vector quantization of speech and speech like waveforms an algorithm for the design of vector quantizers that are locally optimum in the sense of minimizing an average quantitative distortion measure is used to design 1 and 2 bit sample vector quantizers for both real sampled speech and a simulated speech like auto regressive random process both weighted and unweighted squared error distortion measures are considered several comparisons are made and discussed based on the average distortions of the vector quantization schemes the results for the simulated speech are compared to mathematical performance bounds from information theory to provide an indication of how nearly globally optimal vector quantization is for such highly correlated sources a comparison of the results for the real speech and the simulated speech provides a quantitative measure of the accuracy of such models and hence of the applicability of information theory bounds and code designs based on probabilistic models the signal to quantization noise ratios of vector quantizers designed to minimize squared error distortion are compared to those of several popular speech waveform coding systems of similar rates

efficient encoding of colored pictures in r g b components the encoding of colored pictures in components has attracted a lot of attention in this paper for their efficient transmission in the 2 3 bit pel range the direct encoding of the red r green g and blue b primaries is investigated differential pcm with vector quantization is used and the encoding efficiencies are compared to the similar result obtained using the properly converted luminance y and chrominance i q component signals a new quantization scheme is proposed for rgb encoding to improve the picture quality as a result it is shown that rgb encoding can attain a comparable or slightly higher encoding efficiency as compared to yiq encoding and a higher resolution can be obtained for strong color edges defined by the primary colors but the resulting picture quality is much noisier thus it is better suited for such applications in which the edges of primary colors play important roles such as in graphics materials an adaptive vector quantization is introduced in order to apply the proposed rgb encoding scheme to a wider range of pictures the quantity called activity is introduced considering the form of the predictor used the optimum adaptive scheme is derived and its effectiveness is verified through simulations

a predictive classified vector quantizer and its subjective quality evaluation for x ray ct images the authors have developed a new classified vector quantizer cvq using decomposition and prediction which does not need to store or transmit any side information to obtain better quality in the compressed images human visual perception characteristics are applied to the classification and bit allocation this cvq has been subjectively evaluated for a sequence of x ray ct images and compared to a dct coding method nine x ray ct head images from three patients are compressed at 10 1 and 15 1 compression ratios and are evaluated by 13 radiologists the evaluation data are analyzed statistically with analysis of variance and tukey s multiple comparison even though there are large variations in judging image quality among readers the proposed algorithm has shown significantly better quality than the dct at a statistical significance level of 0 05 only an interframe cvq can reproduce the quality of the originals at 10 1 compression at the same significance level while the cvq can reproduce compressed images that are not statistically different from the originals in quality the effect on diagnostic accuracy remains to be investigated

interframe predictive coding of images using hybrid vector quantization the temporal and spatial redundancies of image sequences can be reduced by prediction and vector quantization respectively the robustness of the coder is increased through the use of a hybrid two stage vector quantizer the first stage is of the linde buzo gray type the second stage encodes the residual error of the first stage using a lattice vector quantizer

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

classified vector quantization of images vector quantization vq provides many attractive features for image coding with high compression ratios however initial studies of image coding with vq have revealed several difficulties most notably edge degradation and high computational complexity we address these two problems and propose a new coding method classified vector quantization cvq which is based on a composite source model blocks with distinct perceptual features such as edges are generated from different subsources i e belong to different classes in cvq a classifier determines the class for each block and the block is then coded with a vector quantizer designed specifically for that class we obtain better perceptual quality with significantly lower complexity with cvq when compared to ordinary vq we demonstrate with cvq visual quality which is comparable to that produced by existing coders of similar complexity for rates in the range 0 6 1 0 bits pixel

semi continuity of the entropy of sinai probability measures for partially hyperbolic diffeomorphisms abstract we establish sufficient conditions for the upper semicontinuity and the continuity of the entropy of sinai probability measures invariant by partially hyperbolic diffeomorphisms and discuss their application in several examples

a greedy tree growing algorithm for the design of variable rate vector quantizers image compression a technique for directly designing a variable rate tree structured vector quantizer by growing the tree one node at a time rather than one layer at time is presented the technique is a natural extension of a tree growing method for decision trees when the tree is pruned with a generalized algorithm for optimally pruning trees improvement is measured in the signal to noise ratio at high rates over pruning a fixed rate tree structured vector quantizer of the same initial rate the growing algorithm can be interpreted as a constrained inverse of the pruning algorithm

