minimizing total weighted completion time in a two machine flow shop scheduling under simple linear deterioration abstract in this paper we address a two machine flow shop scheduling problem under simple linear deterioration by a simple linear deterioration function we mean that the processing time of a job is a simple linear function of its execution start time the objective is to find a sequence that minimizes total weighted completion time optimal schedules are obtained for some special cases for the general case several dominance properties and two lower bounds are derived to speed up the elimination process of a branch and bound algorithm a heuristic algorithm is also proposed to overcome the inefficiency of the branch and bound algorithm computational analysis on randomly generated problems is conducted to evaluate the branch and bound algorithm and heuristic algorithm

sample adaptive product quantization asymptotic analysis and examples vector quantization vq is an efficient data compression technique for low bit rate applications however the major disadvantage of vq is that its encoding complexity increases dramatically with bit rate and vector dimension even though one can use a modified vq such as the tree structured vq to reduce the encoding complexity it is practically infeasible to implement such a vq at a high bit rate or for large vector dimensions because of the huge memory requirement for its codebook and for the very large training sequence requirement to overcome this difficulty a structurally constrained vq called the sample adaptive product quantizer sapq has recently been proposed we extensively study the sapq that is based on scalar quantizers in order to exploit the simplicity of scalar quantization through an asymptotic distortion result we discuss the achievable performance and the relationship between distortion and encoding complexity we illustrate that even when sapq is based on scalar quantizers it can provide vq level performance we also provide numerical results that show a 2 3 db improvement over the lloyd max 1982 1960 quantizers for data rates above 4 b point

a pyramid vector quantizer the geometric properties of a memoryless laplacian source are presented and used to establish a source coding theorem motivated by this geometric structure a pyramid vector quantizer pvq is developed for arbitrary vector dimension the pvq is based on the cubic lattice points that lie on the surface of an l dimensional pyramid and has simple encoding and decoding algorithms a product code version of the pvq is developed and generalized to apply to a variety of sources analytical expressions are derived for the pvq mean square error mse and simulation results are presented for pvq encoding of several memoryless sources for large rate and dimension pvq encoding of memoryless laplacian gamma and gaussian sources provides rose improvements of 5 64 8 40 and 2 39 db respectively over the corresponding optimum scalar quantizer although suboptimum in a rate distortion sense because the pvq can encode large dimensional vectors it offers significant reduction in rose distortion compared with the optimum lloyd max scalar quantizer and provides an attractive alternative to currently available vector quantizers

completely solvable models with nearest neighbor interactions on one dimensional lattices abstract the most general exclusion single species reaction diffusion models are investigated which are defined on a one dimensional lattice have nearest neighbor interactions and their corresponding two site hamiltonians are diagonalizable or converted to a jordan form by a direct product of matrices the diagonalizable hamiltonians represent a family of 3 parameter stochastic processes while those which can be transformed into a jordan form have 4 free parameters for the diagonalizable hamiltonians all of the eigenvalues and eigenvectors and some correlation functions are explicitly calculated also both the entropy and the entropy production rate in such systems are studied for those hamiltonians which can be converted to a jordan form some parts of the spectrum are obtained

high resolution quantization theory and the vector quantizer advantage the authors consider how much performance advantage a fixed dimensional vector quantizer can gain over a scalar quantizer they collect several results from high resolution or asymptotic in rate quantization theory and use them to identify source and system characteristics that contribute to the vector quantizer advantage one well known advantage is due to improvement in the space filling properties of polytopes as the dimension increases others depend on the source s memory and marginal density shape the advantages are used to gain insight into product transform lattice predictive pyramid and universal quantizers although numerical prediction consistently overestimated gains in low rate 1 bit sample experiments the theoretical insights may be useful even at these rates

entropy constrained vector quantization an iterative descent algorithm based on a lagrangian formulation for designing vector quantizers having minimum distortion subject to an entropy constraint is discussed these entropy constrained vector quantizers ecvqs can be used in tandem with variable rate noiseless coding systems to provide locally optimal variable rate block source coding with respect to a fidelity criterion experiments on sampled speech and on synthetic sources with memory indicate that for waveform coding at low rates about 1 bit sample under the squared error distortion measure about 1 6 db improvement in the signal to noise ratio can be expected over the best scalar and lattice quantizers when block entropy coded with block length 4 even greater gains are made over other forms of entropy coded vector quantizers for pattern recognition it is shown that the ecvq algorithm is a generalization of the k means and related algorithms for estimating cluster means in that the ecvq algorithm estimates the prior cluster probabilities as well experiments on multivariate gaussian distributions show that for clustering problems involving classes with widely different priors the ecvq outperforms the k means algorithm in both likelihood and probability of error

asymptotically optimal model estimation for quantization using high rate theory approximations we introduce flexible practical quantizers based on possibly non gaussian models in both the constrained resolution cr and the constrained entropy cases we derive model estimation criteria optimizing asymptotic with increasing rate quantizer performance we show that in the cr case the optimal criterion is different from the maximum likelihood criterion commonly used for that purpose and introduce a new criterion that we call constrained resolution minimum description length cr mdl we apply these principles to the generalized gaussian scaled mixture model which is accurate for many real world signals we provide an explanation of the reason why the cr mdl improves quantization performance in the cr case and show that cr mdl can compensate for a possible mismatch between model and data distribution thus this criterion is of a great interest for practical applications our experiments apply the new quantization method to controllable artificial data and to the commonly used modulated lapped transform representation of audio signals we show that both the cr mdl criterion and a non gaussian modeling have significant advantages

the conical point in the ferroelectric six vertex model we examine the last unexplored regime of the asymmetric six vertex model the low temperature phase of the so called ferroelectric model the original publication of the exact solution by sutherland yang and yang and various derivations and reviews published afterward do not contain many details about this regime we study the exact solution for this model by numerical and analytical methods in particular we examine the behavior of the model in the vicinity of an unusual coexistence point that we call the conical point this point corresponds to additional singularities in the free energy that were not discussed in the original solution we show analytically that at this point many polarizations coexist and that unusual scaling properties hold in its vicinity

on uniform quantization with various distortion measures corresp upper bounds are presented for the difference in entropy between that of a uniform scalar quantizer and that of any n dimensional quantizer the bounds are universal in the sense that they suit every input density and every value of distortion bounds were found for some common distortion criteria

non abelian symmetries of stochastic processes derivation of correlation functions for random vertex models and disordered interacting particle systems we consider systems of particles hopping stochastically on d dimensional lattices with space dependent probabilities we map the master equation onto an evolution equation in a fock space where the dynamics are given by a quantum hamiltonian continuous time or a transfer matrix discrete time using non abelian symmetries of these operators we derive duality relations expressing the time evolution of a given initial configuration in terms of correlation functions of simpler dual processes particularly simple results are obtained for the time evolution of the density profile as a special case we show that for any su 2 symmetric system the two point and three point density correlation functions in the n particle steady state can be computed from the probability distribution of a single particle moving in the same environment we apply our results to various models among them partial exclusion a simple diffusion reaction system and the two dimensional six vertex model with space dependent vertex weights for a random distribution of the vertex weights one obtains a version of the random barrier model describing diffusion of particles in disordered media we derive exact expressions for the averaged two point density correlation functions in the presence of weak correlated disorder

