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

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

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

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

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

performance analyses on hybrid mqc m sequence coding over frequency spatial optical cdma system a new two dimensional frequency spatial code for spectral amplitude coding a optical code division multiple access system is proposed the corresponding coder decoder pairs are based on the tunable fiber bragg gratings cooperating with optical splitters combiners and multiple access interference can be eliminated through the proposed decoding mechanism for the performance analysis the effects of phase induced intensity noise shot noise and thermal noise are considered simultaneously bit error rate ber performance is compared with that of the former system using m matrix codes it is shown that the system using these new code matrices not only maintains most advantages of the former one but also allows larger number of active users under a given ber

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

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

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

multiclass multistage and multilevel fiber optic cdma signaling techniques based on advanced binary optical logic gate elements in this paper we introduce and propose novel signaling methods and receiver structures based on advanced binary optical logic gates for fiber optic code division multiple access fo cdma systems using all optical signal processing in the proposed system the users of the network are categorized into multiple classes users of each class transmit at the same power level but different from the levels of the other classes users using a combination of optical or and and xnor logic gates for the receiver structure we show that such a network not only takes the full advantages of all optical signal processing but also demonstrates a considerable throughput efficiency when compared to ordinary fo cdma systems the proposed receiver structure mitigates the effect of interfering users from the other classes by rejecting some specified power level combinations from the other classes the depth of interference cancellation is a function of the corresponding number of power levels and the number of stages applied to the optical logic gates in use in our analysis we choose the generalized form of optical orthogonal codes ooc i e oocs with cross correlation value greater than one as the signature sequence we begin by emphasizing on two level systems that is when the users can select one out of two power levels for signal transmission however for multilevel fo cdma we obtain a closed form relation for the upper bound on the probability of error we will show that under the ideal case the increase in throughput resulting from the proposed multilevel system is proportional to the number of classes or power levels in use our analytical results are compared to the results of an extensive system simulation the numerical closeness between the analytical and system simulation indicates the accuracy with which we have modeled mathematically our proposed signaling using advanced binary optical logic gates in fo cdma

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 lagrange dual lower bound to the error exponent of the typical random code a lagrange dual gallager style lower bound is derived for the error exponent function of the typical random code trc pertaining to the i i d random coding ensemble and mismatched stochastic likelihood decoding while the original expression derived from the method of types the csiszar style expression involves minimization over probability distributions defined on the channel input output alphabets the new lagrange dual formula involves optimization of five parameters independently of the alphabet sizes for both stochastic and deterministic mismatched decoding including maximum likelihood decoding as a special case we provide a rather comprehensive discussion on the insight behind the various ingredients of this formula and describe how its behavior varies as the coding rate exhausts the relevant range among other things it is demonstrated that this expression simultaneously generalizes both the expurgated error exponent function at zero rate and the classical random coding exponent function at high rates where it also meets the sphere packing bound

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

on line inference for multiple changepoint problems we propose an on line algorithm for exact filtering of multiple changepoint problems this algorithm enables simulation from the true joint posterior distribution of the number and position of the changepoints for a class of changepoint models the computational cost of this exact algorithm is quadratic in the number of observations we further show how resampling ideas from particle filters can be used to reduce the computational cost to linear in the number of observations at the expense of introducing small errors and propose two new optimum resampling algorithms for this problem one a version of rejection control allows the particle filter to automatically choose the number of particles required at each time step the new resampling algorithms substantially out perform standard resampling algorithms on examples we consider and we demonstrate how the resulting particle filter is practicable for segmentation of human gc content

the probability of undetected error for binary constant weight codes in this correspondence we study the probability of undetected error for binary constant weight codes first we derive a new formula on the probability of undetected error for binary constant weight codes second using this new formula and linear programming we give two new lower bounds on the probability of undetected error for binary constant weight codes these two new lower bounds improve on previously known lower bounds in certain cases furthermore we show that these two lower bounds are tight if and only if the binary constant weight codes are generated from certain t designs in combinatorial design theory this means that these binary constant weight codes generated from certain t designs are uniformly optimal for error detection along the way we determine the distance distributions of such binary constant weight codes finally several examples are given to illustrate the results obtained in this correspondence

