asymptotically optimal optical orthogonal codes with new parameters optical orthogonal codes oocs are widely used as spreading codes in optical fiber networks an n w a c ooc with size l is a family of l 0 1 sequences with length n weight w maximum autocorrelation a and maximum cross correlation c in this paper we present two new constructions for oocs with a c 1 which are asymptotically optimal with respect to the johnson bound we first construct an asymptotically optimal mpn m 1 1 ooc with size pn 1 m by using the structure of zpn the ring of integers modulo pn where p is an odd prime with m p 1 and n is a positive integer we then present another asymptotically optimal mp1 pk m 1 1 ooc with size p1 pk 1 m from a product of k finite fields where pi is an odd prime and m is a positive integer such that m pi 1 for 1 i k in particular it is optimal in the case that k 1 and m 1 2 p1 1

families of optimal oocs with lambda 2 we provide a new construction yielding one new and one known infinite family of optimal n w 2 optical orthogonal codes w isin 4 6 our construction relies on various techniques in finite projective spaces involving hyperovals in projective planes and singer groups

relative difference families with variable block sizes and their related oocs seven infinite classes of relative difference families with variable block sizes are presented explicitly in particular a balanced gv g k 1 df with g k k k2 k 2 is explicitly given for i k 3 4 5 and every v coprime to 6 ii k 3 4 6 3 5 6 or 3 4 5 6 and every v coprime to 30 as far as the authors are aware these difference families can be viewed as the first explicit constructions of infinite classes of optimal variable weight optical orthogonal codes with more than two weights it is observed however that there are infinitely many values of v for which an optimal v w 1 q ooc exists whatever the set of weights w and the weight distribution sequence q are

linearly constrained global optimization a general solution algorithm with applications this paper presents an efficient enumerative approach to solve general linearly constrained optimization problems this class of optimization problems includes fractional nonlinear network models quadratic convex and non convex programs the unified approach is accomplished by converting the constrained optimization problem to an unconstrained optimization problem through a parametric representation of its feasible region the proposed solution algorithm consists of three phases in phase 1 it finds all interior critical points in phase 2 the parametric representation of the feasible region is constructed to identify any critical points on the edges and faces of the feasible region this is done by a modified version of an algorithm for finding the v representation of the polyhedron then in phase 3 the global optimal value of the objective function is found by evaluating the objective function at the critical points as well as at the vertices for an illustration of the algorithm and a comparison with the existing methods small size numerical examples are presented

performance analysis of optical synchronous cdma communication systems with ppm signaling direct detection optical synchronous code division multiple access cdma systems with m ary pulse position modulation ppm signaling are investigated optical orthogonal codes are used as the signature sequences of our system a union upper bound on the bit error rate is derived taking into account the effect of the background noise multiple user interference and receiver shot noise the performance characteristics are then discussed for a variety of system parameters another upper bound on the probability of error is also obtained based on chernoff inequality this bound is utilized to derive achievable expressions for both the maximum number of users that can communicate simultaneously with asymptotically zero error rate and the channel capacity our results show that under average power and bit error rate constraints there always exists a pulse position multiplicity that permit all the subscribers to communicate simultaneously

new constructions of optimal cyclically permutable constant weight codes three new constructions for families of cyclic constant weight codes are presented all are asymptotically optimum in the sense that in each case as the length of the sequences within the family approaches infinity the ratio of family size to the maximum possible under the johnson upper bound approaches unity

design of signature sequences for overloaded cdma and bounds on the sum capacity with arbitrary symbol alphabets in this paper we explore some of the fundamentals of synchronous code division multiple access cdma as applied to wireless and optical communication systems under very general settings of any size for the user symbols and the signature matrix entries the channel is modeled by real complex additive noise of arbitrary distribution two problems are addressed the first problem concerns whether uniquely detectable overloaded matrices exist in the absence of additive noise under these general settings and if so whether there are any practical optimum detection algorithms the second one is about the bounds for the sum channel capacity when user data and signature matrices employ any real or complex alphabets finite or infinite in response to the first problem we have developed practical maximum likelihood detection algorithms for overloaded cdma systems for a large class of alphabets in response to the second problem a general theorem has been developed in which the sum capacity lower bounds with respect to the number of users spreading gain and signal to noise ratio can be derived to show the power and utility of the main theorem a number of sum capacity bounds for special cases are evaluated an important conclusion of this paper is that the lower and upper bounds of the sum capacity for small medium size cdma systems depend on both the input and the signature symbols this is contrary to the asymptotic results for large scale systems reported in the literature also confirmed in this paper where the signature symbols and statistics disappear for signature matrices and input vectors with i i d entries furthermore upper and asymptotic bounds are derived and compared to other derivations