generalized pairwise interchanges and machine scheduling abstract in this paper a generalization of pairwise interchanges is considered and applied to machine scheduling problems it is shown how these swap operators can be used to compute bounds for branch and bound procedures to prove dominance properties and to define a high performance neighborhood for local search methods

vector quantizer design for memoryless gaussian gamma and laplacian sources locally optimum vector quantizer vq designs are presented for memoryless gaussian gamma and laplacian sources for gaussian sources low 2 6 dimensional vector quantization provides relatively little improvement in mean squared error mse compared to the minimum mean squared error mmse scalar quantizer for laplacian or gamma sources however significant improvement in mse is available with vector quantization the laplacian and gamma 6 bit sixdimensional vector quantizers achieve respectively improvements of 2 and 4 5 db over the corresponding scalar mmse quantizer distortions

quantization based on a novel sample adaptive product quantizer sapq in this paper we propose a novel feedforward adaptive quantization scheme called the sample adaptive product quantizer sapq this is a structurally constrained vector quantizer that uses unions of product codebooks sapq is based on a concept of adaptive quantization to the varying samples of the source and is very different from traditional adaptation techniques for nonstationary sources sapq quantizes each source sample using a sequence of quantizers even when using scalar quantization in sapq we can achieve performance comparable to vector quantization with the complexity still close to that of scalar quantization we also show that important lattice based vector quantizers can be constructed using scalar quantization in sapq we mathematically analyze sapq and propose a algorithm to implement it we numerically study sapq for independent and identically distributed gaussian and laplacian sources through our numerical study we find that sapq using scalar quantizers achieves typical gains of 13 db in distortion over the lloyd max quantizer we also show that sapq can he used in conjunction with vector quantizers to further improve the gains

an algorithm for uniform vector quantizer design a vector quantizer maps a k dimensional vector into one of a finite set of output vectors or points although certain lattices have been shown to have desirable properties for vector quantization applications there are as yet no algorithms available in the quantization literature for building quantizers based on these lattices an algorithm for designing vector quantizers based on the root lattices a n d n and e n and their duals is presented also a coding scheme that has general applicability to all vector quantizers is presented a four dimensional uniform vector quantizer is used to encode laplacian and gamma distributed sources at entropy rates of one and two bits sample and is demonstrated to achieve performance that compares favorably with the rate distortion bound and other scalar and vector quantizers finally an application using uniform four and eight dimensional vector quantizers for encoding the discrete cosine transform coefficients of an image at 0 5 bit pel is presented which visibly illustrates the performance advantage of vector quantization over scalar quantization

multiple local optima in vector quantizers corresp two results are presented on vector quantizers meeting necessary conditions for optimality first a simple generalization of well known centroid and moment properties of the squared error distortion measure to a weighted quadratic distortion measure with an input dependent weighting is presented the second result is an application of the squared error special case of the first result to a simulation study of the design of 1 bit per sample two and three dimensional quantizers for a memoryless gaussian source using the generalized lloyd technique the existence of multiple distinct local optima is demonstrated thereby showing that sufficient conditions for unique local optima do not exist for this simple common case it is also shown that at least three dimensions are required for a vector quantizer to outperform a scalar quantizer for this source

minimizing total completion time in a two machine we consider the problem of minimizing total completion time in a two machine owshop we present a heuristic with worst case bound 2 where and denote the minimum and maximum processing time of all operations furthermore we analyze four special cases equal processing times on the first machine equal processing times on the second machine processing a job on the first machine takes time no less than its processing on the second machine and processing a job on the first machine takes time no more than its processing on the second machine we prove that the rst special case is np hard in the strong sense and present an o n log n approximation algorithm for it with worst case bound 4 3 we repeat the easy polynomial algorithms for the cases two and three and show that problem four is solvable in polynomial time as well

a branch and bound algorithm for three machine flowshop scheduling problem to minimize total completion time with separate setup times in this paper we address the three machine flowshop scheduling problem setup times are considered separate from processing times and the objective is to minimize total completion time we show that the three site distributed database scheduling problem can be modeled as a three machine flowshop scheduling problem a lower bound is developed and a dominance relation is established moreover an upper bound is developed by using a three phase hybrid heuristic algorithm furthermore a branch and bound algorithm incorporating the developed lower bound dominance relation and the upper bound is presented computational analysis on randomly generated problems is conducted to evaluate the lower and upper bounds the dominance relation and the branch and bound algorithm the analysis shows the efficiency of the upper bound and hence it can be used for larger size problems as a heuristic algorithm

an effective differential evolution algorithm for permutation flow shop scheduling problem the permutation flow shop problem pfssp is an np hard problem of wide engineering and theoretical background in this paper a hybrid differential evolution de called l hde is proposed to solve the flow shop scheduling problem which combines the de with the individual improving scheme iis and greedy based local search first to make de suitable for pfssp a new largest rank rule lrv based on a random key is introduced to convert the continuous position in de to the discrete job permutation so that the de can be used for solving pfssp second the neh heuristic was combined with the random initialization to initialize the population with certain quality and diversity third the iis based local search is used for improving the diversity of population and enhancing the quality of the solution with a certain probability fourth the greedy based local search is designed to help the algorithm to escape from local minimum additionally simulations and comparisons based on pfssp benchmarks are carried out which show that our algorithm is both effective and efficient

generalized bethe ansatz solution of a one dimensional asymmetric exclusion process on a ring with blockage we present a model for a one dimensional anisotropic exclusion process describing particles moving deterministically on a ring of lengthl with a single defect across which they move with probability 0 p 1 this model is equivalent to a two dimensional six vertex model in an extreme anisotropic limit with a defect line interpolating between open and periodic boundary conditions we solve this model with a bethe ansatz generalized to this kind of boundary condition we discuss in detail the steady state and derive exact expressions for the currentj the density profilen x and the two point density correlation function in the thermodynamic limitl the phase diagram shows three phases a low density phase a coexistence phase and a high density phase related to the low density phase by a particle hole symmetry in the low density phase the density profile decays exponentially with the distance from the boundary to its bulk value on a length scale on the phase transition line diverges and the currentj approaches its critical valuejc p as a power law jc j 1 2 in the coexistence phase the width of the interface between the high density region and the low density region is proportional tol1 2 if the density f 1 2 and 0 independent ofl if 1 2 the connected two point correlation function turns out to be of a scaling form with a space dependent amplitude n x1 x2 a x2 ake r withr x2 x1 and a critical exponent 0