compositional segmentation and long range fractal correlations in dna sequences a segmentation algorithm based on the jensen shannon entropic divergence is used to decompose long range correlated dna sequences into statistically significant compositionally homogeneous patches by adequately setting the significance level for segmenting the sequence the underlying power law distribution of patch lengths can be revealed some of the identified dna domains were uncorrelated but most of them continued to display long range correlations even after several steps of recursive segmentation thus indicating a complex multi length scaled structure for the sequence on the other hand by separately shuffling each segment or by randomly rearranging the order in which the different segments occur in the sequence shuffled sequences preserving the original statistical distribution of patch lengths were generated both types of random sequences displayed the same correlation scaling exponents as the original dna sequence thus demonstrating that neither the internal structure of patches nor the order in which these are arranged in the sequence is critical therefore long range correlations in nucleotide sequences seem to rely only on the power law distribution of patch lengths textcopyright 1996 the american physical society

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

the generalized stochastic likelihood decoder random coding and expurgated bounds the likelihood decoder is a stochastic decoder that selects the decoded message at random using the posterior distribution of the true underlying message given the channel output in this paper we study a generalized version of this decoder where the posterior is proportional to a general function that depends only on the joint empirical distribution of the output vector and the code word this framework allows both mismatched versions and universal versions of the likelihood decoder as well as the corresponding ordinary deterministic decoders among many others we provide a direct analysis method that yields the exact random coding exponent as opposed to separate upper bounds and lower bounds that turn out to be compatible which were derived earlier by scarlett et al we also extend the result from pure channel coding to combined source and channel coding random binning followed by random channel coding with side information available to the decoder finally returning to pure channel coding we derive also an expurgated exponent for the stochastic likelihood decoder which turns out to be at least as tight and in some cases strictly so as the classical expurgated exponent of the maximum likelihood decoder even though the stochastic likelihood decoder is suboptimal

sequence designs for ultra wideband impulse radio with optimal correlation properties we formulate a combinatorial model of impulse radio sequences irss to study sequence or signal design for ultra wideband uwb radio with unmodulated time hopping using this combinatorial model for irss we develop necessary and sufficient conditions for the existence of irss several novel constructions for irss with optimal correlation properties are given the constructions involve the welch construction for costas arrays a quadratic polynomial construction over finite fields recursive techniques for optical orthogonal codes and combinatorial design techniques using perfect mendelsohn designs pmds

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

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 cdma 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 lambda 1 were considered we consider generalized oocs with 1 leq lambda leq w where w is the weight of the corresponding codes to enhance the performance of such systems we propose that use of optical and gate receiver which in an ideal case e g in the absence of any noise source except the optical multiple access noise is optimum using some basic laws on probability we present direct and exact solutions for oocs with lambda 1 2 3 ldots w with optical and 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 lambdageq 1 in particular we can obtain some simple relations between p e min minimum error rate l min minimum required ooc length and n max maximum number of interfering users to be supported which are the most desired parameters for any optical cdma system design furthermore we show that in most practical cases oocs with lambda 2 or 3 perform better than oocs with 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 sqrt2lambda l where l is the length of the oocs used in systems

multiple changepoint fitting via quasilikelihood with application to dna sequence segmentation summary we consider situations where a step function with a variable number of steps provides an adequate model for a regression relationship while the variance of the observations depends on their mean this model provides for discontinuous jumps at changepoints and for constant means and error variances in between changepoints the basic statistical problem consists of identification of the number of changepoints their locations and the levels the function assumes in between we embed this problem into a quasilikelihood formulation and utilise the minimum deviance criterion to fit the model for the choice of the number of changepoints we discuss a modified schwarz criterion a dynamic programming algorithm makes the segmentation feasible for sequences of moderate length the performance of the segmentation method is demonstrated in an application to the segmentation of the bacteriophage l sequence