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

some results concerning post infeasibility analysis abstract linear constraints are used to model diverse phenomena the number of constraints is large in many practical applications often running into several thousands a system of linear constraints is quite often inconsistent especially at the stage of model formulation a number of different approaches are possible when a system of linear constraints turns out to be inconsistent we prove some results on some plausible approaches and their limitations

optimal variable weight optical orthogonal codes via difference packings variable weight optical orthogonal code ooc was introduced by yang for multimedia optical cdma systems with multiple quality of service qos requirements in this paper the upper bound on the size of variable weight oocs is improved a cyclic t v w q packing is introduced to construct a variable weight ooc an upper bound for the number of blocks of t v w q packings is obtained and an equivalence between optimal cyclic packing and optimal variable weight optical orthogonal code is established recursive constructions for optimal 2 cp w 1 q v s are also presented by using skew starters and these constructions infinite classes of optimal v w 1 1 2 1 2 oocs are obtained for w 3 4 and 4 5

further results on difference triangle sets further results on the upper bounds for difference triangle sets dts are derived from disjoint difference sets and additive sequences of permutations which greatly improve the known bounds

a complete algorithm for linear fractional programs abstract the linear fractional programming lfp algorithms attempt to optimize a quotient of two linear functions subject to a set of linear constraints the existing lfp algorithms are problem dependent and none is superior to others in all cases these algorithms explicitly require i the denominator of the objective function does not vanish in the feasible region ii the denominator of the objective function is positive iii the feasible region is bounded moreover some of these algorithms fail whenever iv some constraints are redundant we present a simplex type algorithm which is compact and efficiently detects conditions i iii and relaxes assumption iv the proposed algorithm is evolutionary in the sense that it builds up in a systematic manner to solve any lfp type problems numerical examples illustrate the algorithm

frame time hopping fiber optic code division multiple access using generalized optical orthogonal codes a new spreading technique for intensity modulation direct detection fiber optic code division multiple access fo cdma communication systems is proposed this new spreading technique is based on generalized optical orthogonal codes ooc with large cardinality and minimal degradation in performance when compared with a more optimum system namely an optical cdma system using ooc with autocorrelation and cross correlation value bounded by one i e ooc spl lambda 1 to obtain the performance of such systems we use a communication scheme namely frame time hopping fth cdma with random coding systems with generalized ooc patterns and random time hopping coding are close in structure and performance furthermore the performance of such systems is near the performance of optical cdma with optimum but low cardinality ooc spl lambda 1 which further renders the practicality of the proposed technique with very large cardinality two new receiver structures for fo cdma namely chip level detector with optimum comparator threshold and correlation receiver with an electrical hard limiter are also proposed the performance analysis for a binary pulse position fth fo cdma network is considered for the correlation receiver chip level detector correlation receiver with an optical hard limiter optimum receiver and the two newly proposed receiver structures the results also show that a chip level detector with optimum comparator threshold is superior to a chip level detector for received low signal powers and predict that the performance of the correlation receiver with an electrical hard limiter is superior to all other considered receiver structures e g requiring one third of transmission power to achieve a desired bit error rate when compared with other receiver structures

a mathematical programming approach to clusterwise regression model and its extensions abstract the clusterwise regression model is used to perform cluster analysis within a regression framework while the traditional regression model assumes the regression coefficient to be identical for all subjects in the sample the clusterwise regression model allows to vary with subjects of different clusters since the cluster membership is unknown the estimation of the clusterwise regression is a tough combinatorial optimization problem in this research we propose a generalized clusterwise regression model which is formulated as a mathematical programming mp problem a nonlinear programming procedure with linear constraints is proposed to solve the combinatorial problem and to estimate the cluster membership and simultaneously moreover by integrating the cluster analysis with the discriminant analysis a clusterwise discriminant model is developed to incorporate parameter heterogeneity into the traditional discriminant analysis the cluster membership and discriminant parameters are estimated simultaneously by another nonlinear programming model

performance analysis of direct detection optical cdma communication systems with avalanche photodiodes direct detection optical code division multiple access cdma communication systems with avalanche photodiode apd photodetectors are investigated a chernoff upper bound modified chernoff upper bound and gaussian approximation on the probability of bit error are presented for general apds and arbitrary

an algebraic approach to the unequal spaced channel allocation problem in wdm lightwave systems to reduce four wave mixing crosstalk in high capacity long haul repeaterless wavelength division multiplexing wdm lightwave systems the use of unequally spaced channels has been proposed instead of being solved by integer linear programming the unequal spaced channel allocation problem is treated by constructing suitable optical orthogonal codes in optical code division multiple access cdma an algebraic framework and three algorithms on finding the frequency locations of unequally spaced wdm channels are introduced where the constructions are based on generating optical cdma codewords with a predetermined pulse separation and aperiodic autocorrelation sidelobes no greater than one the algorithms potentially provide a fast and simple alternative to solve the problem besides the proposed computer search method