two results on the asymptotic performance of quantizers a necessary and sufficient condition is presented for the normalized asymptotic r th power distortion of a mismatched multidimensional quantizer to converge to a certain optimum constant known as bennett s integral the dimensionality of our results is allowed to approach infinity in order to make some universal source coding comparisons to quantization theory

on universal quantization the quantization of n dimensional vectors in r n with an arbitrary probability measure under a mean square error constraint is discussed it is demonstrated that a uniform one dimensional quantizer followed by a noiseless digital variable rate encoder entropy encoding can yield a rate that is for any n no more than 0 754 bit per sample higher than the rate associated with the optimal n dimensionai quantizer regardless of the probabilistic characterization of the input n vector for the allowable mean square error

the progressive transmission disadvantage the disadvantage of progressive transmission compared to transmission in a single step is analyzed for the high rate case using a polytope that is self similar under binary subdivision this disadvantage is calculated to be 0 3424 db or 0 057 bit compared to scalar quantization obtained with a step size of 1 bit per ensemble

fast quantizing and decoding and algorithms for lattice quantizers and codes for each of the lattices a n n geq 1 d n n geq 2 e 6 e 7 e 8 and their duals a very fast algorithm is given for finding the closest lattice point to an arbitrary point if these lattices are used for vector quantizing of uniformly distributed data the algorithm finds the minimum distortion lattice point if the lattices are used as codes for a gaussian channel the algorithm performs maximum likelihood decoding

vector quantizers and predictive quantizers for gauss markov sources low rate vector quantizers are designed and simulated for highly correlated gauss markov sources and the resulting performance is compared with arnstein s optimized predictive quantizer and with huang and schultheiss optimized transform coder two implementations of vector quantizers are considered full search vector quantizers which are optimal but require large codebook searches and tree searched vector quantizers which are suboptimal but require far less searching the various systems are compared on the basis of performance complexity and generality of design techniques

extension of two stage vector quantization lattice vector quantization this paper is the extension of two stage vector quantization spherical lattice vector quantization vq s lvq recently introduced by pan and fischer see ieee trans inform theory vol 41 p 155 1995 first according to high resolution quantization theory generalized vector quantization lattice vector quantization g vq lvq is formulated in order to release the constraint of the spherical boundary for the second stage lattice vector quantization lvq which would provide possibilities of improving this kind of two stage unstructured structured quantizer by using more efficient lvq second among g vq lvq vector quantization pyramidal lattice vector quantization vq plvq is developed which is slightly superior or comparable to vq s lvq in performance but has a much lower complexity simulation results show that for memoryless sources vq plvq achieves a rate distortion performance that is among the best of the fixed rate quantization that we found in the literature therefore vq plvq is an attractive alternative to vq s lvq in practice third transform vq plvq tvq plvq is proposed for sources with memory for encoding 16 d vectors of the gauss markov source t vq plvq has an advantage of close to 1 0 db over vq plvq and is about 0 5 db better than vq s lvq

on the description of the glauber dynamics of one dimensional disordered ising chain abstract the method based on the use of the generating functions of spin correlators was proposed for the description of the glauber dynamics of disordered ising chain the partial differential equations was derived for these generating functions and the formal solutions were obtained the exact solutions for generating functions were found for the ising chain with alternating coupling constants

the two machine flowshop total completion time problem improved lower bounds and a branch and bound algorithm abstract this paper presents a branch and bound algorithm for the two machine flowshop scheduling problem with the objective of minimizing the sum of completion times the main feature of the branch and bound algorithm is a new lower bounding scheme that is based on a network formulation of the problem with extensive computational tests we demonstrate that the branch and bound algorithm can solve problems with up to 60 45 jobs where processing times are uniformly distributed in the 1 10 1 100 range

upper bounds to the asymptotic performance of block quantizers upper bounds to the asymptotic performance of block quantizers with difference distortion measures are derived in many eases these upper bounds approach known lower bounds as the block length of the quantizer approaches infinity a condition for the optimal point density function of the output levels is derived it is shown to particularize to a known result of gersho the behavior of the bounds for large block lengths is investigated

a word counting technique for the solution of stochastic equations a solution method for finding a stationary state of stochastic equations describing one dimensional nonequilibrium systems with random sequential update is proposed it is proved that if such a system with periodic boundary condition allows for a solution with finite range correlations then this solution can be written as a product of cluster functions the solution can then be found by setting the coefficients of the linearly independent word counts occurring for a ring to zero these sets of linearly independent word counts are described generally the extension of these results to an open linear chain is indicated general solutions for 1 and 2 clusters are derived completely solved examples include i a monomer dimer model ii the general pair reaction diffusion system iii an extension of the asymmetric exclusion process to two different types of particles on a ring and on a chain and iv the general exclusion process with dependence on the states of the neighbour sites many more examples are discussed more briefly in all cases with particle conservation the results are corroborated by simulations

the two machine flowshop total completion time problem branch and bound algorithms based on network flow formulation abstract we consider the flowshop problem on two machines with sequence independent setup times to minimize total completion time large scale network flow formulations of the problem are suggested together with strong lagrangian bounds based on these formulations to cope with their size filtering procedures are developed to solve the problem to optimality we embed the lagrangian bounds into two branch and bound algorithms the best algorithm is able to solve all 100 job instances of our testbed with setup times and all 140 job instances without setup times thus significantly outperforming the best algorithms in the literature

a vector quantization approach to universal noiseless coding and quantization a two stage code is a block code in which each block of data is coded in two stages the first stage codes the identity of a block code among a collection of codes and the second stage codes the data using the identified code the collection of codes may be noiseless codes fixed rate quantizers or variable rate quantizers we take a vector quantization approach to two stage coding in which the first stage code can be regarded as a vector quantizer that quantizes the input data of length n to one of a fixed collection of block codes we apply the generalized lloyd algorithm to the first stage quantizer using induced measures of rate and distortion to design locally optimal two stage codes on a source of medical images two stage variable rate vector quantizers designed in this way outperform standard one stage fixed rate vector quantizers by over 9 db the tail of the operational distortion rate function of the first stage quantizer determines the optimal rate of convergence of the redundancy of a universal sequence of two stage codes we show that there exist two stage universal noiseless codes fixed rate quantizers and variable rate quantizers whose per letter rate and distortion redundancies converge to zero as k 2 n sup 1 log n when the universe of sources has finite dimension k this extends the achievability part of rissanen s theorem from universal noiseless codes to universal quantizers further we show that the redundancies converge as o n sup 1 when the universe of sources is countable and as o n sup 1 spl epsiv when the universe of sources is infinite dimensional under appropriate conditions