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

stability of parallel algorithms to evaluate chebyshev series abstract in this paper we present rounding error bounds of recent parallel versions of forsythe s and clenshaw s algorithms for the evaluation of finite series of chebyshev polynomials of the first and second kind the backward errors are studied by using the matrix formulation of the algorithm whereas the forward error is also studied by means of a more direct approach that permits us to obtain sharper bounds the bounds show an almost stable behavior as in the sequential algorithms this fact is illustrated with several numerical tests

regularity of srb entropy for geometric lorenz attractors we consider the classical geometric lorenz attractors showing that the srb entropy admits gamma holder continuity for any 0 gamma 1

predictive classified vector quantization a vector quantization scheme based on the classified vector quantization cvq concept called predictive classified vector quantization pcvq is presented unlike cvq where the classification information has to be transmitted pcvq predicts it thus saving valuable bit rate two classifiers one operating in the hadamard domain and the other in the spatial domain were designed and tested the classification information was predicted in the spatial domain the pcvq schemes achieved bit rate reductions over the cvq ranging from 20 to 32 for two commonly used color test images while maintaining the same acceptable image quality bit rates of 0 70 0 93 bits per pixel bpp were obtained depending on the image and pcvq scheme used

btc image coding using vector quantization this paper describes source encoding of the outputs of a block truncation coder btc namely the overhead statistical information and the truncated block the statistical overhead and the truncated block exhibit properties which can be effectively used for their quantization as vectors vector quantization of these btc outputs results into reduction of the bit rate of the coder the bit rate reduces up to 1 5 bits pel if vector quantization is used on one of the outputs i e either the overhead information or the truncated block by vector quantizing both the btc outputs the bit rate can he reduced up to 1 0 bits pel without introducing many perceivable errors in the reconstructed output

a simple parallel algorithm for polynomial evaluation in this paper we show a simple parallel algorithm for polynomial evaluation by this method we only need 2n p log 2 p steps on p processors where p leqslant o n 1 2 to evaluate a polynomial of degree n on an simd computer or an mimd computer which is a decrease of log 2 p steps as compared with the p order homer method s lakshmivarahan and s k dhall analysis and design of parallel algorithms mcgraw hill new york 1990 and also a decrease of 2 log 2 p 1 2 steps as compared with some other algorithms on an mimd computer j i munro and m paterson j comput system sci 7 1973 pp 189 198 k maruyama ieee trans comput c 22 1973 pp 2 5 the new algorithm is simple in structure and easy to implement

statistical properties of dynamical systems with some hyperbolicity this paper is about the ergodic theory of attractors and conservative dynamical systems with hyperbolic properties on large parts though not necessarily all of their phase spaces the main results are for discrete time systems to put this work into context recall that for axiom a attractors the picture has been fairly complete since the 1970 s see s1 b r2 since then much progress has been made on two fronts there is a general nonuniform theory that deals with properties common to all diffeomorphisms with nonzero lyapunov exponents o p1 ka ly and there are detailed analyses of specific kinds of dynamical systems including for example billiards 1 dimensional and henon type maps s2 bsc hk j bc2 by1 statistical properties such as exponential decay of correlations are not enjoyed by all diffeomorphisms with nonzero lyapunov exponents the goal of this paper is a systematic understanding of these and other properties for a class of dynamical systems larger than axiom a this class will not be defined explicitly but it includes some of the much studied examples by looking at regular returns to sets with good hyperbolic properties one could give systems in this class a simple dynamical representation conditions for the existence of natural invariant measures exponential mixing and central limit theorems are given in terms of the return times these conditions can be checked in concrete situations giving a unified way of proving a number of results some new and some old among the new results are the exponential decay of correlations for a class of scattering billiards and for a positive measure set of henon type maps

a fast search algorithm for vector quantization using mean pyramids of codewords one of the most serious problems for vector quantization especially for high dimensional vectors is the high computational complexity of searching for the closest codeword in the codebook design and encoding phases although quantizing high dimensional vectors rather than low dimensional vectors results in better performance the computation time needed for vector quantization grows exponentially with the vector dimension this makes high dimensional vectors unsuitable for vector quantization to overcome this problem a fast search algorithm under the assumption that the distortion is measured by the squared euclidean distance is proposed using the mean pyramids of codewords the algorithm ran reject many codewords that are impossible matches and hence save a great deal of computation time the algorithm is efficient for high dimensional codeword searches experimental results confirm the effectiveness of the proposed method