a decomposition algorithm for solving large scale quadratic programming problems in this paper an algorithm for solving large scale programming is proposed we decompose a large scale quadratic programming into a serial of small scale ones and then approximate the solution of the large scale quadratic programming via the solutions of these small scale ones it is proved that the accumulation point of the iterates generated by the algorithm is a global minimum point of the quadratic programming the algorithm has performed very well in numerical testing it is a new way of solving large scale quadratic programming problems

a new method for generating inner points of triangulations in two dimensions abstract to obtain a triangulation of a planar domain we assume that the boundary points are given we then develop a method for generating inner points it is a combination of an optimization algorithm and a method that directly places points e g we successively generate the points and at the same time optimize the positions of the already inserted points the inserting routine is relatively simple but the optimization algorithm is more complicated we use a steepest descent method with powell s step size strategy the delaunay triangulation built from the generated points consists of roughly equi angular triangles so nice initial triangulations for adaptive methods can be generated a major advantage of our method is its independance from the complexity of the domain being triangulated the cost of the generation procedure depends only on the number of generated points

constructions for optimal spl upsi 4 1 optical orthogonal codes four direct constructions three of which are by way of skew starters are given in this correspondence for optimal spl upsi 4 1 optical orthogonal codes ooc s these improve the known existence results concerning optimal spl upsi 4 1 oocs in particular it is shown that an optimal spl upsi 4 1 ooc exists for all positive integers spl upsi spl equiv 6 mod 12 or spl upsi spl equiv 24 mod 48 it is also shown that an optimal 12 spl upsi 4 1 ooc exists for any positive integer spl upsi whose prime factors are all congruent to 1 modulo 4

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

construction and applications of crt sequences protocol sequences are used for channel access in the collision channel without feedback each user accesses the channel according to a deterministic zero one pattern called the protocol sequence in order to minimize fluctuation of throughput due to delay offsets we want to construct protocol sequences whose pairwise hamming cross correlation is as close to a constant as possible in this paper we present a construction of protocol sequences which is based on the bijective mapping between one dimensional 1 d sequence and two dimensional 2 d arrays by the chinese remainder theorem crt in the application to the collision channel without feedback a worst case lower bound on system throughput is derived

2 sup n prime sequence codes and coding architecture for optical code division multiple access recent study shows that optical code division multiple access cdma networks cannot be evaluated or designed by only considering the performance i e correlation properties of the optical pseudo orthogonal codes selected the structures of optical encoders and decoders are another important factors to consider and are needed to coordinate with the selected optical codes as much as possible a special family of 2 sup n codes so called 2 sup n prime sequence codes is constructed a general theorem on the cardinality of the new codes is provided the properties and performance of the codes are also studied since these codes pose the algebraic properties of both prime sequence and 2 sup n codes new optical encoding and decoding structures are designed to optimize the system parameters e g power budget and cost of these optical cdma networks this new configuration is particularly attractive for ultrafast optical processing and waveguide implementation for tile future high capacity low loss all optical cdma networks

two dimensional synchronization patterns for minimum ambiguity a number of closely related combinatorial problems corresponding to specific assumptions about the type of time frequency sequence which may be appropriate in a particular application are formulated in terms of square or rectangular arrays of dots with appropriate constraints on the two dimensional correlation function the current state of knowledge concerning each of these problems is summarized it is hoped that more general constructions may be found leading to larger families of solutions as well as better computational algorithms for finding individual solutions which may lie outside of the general families

constraint exploration method for quadratic programming problem in this paper we represent a method which is based on the violated constraints by the unconstrained minimum of the objective function of the quadratic programming problem for exploring locating and computing the optimal solution of the problem without using additional information as have been done in most of the favourite established methods

optical orthogonal signature pattern codes with maximum collision parameter 2 and weight 4 an optical orthogonal signature pattern code oospc finds application in transmitting 2 d images through multicore fiber in code division multiple access cdma communication systems observing a one to one correspondence between an oospc and a certain combinatorial subject called a packing design we present a construction of optimal oospcs with weight 4 and maximum collision parameter 2 which generalizes a well known kohler construction of optimal optical orthogonal codes ooc with weight 4 and maximum collision parameter 2 using this new construction enables one to obtain infinitely many optimal oospcs whose existence was previously unknown we prove that for a multiple n of 4 there exists no optimal oospc of size 6 n with weight 4 and maximum collision parameter 2 together with a report which shows a gap between optimal oocs and optimal oospcs when 6 and n are not coprime we also present a recursive construction of oospcs which are asymptotically optimal with respect to the johnson bound as a by product we obtain an asymptotically optimal m n 4 2 oospc for all positive integers m and n