bennett s integral for vector quantizers this paper extends bennett s 1948 integral from scalar to vector quantizers giving a simple formula that expresses the rth power distortion of a many point vector quantizer in terms of the number of points point density function inertial profile and the distribution of the source the inertial profile specifies the normalized moment of inertia of quantization cells as a function of location the extension is formulated in terms of a sequence of quantizers whose point density and inertial profile approach known functions as the number of points increase precise conditions are given for the convergence of distortion suitably normalized to bennett s integral previous extensions did not include the inertial profile and consequently provided only bounds or applied only to quantizers with congruent cells such as lattice and optimal quantizers the new version of bennett s integral provides a framework for the analysis of suboptimal structured vector quantizers it is shown how the loss in performance of such quantizers relative to optimal unstructured ones can be decomposed into point density and cell shape losses as examples these losses are computed for product quantizers and used to gain further understanding of the performance of scalar quantizers applied to stationary memoryless sources and of transform codes applied to gaussian sources with memory it is shown that the short coming of such quantizers is that they must compromise between point density and cell shapes

sequential scalar quantization of vectors an analysis proposes an efficient vector quantization vq technique called sequential scalar quantization ssq the scalar components of the vector are individually quantized in a sequence with the quantization of each component utilizing conditional information from the quantization of previous components unlike conventional independent scalar quantization isq ssq has the ability to exploit intercomponent correlation at the same time since quantization is performed on scalar rather than vector variables ssq offers a significant computational advantage over conventional vq techniques and is easily amenable to a hardware implementation in order to analyze the performance of ssq the authors appeal to asymptotic quantization theory where the codebook size is assumed to be large closed form expressions are derived for the quantizer mean squared error mse these expressions are used to compare the asymptotic performance of ssq with other vq techniques the authors also demonstrate the use of asymptotic theory in designing ssq for a practical application color image quantization where the codebook size is typically small theoretical and experimental results show that ssq far outperforms isq with respect to mse while offering a considerable reduction in computation over conventional vq at the expense of a moderate increase in mse

branching annihilating random walks in one dimension some exact results we derive a self duality relation for a one dimensional model of branching and annihilating random walkers with an even number of offspring on nearest neighbour sites with the duality relation and by deriving further exact results in some limiting cases involving fast diffusion we obtain new information on the location and nature of the phase transition line between an active stationary state non zero density and an absorbing state extinction of all particles thus clarifying some so far open problems in these limits the transition is mean field like but on the active side of the phase transition line the fluctuation in the number of particles deviates from its mean field value we also show that well within the active region of the phase diagram a finite system approaches the absorbing state very slowly on a time scale which diverges exponentially in system size in the absence of particle diffusion the branching process with infinite annihilation rate is strongly non ergodic

robust vector quantization by a linear mapping of a block code in this paper we propose a novel technique for vector quantizer design where the reconstruction vectors are given by a linear mapping of a binary block code lmbc the lmbc framework provides a relation between the index bits and the reconstruction vectors through mapping properties we define a framework show its flexibility and give optimality conditions we consider source optimized vector quantization vq where the objective is to directly obtain a vq with inherent good channel robustness properties several instructive theoretical results and properties of the distortion experienced due to channel noise are demonstrated these results are used to guide the design process both optimization algorithms and a block code selection procedure are devised experimental results for gauss markov sources show that quantization performance close to an unconstrained vq is obtained with a short block code which implies a constrained vq the resulting vqs have better channel noise robustness than conventional vqs designed with the generalized lloyd algorithm gla and splitting initialization even when a post processing index assignment algorithm is applied to the gla based vq we have thus demonstrated a unique method for direct design resulting in an inherent good index assignment combined with small losses in quantization performance

trellis based scalar vector quantization of sources with memory the trellis based scalar vector quantizer tb svq can achieve the rate distortion performance bound for memoryless sources this paper extends the scope of this quantizer to coding of sources with memory first considered is a simple extension called the predictive tb svq which applies a closed loop predictive coding operation in each survivor path of the viterbi codebook search algorithm although the predictive tb svq outperforms all other known structured fixed rate vector quantizers due to practical reasons it may not approach the rate distortion limit a new quantization scheme motivated by the precoding idea of laroia et al 1993 called the precoded tb svq is also considered the granular gain is realized by the underlying trellis code while the combination of the precoder and the svq structure provides the boundary gain this new quantization scheme is asymptotically optimal and can in principle approach the rate distortion bound for markov sources

distortion bounds for vector quantizers with finite codebook size upper and lower bounds are presented for the distortion of the optimal n point vector quantizer applied to k dimensional signals under certain smoothness conditions on the source distribution the bounds are shown to hold for each and every value of n the codebook size these results extend bounds derived in the high resolution limit which assume that the number of code vectors is arbitrarily large two approaches to the upper bound are presented the first constructive construction achieves the correct asymptotic rate of convergence as well as the correct dependence on the source density although leading to an inferior value for the constant the second construction based on a random coding argument is shown to additionally achieve a value of the constant which is much closer to the best known result derived within the asymptotic theory lower bound results derived in the correspondence are again shown to possess the correct asymptotic form and yield a constant which is almost indistinguishable from the best value achieved in the asymptotic regime finally application of the results to the problem of source coding yields upper bounds on the distortion rate function for a wide class of processes

the asymmetric six vertex model the exact solution of the asymmetric six vertex model published nearly without derivation by sutherlandet al in 1967 is rederived in detail the transfer matrix method and the bethe ansatz solution for the free energy which can be calculated from an integral equation are discussed for some special cases zero or maximal polarization the integral equation can be solved exactly in addition an asymptotic analysis valid for small but nonzero polarization is carried out the analytical properties of the results and their relevance for the bcsos model are discussed

applications of field theoretic renormalization group methods to reaction diffusion problems we review the application of field theoretic renormalization group rg methods to the study of fluctuations in reaction diffusion problems we first investigate the physical origin of universality in these systems before comparing rg methods to other available analytic techniques including exact solutions and smoluchowski type approximations starting from the microscopic reaction diffusion master equation we then pedagogically detail the mapping to a field theory for the single species reaction ka a k we employ this particularly simple but non trivial system to introduce the field theoretic rg tools including the diagrammatic perturbation expansion renormalization and callan symanzik rg flow equation we demonstrate how these techniques permit the calculation of universal quantities such as density decay exponents and amplitudes via perturbative dc d expansions with respect to the upper critical dimension dc with these basics established we then provide an overview of more sophisticated applications to multiple species reactions disorder effects l evy flights persistence problems and the influence of spatial boundaries we also analyse field theoretic approaches to non equilibrium phase transitions separating active from absorbing states we focus particularly on the generic directed percolation universality class as well as on the most prominent exception to this class even offspring branching and annihilating random walks finally we summarize the state of the field and present our perspective on outstanding problems for the future

