple-length codes improves as the code length decreases. This unique property supports "prioritization" in O-CDMA.     

Channel interference reduction using random Manchester codes forboth synchronous and asynchronous fiber-optic CDMA systems

We propose the random Manchester codes (RMC) to improve the bit error probability (BEP) performance in both synchronous and asynchronous fiber-optic code-division multiple-access (CDMA) systems. The spreading sequences used in the synchronous and asynchronous systems are modified prime sequence codes and optical orthogonal codes (OOCs), respectively. Thermal noise, shot noise, and avalanche photodiode (APD) bulk and surface leakage currents are taken into consideration in the BEP analyzes. The results show that the proposed systems can support a larger number of simultaneous users than other systems with similar system complexity under the same bit-error probability constraint     

Multilength two-dimensional codes for optical CDMA system

A new class of multilength, constant-weight and two-dimensional multiwavelength optical orthogonal code （2D MWOOCs） with large capacity and good correlation properties is constructed based on multilength one-dimensional （1D） OOCs. The performance of these new MWOOCs in an OCDMA network with double-services is analyzed. The result shows that media with the shorter codeword performs much better than the media with longer codeword, and OCDMA system with these new multilength MWOOCs performs well. These features allow multimedia transmission of large capacity in OCDMA system.     

Optical orthogonal code design using genetic algorithms

A construction technique for optical orthogonal codes (OOCs) using genetic algorithms (GAs) is proposed. The performance of the GA OOCs is compared to that of four existing OOCs. Results show that the GA OOCs have a lower probability of error     

Multiple-shift code acquisition of optical orthogonal codes in optical CDMA systems

In this paper, we introduce a new and advanced algorithm, namely, multiple-shift algorithm for code acquisition in optical code-division multiple access (CDMA) systems using unipolar optical orthogonal codes (OOCs) as signature sequences. We analyze the performance of the newly proposed algorithm and obtain a bound on its performance and show its advantage in reducing the mean time of synchronization when compared with other synchronization methods. The algorithm can be used with many different receiver structures, like active or passive correlator with or without hardlimiter(s). However, in this paper, we only consider the simple active correlator structure for further discussions and analysis.