m kern 1pt n kern 1pt 3 kern 1pt 1 optical orthogonal signature pattern codes with maximum possible size kitayama proposed a novel code division multiple access cdma network for image transmission called spatial cdma optical orthogonal signature pattern codes oospcs have attracted wide attention as signature patterns of spatial cdma an m n k lambda oospc is a set of m times n 0 1 matrices with hamming weight k and maximum correlation value lambda let theta m n k lambda be the largest possible number of codewords among all m n k lambda oospcs in this paper we concentrate on the calculation of the exact value of theta m n 3 1 and the construction of an m n 3 1 oospc with theta m n 3 1 codewords as a consequence we show that theta m n 3 1 lfloor frac mn 1 6 rfloor 1 when mn equiv 14 20 textrm mod 24 or mn equiv 8 16 textrm mod 24 and gcd m n 4 2 or mn equiv 2 textrm mod 6 and gcd m n 4 4 and theta m n 3 1 lfloor frac mn 1 6 rfloor otherwise

combinatorial constructions of optimal optical orthogonal codes with weight 4 a v k spl lambda optical orthogonal code c is a family of 0 1 sequences of length v and weight k satisfying the following correlation properties 1 spl sigma sub 0 spl les t spl les v 1 x sub t x sub t i spl les spl lambda for any x x sub 0 x sub 1 x sub v 1 spl isin c and any integer i spl ne 0 mod v 2 spl sigma sub 0 spl les t spl les v 1 x sub t y sub t i spl les spl lambda for any x x sub 0 x sub 1 x sub v 1 spl isin c y y sub 0 y sub 1 y sub v 1 spl isin c with x spl ne y and any integer i where the subscripts are taken modulo v a v k spl lambda optical orthogonal code ooc with spl lfloor 1 k spl lfloor v 1 k 2 spl lfloor v 2 k 2 spl lfloor spl middot spl middot spl middot spl lfloor v spl lambda k spl lambda spl rfloor m spl rfloor spl rfloor spl rfloor codewords is said to be optimal oocs are essential for success of fiber optic code division multiple access cdma communication systems the use of an optimal ooc enables the largest possible number of asynchronous users to transmit information efficiently and reliably in this paper various combinatorial constructions for optimal v 4 1 oocs such as those via skew starters and weil s theorem on character sums are given for v spl equiv 0 mod 12 these improve the known existence results on optimal oocs in particular it is shown that an optimal v 4 1 ooc exists for any positive integer v spl equiv 0 mod 24

two new families of synchronous optical codes for cdma based passive optical networks in this paper two new families of synchronous optical codes called 1 d and 2 d synchronous multilevel prime codes smpcs are constructed and analyzed for incoherent optical code division multiple access o cdma with the benefit of synchronous transmission the new algebraic codes have expanded cardinality and substantially increase the number of possible subscribers thus potentially supporting rapid code switching and obscure nature privacy and military communications in addition the smpcs can be partitioned into a tree structure of multiple levels of subsets of codewords different cross correlation functions are obtained from codewords coming from different subsets code orthogonality is achieved among the codewords within each subset of the lowest level as code performance is a strong function of the cross correlation function the performance of the codewords in use can be adjusted by choosing the subsets from which the codewords originate the performances of the smpcs are formulated and also verified by computer simulation our analysis shows that code performance can be optimized by applying an in order subset by subset code assignment method to simultaneous users besides supporting time spreading and wavelength time o cdma schemes the new codes also find applications in passive optical networks and in spectral amplitude coding schemes

two dimensional optical orthogonal codes and semicyclic group divisible designs a nxm k two dimensional optical orthogonal code 2 d ooc c is a family of nxm 0 1 arrays of constant weight k such that i 1n j 0m 1a i j b i j m for any arrays a b in c and any integer except when a b and 0 mod m where m denotes addition modulo m such codes are of current practical interest as they enable optical communication at lower chip rate to simplify practical implementation the am oppw at most one pulse per wavelength restriction is often appended to a 2 d ooc an am oppw 2 d ooc is optimal if its size is the largest possible in this paper the notion of a perfect am oppw 2 d ooc is proposed which is an optimal nxm k am oppw 2 d ooc with cardinality m n n 1 n k k 1 k a link between optimal nxm k am oppw 2 d oocs and block designs is developed some new constructions for such optimal codes are described by means of semicyclic group divisible designs several new infinite families of perfect nxm k 1 am oppw 2 d oocs with k 2 3 4 are thus produced

cyclic constant weight codes upper bounds and new optimal constructions in this paper we consider optimal q ary cyclic constant weight codes of length n minimum distance d and weight w briefly cyclic n d w q codes we introduce the pure and mixed difference method to present a combinatorial description for a cyclic n d w q code and then obtain some tight upper bounds on the sizes of optimal cyclic n d w q codes finally by using skolem type sequences we completely determine the sizes of optimal cyclic n d 3 3 codes with minimum distance 1 leq d leq 6