static and dynamic phase transitions in multidimensional voting models on continua a voting model or a generalization of the glauber model at zero temperature on a multidimensional lattice is defined as a system composed of a lattice each site of which is either empty or occupied by a single particle the reactions of the system are such that two adjacent sites one empty the other occupied may evolve to a state where both of these sites are either empty or occupied the continuum version of this model in a d dimensional region with a boundary is studied and two general behaviors of such systems are investigated the stationary behavior of the system and the dominant way of relaxation of the system toward its stationary state based on the first behavior a static phase transition discontinuous changes in the stationary profiles of the system is studied based on the second behavior a dynamical phase transition discontinuous changes in the relaxation times of the system is studied it is shown that the static phase transition is induced by the bulk reactions only while the dynamical phase transition is a result of both bulk reactions and boundary conditions

dcrvq a new strategy for efficient entropy coding of vector quantized images this paper presents a novel predictive coding scheme for image data compression by vector quantization vq on the basis of a prediction further compression is achieved by using a dynamic codebook reordering strategy that allows a more efficient huffman encoding of vector addresses the proposed method is lossless for it increases the compression performances of a baseline vector quantization scheme without causing any further image degradation results are presented and a comparison with cache vq is made

efficient quadtree coding of images and video the quadtree data structure is commonly used in image coding to decompose an image into separate spatial regions to adaptively identify the type of quantizer used in various regions of an image the authors describe the theory needed to construct quadtree data structures that optimally allocate rate given a set of quantizers a lagrange multiplier method finds these optimal rate allocations with no monotonicity restrictions they use the theory to derive a new quadtree construction method that uses a stepwise search to find the overall optimal quadtree structure the search can be driven with either actual measured quantizer performance or ensemble average predicted performance they apply this theory to the design of a motion compensated interframe video coding system using a quadtree with vector quantization

adaptive entropy coded subband coding of images the authors describe a design approach called 2 d entropy constrained subband coding ecsbc based upon recently developed 2 d entropy constrained vector quantization ecvq schemes the output indexes of the embedded quantizers are further compressed by use of noiseless entropy coding schemes such as huffman or arithmetic codes resulting in variable rate outputs depending upon the specific configurations of the ecvq and the ecpvq over the subbands many different types of sbc schemes can be derived within the generic 2 d ecsbc framework among these the authors concentrate on three representative types of 2 d ecsbc schemes and provide relative performance evaluations they also describe an adaptive buffer instrumented version of 2 d ecsbc called 2 d ecsbc aec for use with fixed rate channels which completely eliminates buffer overflow underflow problems this adaptive scheme achieves performance quite close to the corresponding ideal 2 d ecsbc system

new permutation codes using hadamard unscrambling corresp a new class of codes for data compression is described that combines permutations with the fast hadamard transform fht it was invented for digital speech compression based on linear predictive coding lpc but may be useful for other data compression applications one particular code with rate frac 1 2 is considered a 16 bit code for a block length of 32 samples all coding and decoding steps are fast so that real time applications with cheap hardware can be anticipated

least squares quantization in pcm it has long been realized that in pulse code modulation pcm with a given ensemble of signals to handle the quantum values should be spaced more closely in the voltage regions where the signal amplitude is more likely to fall it has been shown by panter and dite that in the limit as the number of quanta becomes infinite the asymptotic fractional density of quanta per unit voltage should vary as the one third power of the probability density per unit voltage of signal amplitudes in this paper the corresponding result for any finite number of quanta is derived that is necessary conditions are found that the quanta and associated quantization intervals of an optimum finite quantization scheme must satisfy the optimization criterion used is that the average quantization noise power be a minimum it is shown that the result obtained here goes over into the panter and dite result as the number of quanta become large the optimum quautization schemes for 2 b quanta b 1 2 cdots 7 are given numerically for gaussian and for laplacian distribution of signal amplitudes

reaction diffusion processes of hard core particles we study a 12 parameter stochastic process involving particles with two site interaction and hard core repulsion on ad dimensional lattice in this model which includes the asymmetric exclusion process contact processes and other processes the stochastic variables are particle occupation numbers taking valuesn x 0 1 we show that on a ten parameter submanifold thek point equal time correlation functions n x1 n xk satisfy linear differential difference equations involving no higher correlators in particular the average density n x satisfies an integrable diffusion type equation these properties are explained in terms of dual processes and various duality relations are derived by defining the time evolution of the stochastic process in terms of a quantum hamiltonianh the model becomes equivalent to a lattice model in thermal equilibrium ind 1 dimensions we show that the spectrum ofh is identical to the spectrum of the quantum hamiltonian of ad dimensional anisotropic spin 1 2 heisenberg model in one dimension our results hint at some new algebraic structure behind the integrability of the system

similarity transformation in one dimensional reaction diffusion systems the voting model as an example the exact solution for a system with two particle annihilation and decoagulation has been studied the spectrum of the hamiltonian of the system is found it is shown that the steady state is twofold degenerate the average number density at each site ni t and the equal time two point functions ni t nj t are calculated any equal time correlation functions at large times ni nj are also calculated the relaxation behaviour of the system toward its final state is investigated and it is shown that generally it is exponential as expected for the special symmetric case the relaxation behaviour of the system is a power law for the asymmetric case it is shown that the profile of deviation from the final values is an exponential function of the position

a vector quantizer for the laplace source the low complexity nearly optimal vector quantizer vq is a generalization of t r fischer s 1986 pyramid vq and is similar in structure to the unrestricted polar quantizers previously presented for the independent gaussian source an analysis of performance is presented with results for both the product code pyramid vq and the unrestricted version this analysis although asymptotic in nature helps to demonstrate the performance advantages of the vq implementation issues of the vq are discussed nonasymptotic results are considered in particular the author presents an approximate design algorithm for finite bit rate and demonstrates the usefulness of this vq through several example designs with monte carlo simulations of performance for the restricted form the pyramid vq the author provides further implementational information and low dimension analytical results

video signal coding with dct and vector quantization an image coding scheme using the discrete cosine transform is analyzed when the transform coefficients are vector quantized the coding method is based on the known scheme proposed by chen and smith 1977 which sorts the picture blocks into classes according to the level of image activity the coding scheme is modified to allow for vector quantization of the ac coefficients in particular a pyramid vector quantizer pvq is used this is based on the statistical and geometric properties of a laplacian source which in fact is the best model for the ac coefficients of the two dimensional discrete cosine transform 2d dct of an image a method for forming almost statistically independent vectors is also suggested and improves quantization performance images are encoded with both the pvq and standard scalar quantizer transform coders demonstrating that the pvq coder reduces the mean square encoding error and improves image quality in particular emphasis is given to how the use of fractional bit rates affects the objective and subjective gains obtained the results presented i e mean square error values and printed images have been obtained experimentally working with a statistical criterion in a group of images whose size was in accordance with the 50 hz ccir recommendation 601 standard