a vector quantizer with minimum visible distortion a method for designing codebooks for vector quantization vq based on minimum error visibility in a reconstructed picture is described the method uses objective measurements to define visibility for the picture being coded the proposed vq is switched type i e the codebook is divided into subcodebooks each of which is related to a given subrange of error visibility codebook optimization is carried out on the basis of a particular definition of visible distortion of the reconstructed image subjective judgment of the test results carried out at 0 5 b pel bit rate indicates that the proposed vq enables low distortion images to be reconstructed even when subcodebooks with a small number of codewords are used thus reducing the codebook search time to about 10 of that required by a fixed vq both inside and outside the training set

image compression using adaptive vector quantization the paper demonstrates the application of adaptive vector quantization techniques to the coding of monochromatic and color pictures codebooks of representative vectors are generated for different portions of the image by means of extensive simulations the performance of the coder for monochrome images is estimated as a function of the various coding parameters vector dimensionality number of representative vectors and degree of adaptivity it is shown that for a vector size of dimension 4 there is a zone of operation ranging from 1 0 to 1 5 bits pixel where adaptive vector quantization is advantageous despite the simplicity of the decoder the performance of the adaptive vector quantizer is found to be comparable with block transform coding schemes for both monochrome and color pictures

on iterations of 1 ax 2 on 1 1 on etudie des iterations de f x a 1 ax u 2 1 x 1 ou a est un parametre dans l intervalle 0 2 on etablit la non existence de cycles attractifs on definit une partition on donne une estimation uniforme de la a derivee

an algorithm for the design of labeled transition finite state vector quantizers a finite state vector quantizer fsvq is a switched vector quantizer where the sequence of quantizers selected by the encoder can be tracked by the decoder it can be viewed as an adaptive vector quantizer with backward estimation a vector generalization of an aqb system recently a family of algorithms for the design of fsvq s for waveform coding application has been introduced these algorithms first design an initial set of vector quantizers together with a next state function giving the rule by which the next quantizer is selected the codebooks of this initial fsvq are then iteratively improved by a natural extension of the usual memoryless vector quantizer design algorithm the next state function however is not modified from its initial form in this paper we present two extensions of the fsvq design algorithms first the algorithm for fsvq design for waveform coders is extended to fsvq design of linear predictive coded lpc speech parameter vectors using an itakura saito distortion measure second we introduce a new technique for the iterative improvement of the next state function based on an algorithm from adaptive stochastic automata theory the design algorithms are simulated for an lpc fsvq and the results are compared with each other and to ordinary memoryless vector quantization several open problems suggested by the simulation results are presented

image sequence coding using vector quantization in this paper a new interframe coding technique based upon vector quantization is presented this algorithm has as its basis twodimensional block vector quantization at the frame level onto which is grafted the concept of adaptive codebook replenishment and frame replenishment this algorithm includes three strategies label replenishment label replenishment with mean shift and label replenishment with mean shift and selective codeword replacement the last two strategies efficiently update the codebook to track the changes in local statistics on a frame basis compared with three dimensional block vector quantization 16 for bit rates between 0 5 and 0 65 the normalized mean squared error nmse is reduced by a factor ranging between 2 and 2 5 by the use of replenishment

on the continuity of the srb entropy for endomorphisms we consider classes of dynamical systems admitting markov induced maps under general assumptions which in particular guarantee the existence of srb measures we prove that the entropy of the srb measure varies continuously with the dynamics we apply our result to a vast class of non uniformly expanding maps of a compact manifold and prove the continuity of the entropy of the srb measure in particular we show that the srb entropy of viana maps varies continuously with the map

absolutely continuous invariant measures for one parameter families of one dimensional maps given a one parameter familyf x of maps of the interval 0 1 we consider the set of parameter values for whichf has an invariant measure absolutely continuous with respect to lebesgue measure we show that this set has positive measure for two classes of maps i f x f x where 0 4 andf x is a functionc3 near the quadratic mapx 1 x and ii f x f x mod 1 wheref isc3 f 0 f 1 0 andf has a unique nondegenerate critical point in 0 1