general constructions of optimal variable weight optical orthogonal codes variable weight optical orthogonal code ooc was introduced by yang for multimedia optical cdma systems with multiple quality of service qos requirements in this paper four general constructions for optimal cyclic packings and optimal variable weight oocs are presented many new infinite classes of optimal v w 1 q oocs are obtained new infinite classes of optimal v w 1 q oocs for w 4 are easily obtained by the constructions

optimal 2 d n times m 3 2 1 optical orthogonal codes optical orthogonal codes are commonly used as signature codes for optical code division multiple access systems so far research on 2 d optical orthogonal codes has mainly concentrated on the same autocorrelation and cross correlation constraints in this paper we are concerned about optimal 2 d optical orthogonal codes with the autocorrelation a and the cross correlation 1 some combinatorial constructions for 2 d n m k a 1 optical orthogonal codes are presented when k 3 and a 2 the exact number of codewords of an optimal 2 d n m 3 2 1 optical orthogonal code is determined for any positive integers n 0 1 3 6 9 10 mod 12 and m 2 mod 4

classroom note initialization of the simplex algorithm an artificial free approach the simplex algorithm requires artificial variables for solving linear programs which lack primal feasibility at the origin point we present a new general purpose solution algorithm which obviates the use of artificial variables the algorithm searches for a feasible segment of a boundary hyperplane a face of feasible region or an intersection of several faces by using rules similar to the ordinary simplex

multiuser detections for optical cdma networks based on expectation maximization algorithm in this paper we introduce new unblind and blind multiuser detectors for an optical code division multiple access system the detectors have two soft and hard stages in the soft stage a soft estimation of the interference is obtained by solving an unconstrained maximum likelihood problem via the iterative expectation maximization em algorithm then the hard stage detects the user information bit by solving a one dimensional boolean constrained problem conditioned on knowing the interference our results reveal that the proposed detectors have very low complexity and are robust against changes in parameters moreover the numerical results illustrate that despite of their simplicities our detectors substantially outperform other well known suboptimum detectors such as multistage and decorrelating detectors

determination of the exact value for psi m k k 1 impulse radio sequences irss were first introduced by chu and colbourn in ieee trans inf theory vol 50 pp 2402 2407 2004 let m k denote the maximal possible number of sequences in an m k irs in this paper a fundamental equivalence between impulse radio sequences and strictly cyclic packing having the impulse position property is established with their relationship the exact value of m k k 1 is finally determined for any positive integers m and k

bounds and constructions of optimal n 4 2 1 optical orthogonal codes in this paper a tight upper bound on the maximum possible code size of n 4 2 1 oocs and some direct and recursive constructions of optimal n 4 2 1 oocs attaining the upper bound are give

optical orthogonal codes design analysis and applications an optical orthogonal code ooc is a family of 0 1 sequences with good auto and cross correlation properties i e the autocorrelation of each sequence exhibits the thumbtack shape and the cross correlation between any two sequences remains low throughout the use of optical orthogonal codes enables a large number of asynchronous users to transmit information efficiently and reliably the thumbtack shaped autocorrelation facilitates the detection of the desired signal and low profile cross correlation reduces interference from unwanted signals theoretical upper and lower bounds on the maximum possible size of oocs are derived methods for the design and analysis of oocs using tools from projective geometry the greedy algorithm iterative constructions algebraic coding theory block design and various other combinational disciplines are discussed

new families of optimal variable weight optical orthogonal codes with high weights 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

optical orthogonal codes their bounds and new optimal constructions a v k spl lambda sub a spl lambda sub c optical orthogonal code ooc c is a family of 0 1 sequences of length v and weight k satisfying the following two correlation properties 1 spl sigma sub 0 spl les t spl les v 1 x sub t x sub t i spl les spl lambda sub a for any x x sub 0 x sub 1 spl middot spl middot spl middot x sub v 1 spl isin c and any integer i not equivalent 0 mod v and 2 spl sigma sub 0 spl les t spl les v 1 x sub t y sub t i spl les spl lambda sub b for any x x sub 0 x sub 1 spl middot spl middot spl middot x sub v 1 spl isin c y y sub 0 y sub 1 spl middot spl middot spl middot y sub v 1 spl isin c with x spl ne y and any integer i where the subscripts are taken modulo v the study of optical orthogonal codes is motivated by an application in optical code division multiple access communication systems in this paper upper bounds on the size of an optical orthogonal code are discussed several new constructions for optimal optical orthogonal codes with weight k spl ges 4 and correlation constraints spl lambda sub a spl lambda sub c 1 are described by means of optimal cyclic packings many new infinite series of such optimal optical orthogonal codes are thus produced