the two machine total completion time flow shop problem in this paper we study the np hard scheduling problem of minimizing total completion time in a two machine flow shop five known lower bounds are discussed and two new ones are presented a new dominance criterion is also proposed several versions of a branch and bound method are derived by applying both individually and combined these lower bounds a heuristic procedure is also presented that uses a constructive o n2 time method which computes a good starting solution together with a neighborhood search based on pairwise interchanges computational results show that the exact method can handle problems of up to 30 jobs in size within a reasonable amount of time and that the heuristic procedure has an average error of less than 0 5 from the optimal value and less than 2 7 from the lower bound

the art of signaling fifty years of coding theory in 1948 shannon developed fundamental limits on the efficiency of communication over noisy channels the coding theorem asserts that there are block codes with code rates arbitrarily close to channel capacity and probabilities of error arbitrarily close to zero fifty years later codes for the gaussian channel have been discovered that come close to these fundamental limits there is now a substantial algebraic theory of error correcting codes with as many connections to mathematics as to engineering practice and the last 20 years have seen the construction of algebraic geometry codes that can be encoded and decoded in polynomial time and that beat the gilbert varshamov bound given the size of coding theory as a subject this review is of necessity a personal perspective and the focus is reliable communication and not source coding or cryptography the emphasis is on connecting coding theories for hamming and euclidean space and on future challenges specifically in data networking wireless communication and quantum information theory

finite size scaling studies of one dimensional reaction diffusion systems part i analytical results we consider two single species reaction diffusion models on one dimensional lattices of lengthl the coagulation decoagulation model and the annihilation model for the coagulation model the system of differential equations describing the time evolution of the empty interval probabilities is derived for periodic as well as for open boundary conditions this system of differential equations grows quadratically withl in the latter case the equations are solved analytically and exact expressions for the concentration are derived we investigate the finite size behavior of the concentration and calculate the corresponding scaling functions and the leading corrections for both types of boundary conditions we show that the scaling functions are independent of the initial conditions but do depend on the boundary conditions a similarity transformation between the two models is derived and used to connect the corresponding scaling functions

integrable stochastic ladder models a general way to construct ladder models with certain lie algebraic or quantum lie algebraic symmetries is presented these symmetric models give rise to a series of integrable systems it is shown that corresponding to these su 2 symmetric integrable ladder models there are exactly solvable stationary discrete time resp continuous time markov processes with transition matrices resp intensity matrices having spectra which coincide with the ones of the corresponding integrable models

image coding using adaptive recursive interpolative dpcm a predictive image coder having minimal decoder complexity is presented the image coder utilizes recursive interpolative dpcm in conjunction with adaptive classification entropy constrained trellis coded quantization and optimal rate allocation to obtain signal to noise ratios snrs in the range of those provided by the most advanced transform coders

complexity constrained trellis quantizers a reasonable measure of quantizer complexity is the expected number of quanta per input sample for which distortion is computed given this measure a rate distortion complexity theory is obtained by extending earlier work in alphabet constrained rate distortion theory numerical results show that operation on the alphabet constrained rate distortion bound can be obtained with a complexity of two furthermore lloyd max conditions are shown to describe the minimum of a slightly constrained version of the rate distortion complexity problem complexity constrained design methods are applied first to trellis coded quantizers where they are shown to reduce arithmetic operations by at least 25 they are then used to develop model based trellis quantizers the trellises of which are derived from a markov model of the source simulation results confirm that excellent performance can be obtained with modest complexity

voronoi regions of lattices second moments of polytopes and quantization if a point is picked at random inside a regular simplex octahedron 600 cell or other polytope what is its average squared distance from the centroid in n dimensional space what is the average squared distance of a random point from the closest point of the lattice a n or d n e n a n ast or d n ast the answers are given here together with a description of the voronoi or nearest neighbor regions of these lattices the results have applications to quantization and to the design of signals for the gaussian channel for example a quantizer based on the eight dimensional lattice e8 has a mean squared error per symbol of 0 0717 cdots when applied to uniformly distributed data compared with 0 08333 cdots for the best one dimensional quantizer

on the structure of vector quantizers vector quantization is intrinsically superior to predictive coding transform coding and other suboptimal and em ad hoc procedures since it achieves optimal rate distortion performance subject only to a constraint on memory or block length of the observable signal segment being encoded the key limitation of existing techniques is the very large randomly generated code books which must be stored and the computational complexity of the associated encoding procedures the quantization operation is decomposed into its rudimentary structural components this leads to a simple and elegant approach to derive analytical properties of optimal quantizers some useful properties of quantizers and algorithmic approaches are given which are relevant to the complexity of both storage and processing in the encoding operation highly disordered quantizers which have been designed using a clustering algorithm are considered finally lattice quantizers are examined which circumvent the need for a code book by using a highly structured code based on lattices the code vectors are algorithmically generated in a simple manner rather than stored in a code book and fast algorithms perform the encoding algorithm with negligible complexity

lattice vector quantization of generalized gaussian sources many important sources of data including sub band image and speech coefficients are highly peaked and can be well modeled by the family of generalized gaussian gg pdfs parameterized by a shape parameter spl nu we present here algorithms for defining and quantizing to a z lattice in which the boundary is optimized to the characteristics of gg sources and show that these techniques lead to high performance and low complexity for bit rates and dimensions that are of interest in a number of practical coding applications we derive an analytical description of the granular and overload distortion valid for low and moderate bit rates and also provide a description of quantizer performance in the limit of high rate and dimension

on finite block length quantization distortion we investigate the upper and lower bounds on the quantization distortions for independent and identically distributed continuous sources in the finite block length regime we derive a lower bound on the quantization distortion as well as an upper bound on the quantization distortion based on random quantization codebooks moreover we apply the obtained bounds to the continuous gaussian source for the gaussian source we propose a computationally tractable method to numerically compute the upper and lower bounds for both bounded and unbounded quantization codebooks numerical results show that the gap between the upper and lower bounds is small for the block length of several hundreds and the upper and lower bounds are tighter than those proposed in the existing works

asymptotic quantization error of continuous signals and the quantization dimension extensions of the limiting qnanfizafion error formula of bennet are proved these are of the form d s k n f n beta b where n is the number of output levels d s k n f is the s th moment of the metric distance between quantizer input and output beta b 0 k s beta is the signal space dimension and f is the signal distribution if a suitably well behaved k dimensional signal density f x exists b b s k int f rho x dx 1 rho rho k s k and b s k does not depend on f for k 1 s 2 this reduces to bennett s formula if f is the cantor distribution on 0 1 0 and this k equals the fractal dimension of the cantor set 12 13 random quantization optimal quantization in the presence of an output information constraint and quantization noise in high dimensional spaces are also investigated