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

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

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

new upper bounds for impulse radio sequences impulse radio sequences irss were first introduced by chu and colbourn in ieee trans inf theory vol 50 pp 2402 2407 2004 in this correspondence we investigate the upper bound for this class of sequences by using the relationship between irss and cps a new upper bound for m k 1 irs is given which improves the johnson bound

error exponents of typical random codes we define the error exponent of the typical random code trc as the long block limit of the negative normalized expectation of the logarithm of the error probability of the random code as opposed to the traditional random coding error exponent which is the limit of the negative normalized logarithm of the expectation of the error probability for the ensemble of uniformly randomly drawn fixed composition codes we provide exact error exponents of trcs for a general discrete memoryless channel and a wide class of stochastic decoders collectively referred to as the generalized likelihood decoder gld this ensemble of fixed composition codes is shown to be no worse than any other ensemble of independent codewords that are drawn under a permutation invariant distribution e g independent identically distributed codewords we also present relationships between the error exponent of the trc and the ordinary random coding error exponent as well as the expurgated exponent for the gld finally we demonstrate that our analysis technique is applicable also to more general communication scenarios such as list decoding for fixed size lists as well as the decoding with an erasure list option in forney s sense

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

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

exact bayesian curve fitting and signal segmentation we consider regression models where the underlying functional relationship between the response and the explanatory variable is modeled as independent linear regressions on disjoint segments we present an algorithm for perfect simulation from the posterior distribution of such a model even allowing for an unknown number of segments and an unknown model order for the linear regressions within each segment the algorithm is simple can scale well to large data sets and avoids the problem of diagnosing convergence that is present with monte carlo markov chain mcmc approaches to this problem we demonstrate our algorithm on standard denoising problems on a piecewise constant ar model and on a speech segmentation problem

coherent optical pulse cdma systems based on coherent correlation detection passive optical matched filtered detection mfd has been employed in many proposed optical pulse code division multiple access cdma system implementations driving the development of unipolar pseudo orthogonal codes incoherent coherent optical pulse cdma systems based on coherent correlation detection ccd through homodyne correlation detection hcd and self hcd directly in the optical domain is proposed with hcd optical sequences from a pulsed laser modulated by the data and encoded by an optical tapped delay line encoder are multiplexed in an optical fiber network at the receiver the optical code sequence of the intended user is locally generated through proper code and carrier phase synchronization the local optical code is multiplied with the received signal chip by chip via an optical correlator consisting of a 3 db coupler and a balanced detector thresholding is performed in the electrical domain after integration of the optical correlator output over one bit interval the self hcd approach utilizes two bipolar code sequences multiplexed alternately in time obviating the need for the generation of a local code at the receiver the received signal is divided at the receiver decoded by two encoders matched to those at the transmitters and correlated via the optical correlator the removal for the need of the local oscillator avoids the stringent implementation issues with hcd such as optical frequency stability and carrier phase noise following a description of the two implementations system performances are theoretically analyzed and a comparison of the several approaches given

statistical mechanics of error exponents for error correcting codes error exponents characterize the exponential decay when increasing message length of the probability of error of many error correcting codes to tackle the long standing problem of computing them exactly we introduce a general thermodynamic formalism that we illustrate with maximum likelihood decoding of low density parity check codes on the binary erasure channel and the binary symmetric channel in this formalism we apply the cavity method for large deviations to derive expressions for both the average and typical error exponents which differ by the procedure used to select the codes from specified ensembles when decreasing the noise intensity we find that two phase transitions take place at two different levels a glass to ferromagnetic transition in the space of codewords and a paramagnetic to glass transition in the space of codes

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

a bayesian analysis for change point problems a sequence of observations undergoes sudden changes at unknown times we model the process by supposing that there is an underlying sequence of parameters partitioned into contiguous blocks of equal parameter values the beginning of each block is said to be a change point observations are then assumed to be independent in different blocks given the sequence of parameters in a bayesian analysis it is necessary to give probability distributions to both the change points and the parameters we use product partition models barry and hartigan 1992 which assume that the probability of any partition is proportional to a product of prior cohesions one for each block in the partition and that given the blocks the parameters in different blocks have independent prior distributions given the observations a new product partition model holds with posterior cohesions for the blocks and new independent block posterior distributions for parameters the product model thus provides a convenient machinery for allo