performance analysis of single user and multiuser detectors for optical code division multiple access communication systems code division multiple access cdma is a powerful multiplexing scheme particularly suited to the optical domain with its broad spectrum unfortunately analysis of optical cdma ocdma systems has been almost exclusively restricted to systems employing a correlation detector which suffer high degradation when received user powers are dissimilar this study examines the performance of an optimum single user detector and two multiuser detectors for ocdma in the presence of additive light intensity noise and poisson detection the optimized single user detector is the maximum likelihood detector given the interference from other users is a random process with known distribution one multiuser detector is based on a local search algorithm for maximizing the likelihood function the second multiuser detector is a generalization of the optical multistage detector to accept soft decision from the previous stage approximations to the error probabilities of the ocdma system based on either random signature sequences or deterministic codes are derived for each detector using a large deviations theory approach the asymptotic multiuser efficiency is found to be related to the large deviations rate function the analysis shows that the correlation detector performance decreases rapidly as the number of users increases while the optimized single user detector and the two multiuser detectors proposed perform considerably better and show less sensitivity to unequal received user powers

a practical anti cycling procedure for linearly constrained optimization a procedure is described for preventing cycling in active set methods for linearly constrained optimization including the simplex method the key ideas are a limited acceptance of infeasibilities in all variables and maintenance of a working feasibility tolerance that increases over a long sequence of iterations the additional work per iteration is nominal and stalling cannot occur with exact arithmetic the method appears to be reliable based on computational results for the first 53 linear programming problems in thenetlib set

on the structure of function spaces in optimal recovery of point functionals for eno schemes by radial basis functions radial basis functions are used in the recovery step of finite volume methods for the numerical solution of conservation laws being conditionally positive definite such functions generate optimal recovery splines in the sense of micchelli and rivlin in associated native spaces we analyse the solvability to the recovery problem of point functionals from cell average values with radial basis functions furthermore we characterise the corresponding native function spaces and provide error estimates of the recovery scheme finally we explicitly list the native spaces to a selection of radial basis functions thin plate splines included before we provide some numerical examples of our method

large families of asymptotically optimal two dimensional optical orthogonal codes 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

perfect constant weight codes in his pioneering work from 1973 delsarte conjectured that there are no nontrivial perfect codes in the johnson scheme many attempts were made during the years which followed to prove delsarte s conjecture but only partial results have been obtained we survey all these attempts and prove some new results having the same flavor we also present a new method taking a different approach which we hope can lead to the settling of this conjecture we show how this new method rules out sets of parameters as well as specific given parameters

a generalized gilbert varshamov bound derived via analysis of a code search algorithm a generalization of the gilbert varshamov bound that is applicable to block codes whose codewords must be drawn from irregular sets is derived the bound improves by a factor of four a similar result derived by v d kolesnik and v y krachkovsky 1991 this generalization is derived by analysing a code search algorithm referred to as the altruistic algorithm this algorithm iteratively deletes potential codewords so that at each iteration the candidate is removed the bound is derived by demonstrating that as the algorithm proceeds the average volume of a sphere of a given radius approaches the maximum such volume and so a bound previously expressed in terms of the maximum volume can in fact be expressed in terms of the average volume examples of applications where the bound is relevant include error correcting d k codes and binary codes for code division multiple access

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 recursive construction for optical orthogonal codes we present a new recursive construction for n spl omega spl lambda sub a spl lambda sub c optical orthogonal codes for the case of spl lambda sub a spl lambda sub c spl lambda this recursive construction enlarges the original family with spl lambda unchanged and produces a new family of asymptotically optimal codes if the original family is asymptotically optimal we call a code asymptotically optimal following the definition of o moreno et al see ibid vol 41 p 448 55 1995 if as n the length of code goes to infinity the ratio of the number of codewords to the corresponding johnson bound approaches unity

combinatorial constructions for optimal two dimensional optical orthogonal codes optical orthogonal codes oocs have been designed for ocdma a one dimensional 1 d optical orthogonal code 1 d ooc is a set of one dimensional binary sequences having good auto and cross correlations one limitation of 1 d ooc is that the length of the sequence increases rapidly when the number of users or the weight of the code is increased which means large bandwidth expansion is required if a big number of codewords is needed to lessen this problem two dimensional 2 d coding also called multiwavelength oocs was invested a two dimensional 2 d optical orthogonal code 2 d ooc is a set of utimesv matrices with 0 1 elements having good auto and cross correlations recently many researchers are working on constructions and designs of 2 d oocs in this paper we shall reveal the combinatorial properties of 2 d oocs and give an equivalent combinatorial description of a 2 d ooc based on this we are able to use combinatorial methods to obtain many optimal 2 d oocs