product code vector quantizers for waveform and voice coding memory and computation requirements imply fundamental limitations on the quality that can be achieved in vector quantization systems used for speech waveform coding and linear predictive voice coding lpc one approach to reducing storage and computation requirements is to organize the set of reproduction vectors as the cartesian product of a vector codebook describing the shape of each reproduction vector and a scalar codebook describing the gain or energy such shape gain vector quantizers can be applied both to waveform coding using a quadratic error distortion measure and to voice coding using an itakura saito distortion measure in each case the minimum distortion reproduction vector can be found by first selecting a shape code word and then based on that choice selecting a gain codeword several algorithms are presented for the design of shape gain vector quantizers based on a traning sequence of data or a probabilistic model the algorithms are used to design shape gain vector quantizers for both the waveform coding and voice coding application the quantizers are simulated and their performance is compared to that of previously reported vector quantization systems

minimizing total completion time in a two machine flow shop with deteriorating jobs this paper considers a two machine flow shop scheduling problem with deteriorating jobs by a deteriorating job we mean that the processing time of a job is an increasing function of its execution start time a simple linear deterioration function is assumed the objective is to find a sequence that minimizes total completion time optimal solutions are obtained for some special cases for the general case several dominance properties and two lower bounds are derived to speed up the elimination process of a branch and bound algorithm a heuristic algorithm is also proposed to overcome the inefficiency of the branch and bound algorithm computational results show that the proposed heuristic algorithm performs effectively and efficiently

joint wyner ziv dirty paper coding by modulo lattice modulation the combination of source coding with decoder side information the wyner ziv problem and channel coding with encoder side information the gel fand pinsker problem can be optimally solved using the separation principle in this work we show an alternative scheme for the quadratic gaussian case which merges source and channel coding this scheme achieves the optimal performance by applying a modulo lattice modulation to the analog source thus it saves the complexity of quantization and channel decoding and remains with the task of ldquoshapingrdquo only furthermore for high signal to noise ratio snr the scheme approaches the optimal performance using an snr independent encoder thus it proves for this special case the feasibility of universal joint source channel coding

the two machine flowshop scheduling problem with sequence independent setup times new lower bounding strategies abstract the two machine flowshop environment with sequence independent setup times has been intensely investigated both from theoretical and practical perspectives in the scheduling literature nevertheless very scant attention has been devoted to deriving effective lower bounding strategies in this paper we propose new lower bounds for the total completion time minimization criterion these bounds are based on three relaxation schemes namely the waiting time based relaxation scheme the single machine based relaxation scheme and the lagrangian relaxation scheme extensive computational study carried on instances with up to 500 jobs reveals that embedding the waiting time based bounding strategy within the lagrangian relaxation framework yields the best performance while requiring negligible cpu time

fourier transform vector quantization for speech coding design algorithms and simulation results are presented for vector quantizers for fourier transformed data transforming the data prior to quantization has two potential advantages first each sample in the transform domain depends on many samples in the original domain thus even scalar quantization in the transform domain is a form of vector quantization or block source coding in the original waveform domain and the basic coding theorems of information theory show that such block codes can provide better performance than scalar codes even for memoryless sources second vector quantization of fourier transformed speech waveforms provides distinctly better subjective quality than ordinary vector quantization of the waveform using codes of comparable complexity while the system is of course more complicated due to the need to take fourier transforms its envisioned application is as a coder for the output of fft chips currently available or under development the proposed implementation of a fourier transform vector quantizer ftvq uses a product code structure providing different codes for different coefficient vectors corresponding to different frequency bands this is a form of subband coding and yields a simple means of optimizing bit allocations among the subcodes two coding structures with corresponding distortion measures are considered those that quantize vectors of pairs of real and imaginary coefficients and those that quantize separate vectors of magnitude and phase coefficients both structures yield good performance for the given complexity in comparison to waveform vector quantizers for speech coding a magnitude phase ftvq yields better subjective quality than a real imaginary ftvq when the rate allocation is properly chosen

stronger lagrangian bounds by use of slack variables applications to machine scheduling problems lagrangian relaxation is a powerful bounding technique that has been applied successfully to manynp hard combinatorial optimization problems the basic idea is to see annp hard problem as an easy to solve problem complicated by a number of nasty side constraints we show that reformulating nasty inequality constraints as equalities by using slack variables leads to stronger lower bounds the trick is widely applicable but we focus on a broad class of machine scheduling problems for which it is particularly useful we provide promising computational results for three problems belonging to this class for which lagrangian bounds have appeared in the literature the single machine problem of minimizing total weighted completion time subject to precedence constraints the two machine flow shop problem of minimizing total completion time and the single machine problem of minimizing total weighted tardiness

optimality and suboptimality of multiple description vector quantization with a lattice codebook the asymptotic analysis of multiple description vector quantization mdvq with a lattice codebook for sources with smooth probability density functions pdfs is considered in this correspondence goyal et al 2002 observed that as the side distortion decreases and the central distortion correspondingly increases the quantizer cells farther away from the coarse lattice points shrink in a spatially periodic pattern in this correspondence two special classes of index assignments are used along strategic groupings of central quantizer cells to derive a straightforward asymptotic analysis which provides an analytical explanation for the aforementioned observation mdvq with a lattice codebook was shown earlier to be asymptotically optimal in high dimensions with a curious converging property that the side quantizers achieve the space filling advantage of an n dimensional sphere instead of an n dimensional optimal polytope the analysis presented here explains this behavior readily while central quantizer cells on a uniform lattice are asymptotically optimal in high dimensions the present authors have shown that by using nonuniform rather than uniform central quantizer cells the central side distortion product in an mdsq can be reduced by 0 4 db at asymptotically high rate the asymptotic analysis derived here partially unifies these previous results in the same framework though a complete characterization is still beyond reach

transform coding with integer to integer transforms a new interpretation of transform coding is developed that downplays quantization and emphasizes entropy coding allowing a comparison of entropy coding methods with different memory requirements with conventional transform coding based on computing karhunen loeve transform coefficients and then quantizing them vector entropy coding can be replaced by scalar entropy coding without an increase in rate thus the transform coding advantage is a reduction in memory requirements for entropy coding this paper develops a transform coding technique where the source samples are first scalar quantized and then transformed with an integer to integer approximation to a nonorthogonal linear transform among the possible advantages is to reduce the memory requirement further than conventional transform coding by using a single common scalar entropy codebook for all components the analysis shows that for high rate coding of a gaussian source this reduction in memory requirements comes without any degradation of rate distortion performance