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

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

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

error exponent for multiple access channels upper bounds the problem of bounding the reliability function of a multiple access channel mac is studied two new upper bounds on the error exponent of a two user discrete memoryless dm mac are derived the first bound sphere packing is an upper bound on the exponent of the average probability of error and is the first bound of this type that is zero outside the capacity region and thus results in a tighter sphere packing exponent when compared with the tightest known exponent derived by haroutunian the second bound minimum distance is an upper bound on the exponent of the maximal as opposed to average probability of error to obtain this bound first an upper bound on the minimum bhattacharyya distance between codeword pairs is derived for a certain class of two user dm macs an upper bound on the exponent of maximal probability of error is derived as a consequence of the upper bound on the minimum bhattacharyya distance we analytically evaluate the sphere packing bound for uniform composition codes for an additive and nonsymmetric channel and show that it is tight near the boundary of the capacity region i e equal to the random coding lower bound

multi threshold accelerated failure time model a two stage procedure for simultaneously detecting multiple thresholds and achieving model selection in the segmented accelerated failure time aft model is developed in this paper in the first stage we formulate the threshold problem as a group model selection problem so that a concave 2 norm group selection method can be applied in the second stage the thresholds are finalized via a refining method we establish the strong consistency of the threshold estimates and regression coefficient estimates under some mild technical conditions the proposed procedure performs satisfactorily in our simulation studies its real world applicability is demonstrated via analyzing a follicular lymphoma data

bayesian analysis of isochores statistical identification of isochore structure the variation in large scale gc composition proportion of dna bases that are g or c as opposed to a or t of mammalian genomes is a necessary requirement for understanding both the evolution of base composition and the many genomic features such as mutation and recombination rates which covary with base composition we have developed a bayesian method for isochore analysis that we demonstrate to be more accurate than the commonly used binary segmentation approach implemented within the program isofinder the method accounts for both fine scale and large scale structure we adapt direct simulation methods to allow for iid samples from the posterior distribution of our model and provide an accurate approximation to this that can analyze data from a chromosome in a matter of seconds we apply our method to human chromosome 1 the resulting estimate of how gc content varies across this region is shown to be a better predictor of local recombination rates t

large deviations behavior of the logarithmic error probability of random codes this work studies the deviations of the error exponent of the constant composition code ensemble around its expectation known as the error exponent of the typical random code trc in particular it is shown that the probability of randomly drawing a codebook whose error exponent is smaller than the trc exponent is exponentially small upper and lower bounds for this exponent are given which coincide in some cases in addition the probability of randomly drawing a codebook whose error exponent is larger than the trc exponent is shown to be double exponentially small upper and lower bounds to the double exponential exponent are given the results suggest that codebooks whose error exponent is larger than the error exponent of the trc are extremely rare the key ingredient in the proofs is a new large deviations result of type class enumerators with dependent variables

graph decomposition a new key to coding theorems a new and simple method is proposed for finding good encoders both for channels and for sources with side information this method relies on the continuous version of a graph decomposition result of lovasz the presently known best exponential error bounds for both problems follow in a unified manner with an improvement on the source coding bound the previous bounds for universal codes of the authors and marton are also improved

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

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

geometric orthogonal codes of size larger than optical orthogonal codes the class of geometric orthogonal codes gocs was introduced by doty and winslow 2016 for more robust macrobonding in dna origami they observed that gocs are closely related to optical orthogonal codes oocs it is possible for gocs to have size greater than oocs of corresponding parameters due to slightly more relaxed constraints on correlations however the existence of gocs exceeding the size of optimal oocs of corresponding parameters has never been demonstrated this paper gives the first infinite family of gocs of size greater than optimal oocs

multiscale change point inference summary we introduce a new estimator the simultaneous multiscale change point estimator smuce for the change point problem in exponential family regression an unknown step function is estimated by minimizing the number of change points over the acceptance region of a multiscale test at a level the probability of overestimating the true number of change points k is controlled by the asymptotic null distribution of the multiscale test statistic further we derive exponential bounds for the probability of underestimating k by balancing these quantities will be chosen such that the probability of correctly estimating k is maximized all results are even non asymptotic for the normal case on the basis of these bounds we construct asymptotically honest confidence sets for the unknown step function and its change points at the same time we obtain exponential bounds for estimating the change point locations which for example yield the minimax rate up to a log term finally the simultaneous multiscale change point estimator achieves the optimal detection rate of vanishing signals as n even for an unbounded number of change points we illustrate how dynamic programming techniques can be employed for efficient computation of estimators and confidence regions the performance of the multiscale approach proposed is illustrated by simulations and in two cutting edge applications from genetic engineering and photoemission spectroscopy

rejection control and sequential importance sampling abstract we discuss ways of combining rejection sampling and importance sampling methods in monte carlo computations and demonstrate their usefulness in updating dynamic systems specifically we propose the rejection controlled sequential importance sampling rc sis algorithm which is designed to simultaneously reduce monte carlo variation and retain independent samples in sequential importance sampling the proposed method is demonstrated by three examples taken from econometrics hierarchical bayes analysis and digital telecommunications they all show significant improvements over previous results