crc handbook of combinatorial designs balanced incomplete block designs and t designs2 v k l designs of small orderbibds with small block sizet designs t 3steiner systemssymmetric designsresolvable and near resolvable designslatin squares mols and orthogonal arrayslatin squaresmutually orthogonal latin squares mols incomplete molsorthogonal arrays of index more than oneorthogonal arrays of strength more than twopairwise balanced designspbds and gdds the basicspbds recursive constructionspbd closurepairwise balanced designs as linear spacespbds and gdds of higher indexpbds frames and resolvabilityother combinatorial designsassociation schemesbalanced part ternary designsbalanced tournament designsbhaskar rao designscomplete mappings and sequencings of finite groupsconfigurationscostas arrayscoveringscycle systemsdifference familiesdifference matricesdifference sets abeliandifference sets nonabeliandifference triangle setsdirected designsd optimal matricesembedding partial quasigroupsequidistant permutation arraysfactorial designsfrequency squaresgeneralized quadranglesgraph decompositions and designsgraphical designshadamard matrices and designshall triple systemshowell designsmaximal sets of molsmendelsohn designsthe oberwolfach problemordered designs and perpendicular arraysorthogonal designsorthogonal main effect planspackingspartial geometriespartially balanced incomplete block designsquasigroupsquasi symmetric designs r l designsroom squaresself orthogonal latin squares sols sols with a symmetric orthogonal mate solssom sequences with zero autocorrelationskolem sequencesspherical t designsstarterstrades and defining sets t m s netstuscan squarest wise balanced designsuniformly resolvable designsvector space designsweighing matrices and conference matriceswhist tournamentsyouden designs generalizedyouden squaresapplicationscodescomputer science selected applicationsapplications of designs to cryptographyderandomizationoptimality and efficiency comparing block designsgroup testingscheduling a tournamentwinning the lotteryrelated mathematics and computational methodsfinite groups and designsnumber theory and finite fieldsgraphs and multigraphsfactorizations of graphsstrongly regular graphstwo graphsclassical geometriesprojective planes nondesarguesiancomputational methods in design theoryindex

a new sqp method of feasible directions for nonlinear programming in this paper a new sequential quadratic programming sqp method of feasible directions is proposed and analyzed for nonlinear programming where a feasible direction of descent can be derived from solving only one qp subproblem in particular this method can produce automatically a revised direction with the explicit expression which can avoid maratos effect without solving qp subproblem the theoretical analysis shows that global and superlinear convergence can be induced in the end numerical experiment is given to illustrate the effectiveness of the method

extended reed solomon codes for optical cdma in this paper the extended reed solomon codes are modified to construct a new family of 2 d codes for asynchronous optical code division multiple access o cdma in addition of having expanded and asymptotically optimal cardinality these 2 d asynchronous optical codes can be partitioned into multiple tree structures of code subsets in which code cardinality is a function of the periodic cross correlation value assigned to the subset the performance of these 2 d optical codes is analyzed and compared with that of the multilevel prime codes our results show that the unique partition property of the new optical codes supports a trade off between code cardinality and performance for meeting different system requirements such as user capacity and throughput in addition the multiple tree structures of the new codes potentially support applications that require rapid switching of many codewords such as in o cdma network gateway or in strategic environments where code obscurity is essential

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

multiple wavelength optical orthogonal codes under prime sequence permutations for optical cdma a new family of two dimensional 2 d wavelength hopping time spreading codes which employs wavelength hopping algebraically under prime sequence permutations on top of time spreading optical orthogonal codes is studied and analyzed different from other 2 d codes our new codes allow the number of wavelengths and code length to be chosen independently and at the same time the code cardinality is a quadratic function of the number of wavelengths without sacrificing the maximum cross correlation value i e still at most one they are particularly suitable for high bit rate optical code division multiple access systems with broadband mode locked lasers in which the number of time slots is very limited and system capacity can only be grown by increasing the number of wavelengths rather than code length finally a novel wavelength aware detector for wavelength hopping time spreading codes is discussed and shown to provide improved code performance

a dual active set algorithm for positive semi definite quadratic programming because of the many important applications of quadratic programming fast and efficient methods for solving quadratic programming problems are valued goldfarb and idnani 1983 describe one such method well known to be efficient and numerically stable the goldfarb and idnani method suffers only from the restriction that in its original form it cannot be applied to problems which are positive semi definite rather than positive definite in this paper we present a generalization of the goldfarb and idnani method to the positive semi definite case and prove finite termination of the generalized algorithm in our generalization we preserve the spirit of the goldfarb and idnani method and extend their numerically stable implementation in a natural way

construction of optimal 2d optical codes using n w 2 2 optical orthogonal codes two dimensional 2d wavelength time coding schemes have recently been studied for optical code division multiple access in this paper we propose a new family of 2d codes which use synchronized quadratic congruence sequences for wavelength hopping and n w 2 2 optical orthogonal codes for time spreading the new 2d codes provide larger asymptotically optimal code cardinality than other 2d codes by relaxing the maximum cross correlation function from one to two our study shows that the heavier code weight supported by our 2d codes results in better code performance than some of previously proposed 2d codes of the maximum cross correlation functions of one and two the new codes potentially support more subscribers and heavier bursty asynchronous traffic with gradual performance degradation as traffic load increases