successive refinement lattice vector quantization lattice vector quantization lvq solves the complexity problem of lbg based vector quantizers yielding very general codebooks however a single stage lvq when applied to high resolution quantization of a vector may result in very large and unwieldy indices making it unsuitable for applications requiring successive refinement the goal of this work is to develop a unified framework for progressive uniform quantization of vectors without having to sacrifice the mean squared error advantage of lattice quantization a successive refinement uniform vector quantization methodology is developed where the codebooks in successive stages are all lattice codebooks each in the shape of the voronoi regions of the lattice at the previous stage such voronoi shaped geometric lattice codebooks are named voronoi lattice vqs vlvq measures of efficiency of successive refinement are developed based on the entropy of the indices transmitted by the vlvqs additionally a constructive method for asymptotically optimal uniform quantization is developed using tree structured subset vlvqs in conjunction with entropy coding the methodology developed here essentially yields the optimal vector counterpart of scalar bitplane wise refinement unfortunately it is not as trivial to implement as in the scalar case furthermore the benefits of asymptotic optimality in tree structured subset vlvqs remain elusive in practical nonasymptotic situations nevertheless because scalar bitplane wise refinement is extensively used in modern wavelet image coders we have applied the vlvq techniques to successively refine vectors of wavelet coefficients in the vector set partitioning vspiht framework the results are compared against spiht and the previous successive approximation wavelet vector quantization sa w vq results of sampson da silva and ghanbari 1996

near ellipsoidal voronoi coding we consider a special case of voronoi coding where a lattice spl lambda in spl ropf sup n is shaped or truncated using a lattice spl lambda m sub 1 x sub 1 m sub n x sub n x sub 1 x sub n spl isin spl lambda for a fixed m m sub 1 m sub n spl isin spl nopf spl bsol 0 1 sup n using this technique the shaping boundary is near ellipsoidal it is shown that the resulting codes can be indexed by standard voronoi indexing algorithms plus a conditional modification step as far as spl lambda is a sublattice of spl lambda we derive the underlying conditions on m and present generic near ellipsoidal voronoi indexing algorithms examples of constraints on m and conditional modification are provided for the lattices a sub 2 d sub n n spl ges 2 and 2d sub n sup n even spl ges 4

lattice and trellis quantization with lattice and trellis bounded codebooks high rate theory for memoryless sources high rate lattice and trellis quantizers for nonuniform sources are introduced and analyzed the performance of these quantizers is determined by two separable quantities the granular gain and the boundary gain which are determined by the shapes of the granular cells and of the support region respectively the granular gain and boundary gain are the duals of shaping and coding gain in data transmission applications using this duality it is shown for gaussian sources that the ultimate achievable boundary gain with high rate lattice bounded lattice codebooks is the same as the ultimate gain that can be obtained from variable rate entropy coding it is observed that if lattice codebooks can achieve the ultimate granular gain of 0 255 b per dimension then lattice bounded lattice codebooks can approach the rate distortion limit the performance of lattice quantizers is compared to that of optimum vector quantizers

compression of sar raw data through range focusing and variable rate trellis coded quantization there is an ever growing interest in the compression of sar data because of the huge resources required for storage and transmission this is especially true for spaceborne sensors given the limited capacity of the downlink channel unfortunately sar data lack the useful properties on which compression algorithms rely indeed these are present in the focused images but focusing is too complex for on board implementation at this time poggi et al 2000 proposed to perform on the satellite only the low complexity range focusing which increases the data correlation and better concentrates their energy these properties were then exploited by adopting a variable rate vector quantizer with a clear performance improvement with respect to reference techniques however vector quantization vq is too complex for actual on board implementation and therefore here we replace vq with trellis coded vq to limit complexity only small vectors are used which reduces vq s ability to exploit data dependencies on the other hand trellis coding allows one to encode large blocks of data at once and to obtain a better partition of the input space experiments on real sar data show that the overall performance is comparable to that of poggi et al but the complexity is much lower making on board implementation possible

distortion rate models for entropy coded lattice vector quantization the increasing demand for real time applications requires the use of variable rate quantizers having good performance in the low bit rate domain in order to minimize the complexity of quantization as well as maintaining a reasonably high psnr ratio we propose to use an entropy coded lattice vector quantizer eclvq these quantizers have proven to outperform the well known ezw algorithm s performance in terms of rate distortion tradeoff we focus our attention on the modeling of the mean squared error mse distortion and the prefix code rate for eclvq first we generalize the distortion model of jeong and gibson 1993 on fixed rate cubic quantizers to lattices under a high rate assumption second we derive new rate models for eclvq efficient at low bit rates without any high rate assumptions simulation results prove the precision of our models

an improved branch and bound algorithm for the two machine total completion time flow shop problem we consider the two machine total completion time flow shop scheduling problem this problem is known to be np hard in the strong sense an improved lagrangean relaxation approach is proposed two new dominance criteria are introduced to curtail the enumeration tree a branch and bound algorithm capable of solving to optimality medium size problem instances is presented

trellis based scalar vector quantizer for memoryless sources the paper describes a structured vector quantization approach for stationary memoryless sources that combines the scalar vector quantizer svq ideas laroia and farvardin 1993 with trellis coded quantization marcellin and fischer 1990 the resulting quantizer is called the trellis based scalar vector quantizer tb svq the svq structure allows the tb svq to realize a large boundary gain while the underlying trellis code enables it to achieve a significant portion of the total granular gain for large block lengths and powerful possibly complex trellis codes the tb svq can in principle achieve the rate distortion bound as indicated by the results obtained even for reasonable block lengths and relatively simple trellis codes the tb svq outperforms all other fixed rate quantizers at reasonable complexity

a lower bound on the average error of vector quantizers corresp a lower bound is proposed for the mean squared error of an n dimensional vector quantizer with a large number of output points

equivalences between stochastic systems time dependent correlation functions of unstable particles undergoing biased or unbiased diffusion coagulation and annihilation are studied this is achieved by similarity transformations between different stochastic models and between stochastic and soluble nonstochastic models for special cases we obtain exact results which are in good agreement with experiments on one dimensional annihilation coagulation processes

scalar versus vector quantization worst case analysis we study the potential merits of vector quantization and show that there can be an arbitrary discrepancy between the worst case rates required for scalar and vector quantization specifically we describe a random variable and a distortion measure where quantization of a single instance to within a given distortion requires an arbitrarily large number of bits in the worst case but quantization of multiple independent instances to within the same distortion requires an arbitrarily small number of bits per instance in the worst case we relate this discrepancy to expander graphs representation and cover numbers of set systems and a problem studied by slepian wolf and wyner 1973

optimization of lattices for quantization a training algorithm for the design of lattices for vector quantization is presented the algorithm uses a steepest descent method to adjust a generator matrix in the search for a lattice whose voronoi regions have minimal normalized second moment the numerical elements of the found generator matrices are interpreted and translated into exact values experiments show that the algorithm is stable in the sense that several independent runs reach equivalent lattices the obtained lattices reach as low second moments as the best previously reported lattices or even lower specifically we report lattices in nine and ten dimensions with normalized second moments of 0 0716 and 0 0708 respectively and nonlattice tessellations in seven and nine dimensions with 0 0727 and 0 0711 which improves on previously known values the new nine and ten dimensional lattices suggest that conway and sloane s 1993 conjecture on the duality between the optimal lattices for packing and quantization might be false a discussion of the application of lattices in vector quantizer design for various sources uniform and nonuniform is included