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

error exponents of typical random codes for the colored gaussian channel the error exponent of the typical random code is defined as the asymptotic normalized expectation of the logarithm of the probability of error as opposed to the traditional definition of the random coding exponent as the normalized logarithm of the expectation of the probability of error with respect to a given ensemble of codes for a certain ensemble of independent codewords with a given power spectrum and a generalized stochastic mismatched decoder we characterize the error exponent of the typical random codes trc for the colored gaussian channel with emphasis on the range of low rates where the trc error exponent differs in value from the ordinary random coding error exponent the error exponent formula which is exponentially tight at some range of low rates is presented as the maximum of a certain function with respect to one parameter only in the spirit of gallager s formulas in the case of matched decoding and two parameters in the case of mismatched decoding several aspects of the main results are discussed these include general properties a parametric representation critical rates phase transitions optimal input spectrum water pouring and comparison to the random coding exponent

optical orthogonal code division multiple access system ii multibits sequence period oocdma for part i see ibid vol 42 no 7 p 2470 1994 in a recently proposed optical orthogonal code division multiple access oocdma system one bit of user s data is transmitted per sequence period and a threshold is employed for the final bit decision in this paper a system that can transmit multibits per sequence period is introduced and avalanche photodiode apd noise thermal noise and interference are included this system derived by exploiting orthogonal properties of the oocdma code sequence and using a maximum search instead of a threshold in the final decision is log sub 2 f times higher in throughput where f is sequence period for example four orders of magnitude are better in bit error probability at 56 dbw received laser power with f 1000 chips 10 marks in a sequence and 10 users of 30 mb s data rate for one bit sequence period and 270 mb s data rate for multibits sequence period system furthermore an exact analysis is performed for the log sub 2 f bits sequence period system with a hard limiter placed before the receiver and its performance is compared to the performance without hard limiter for the chip synchronous case the improvement from using a hard limiter is significant in the log sub 2 f bits sequence period occdma system while it is not in a one bit sequence period oocdma system proposed in part i

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

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

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

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

disjoint difference sets difference triangle sets and related codes disjoint difference sets dds difference triangle sets dts and related codes are discussed and a recursive construction for dds is given with this construction and the relationship between dds and dts many new upper bounds for dts and some better orthogonal codes are obtained

maximum likelihood estimation of order m for stationary stochastic processes sometimes the likelihood cannot be computed even introducing approximations whose effect is asymptotically negligible to overcome this problem for inference from a stochastic process we approximate the log likelihood by a sum whose generic term is the density function of the corresponding sample element conditional on the m most recent observations for some m s 0 general results on the asymptotic properties of the associated estimates are given and numerical comparisons with other estimators are carried out in special cases

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

an exact gibbs sampler for the markov modulated poisson process a markov modulated poisson process mmpp is a poisson process whose intensity varies according to a markov process we present a novel technique for simulating from the exact distribution of a continuous time markov chain over an interval given the start and end states and the infinitesimal generator and use this to create a gibbs sampler which samples from the exact distribution of the hidden markov chain in an mmpp we apply the gibbs sampler to modelling the occurrence of a rare dna motif the chi site and to inferring regions of the genome with evidence of high or low intensities for occurrences of this site

product partition models for change point problems product partition models assume that observations in different components of a random partition of the data are independent if the probability distribution of random partitions is in a certain product form prior to making the observations it is also in product form given the observations the product model thus provides a convenient machinery for allowing the data to weight the partitions likely to hold and inference about particular future observations may then be made by first conditioning on the partition and then averaging over all partitions these models apply with special computational simplicity to change point problems where the partitions divide the sequence of observations into components within which different regimes hold we show with appropriate selection of prior product models that the observations can eventually determine approximately the true partition

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