constructions of optimal 2 d optical orthogonal codes via generalized cyclotomic classes optical orthogonal codes oocs are widely used as spreading codes in optical fiber networks in this paper a bound on the code size of 2 d oocs with both at most one pulse per wavelength am oppw and at most one pulse per time slot am oppts is derived accordingly two constructions of optimal 2 d oocs with both am oppw and am oppts are proposed via the generalized cyclotomic classes furthermore optimal 2 d ooc with am oppw can be also constructed by adding more codewords into the 2 d oocs with both am oppw and am oppts

new cyclic relative difference sets constructed from d homogeneous functions with difference balanced property for a prime power q we show that a cyclic relative difference set with parameters q sup n 1 q 1 q 1 q sup n 1 q sup n 2 can be constructed from a d homogeneous function from f sub q sup n spl bsol 0 onto f sub q with difference balanced property where f sub q sup n is the finite field with q sup n elements this construction method enables us to construct several new cyclic relative difference sets with parameters p sup n 1 p sup l 1 p sup l 1 p sup n l p sup n 2l from p ary sequences of period p sup n 1 with ideal autocorrelation property introduced by helleseth and gong using a lifting idea other new cyclic relative difference sets can be constructed from the helleseth gong hg sequences also the 3 ranks and the trace representation of the characteristic sequences of cyclic relative difference sets from a specific class of ternary hg sequences and ternary lin sequences are derived

a new class of optimal optical orthogonal codes with weight five a v k 1 optical orthogonal code ooc or briefly a v k 1 ooc c is a family of 0 1 sequences of length v and weight k satisfying the following two properties 1 spl sigma sub 0 spl les t spl les v 1 x sub t x sub t i spl les 1 for any x x sub 0 x sub 1 x sub v 1 spl isin c and any integer i spl ne 0 mod v 2 spl sigma sub 0 spl les t spl les v 1 x sub t y sub t i spl les 1 for any x x sub 0 x sub 1 x sub v 1 spl isin c y y sub 0 y sub 1 y sub v 1 spl isin c with x spl ne y and any integer i where the subscripts are reduced modulo v a v k 1 ooc is optimal if it contains spl lfloor v 1 k k 1 spl rfloor codewords in this note we establish that there exists an optimal 3 sup s 5v 5 1 ooc for any nonnegative integer s whenever visa product of primes congruent to 1 modulo 4 this improves the known existence results concerning optimal oocs

combinatorial constructions of optimal three dimensional optical orthogonal codes in this paper we study three dimensional u x v x w k lambda optical orthogonal codes oocs with at most one optical pulse per wavelength time plane am opp restriction which is denoted by am opp 3 d u x v x w k lambda ooc we build an equivalence relation between such an ooc and a certain combinatorial subject called a w cyclic group divisible packing of type vw u by this link the upper bound of the number of codewords is improved and some new combinatorial constructions are presented as an application the exact number of codewords of an optimal am opp 3 d uxvxw 3 1 ooc is determined for any positive integers v w and u sic 2 mod 6 with some possible exceptions

generalized multiresolution analysis on unstructured grids efficiency of high order essentially non oscillatory eno approximations of conservation laws may be drastically improved if ideas of multiresolution analysis are taken into account these methods of data compression not only reduce the necessary amount of discrete data but can also serve as tools in detecting local low dimensional features in the numerical solution we describe the mathematical background of the generalized multiresolution analysis as developed by abgrall and harten in 2 5 6 the functional analytic background is ultimately reduced to matrix vector operations of linear algebra we consider the important case of multiresolution analysis of cell average data which is used in finite volume approximations

new construction of multiwavelength optical orthogonal codes we investigate multiwavelength optical orthogonal codes mwoocs for optical code division multiple access particularly we present a new construction method for mn spl lambda 2 spl lambda mwoocs with the number of available wavelengths m codeword length n and constant hamming weight spl lambda 2 that have autocorrelation and cross correlation values not exceeding spl lambda in the proposed scheme there is no constraint on the relationship between the number of available wavelengths and the codeword length and it is also possible to use an arbitrary spl lambda we show that the constructed code is optimal especially for spl lambda 1 finally we analyze the bit error rate of the new code and compare it with that of other optical codes

a note on the equivalence between strict optical orthogonal codes and difference triangle sets zhang see ieee trans commun vol 47 p 967 973 july 1999 proposed a special family of optical address codes called strict optical orthogonal codes s oocs was proposed for fiber optic code division multiple access fo cdma networks such codes can strictly guarantee both cross correlation and autocorrelation functions constrained to have the value one in fully asynchronous data communications and ultra fast switching in zhang s work the theory and designs of s ooc plus several examples comparison tables and performance analyses were presented in this article we set up the equivalence between s ooc and so called difference triangle sets dts which have been extensively studied previously thus all the known constructions bounds and analyses for dts can be directly applied to s ooc