a reversible compression code hiding using soc and smvq indices reversible data hiding recovers the original images without distortion after the secret data are extracted so it has received considerable attention among researchers in recent years this work presents a novel reversible data hiding scheme based on the search order coding soc algorithm and side match vector quantization smvq the compression performance is improved by encoding the index with either soc or smvq during the data embedding phase the index of an image block also is encoded by using a few bits thus improving the compression rate during the extracting phase the receiver uses simple steps to extract the secret data and reconstruct the original smvq compression code our experimental results indicated that using a size 64 state codebook the average compression rate with our scheme was 0 41bpp which is much better than the compression rates of chang et al s yang and lin s and yang et al s schemes i e 0 50 0 54 and 0 56bpp respectively furthermore in addition to reducing the time required for the embedding and extracting phases the proposed scheme yields a higher embedding rate than the schemes of yang and lin and yang et al

a complexity reduction technique for image vector quantization a technique for reducing the complexity of spatial domain image vector quantization vq is proposed the conventional spatial domain distortion measure is replaced by a transform domain subspace distortion measure due to the energy compaction properties of image transforms the dimensionality of the subspace distortion measure can be reduced drastically without significantly affecting the performance of the new quantizer a modified lbg algorithm incorporating the new distortion measure is proposed unlike conventional transform domain vq the codevector dimension is not reduced and a better image quality is guaranteed the performance and design considerations of a real time image encoder using the techniques are investigated compared with spatial domain a speed up in both codebook design time and search time is obtained for mean residual vq and the size of fast ram is reduced by a factor of four degradation of image quality is less than 0 4 db in psnr

stability of parallel algorithms for polynomial evaluation abstract in this paper we analyse the stability of parallel algorithms for the evaluation of polynomials written as a finite series of orthogonal polynomials the basic part of the computation is the solution of a triangular tridiagonal linear system this fact allows us to present a more detailed analysis the theoretical results show that the parallel algorithms are almost as stable as their sequential counterparts for practical applications extensive numerical experiments confirm the theoretical conclusions

subband coding of images subband coding has become quite popular for the source encoding of speech this paper presents a simple yet efficient extension of this concept to the source coding of images we specify the constraints for a set of two dimensional quadrature mirror filters qmf s for a particular frequency domain partition and show that these constraints are satisfied by a separable combination of one dimensional qmf s bits are then optimally allocated among the subbands to minimize the mean squared error for dpcm coding of the subbands also an adaptive technique is developed to allocate the bits within each subband by means of a local variance mask optimum quantization is employed with quantizers matched to the laplacian distribution subband coded images are presented along with their signal to noise ratios snr s the snr performance of the subband coder is compared to that of the adaptive discrete cosine transform dct vector quantization and differential vector quantization for bit rates of 0 67 1 0 and 2 0 bits per pixel for 256 256 monochrome images the adaptive subband coder has the best snr performance

srb measures and pesin s entropy formula for endomorphisms a celebrated result conjectured by ruelle and proved by ledrappier strelcyn and young in the smooth ergodic theory of diffeomorphisms is that an invariant measure of a c 2 diffeomorphism satisfies pesin s entropy formula if and only if it has absolutely continuous conditional measures on unstable manifolds 41 42 the later property is known as srb property of the invariant measure this result was also successfully generalized to random dynamical systems of diffeomorphisms 51

parallelizable approximate solvers for recursions arising in preconditioning abstract for the recursions used in the modified incomplete lu preconditioner namely the construction of incomplete decomposition the forward elimination and the back substitution parallelizable approximate solvers are introduced the analysis shows that the solutions of the recursions depend only weakly on their initial conditions which may be interpreted to indicate that the inexact solution is close in some sense to the exact one the method is based on a domain decomposition approach suitable for parallel implementations on message passing architectures it requires a small number of communication steps per preconditioned iteration independent of the number of subdomains and the size of the problem the overlapping subdomains are either squares suitable for mesh connected arrays of processors or defined by the data flow rule of the recursions suitable for line connected arrays of simd or vector processors numerical examples show that in both cases the overhead in the number of preconditioned iterations required for convergence is small in comparison with the speedup gained

fuzzy reasoning for image compression using adaptive triangular plane patches in this article we present a method called adaptive patch adjustment that improves the performance of digital image data compression using triangular plane patches the method is designed to adaptively adjust the three dimension position of triangular plane patches that approximate the corresponding luminance curved surfaces of an original image such an adjustment considers the influence of all pixels contained in the projection of a patch instead of defining a patch by only three pixels at the vertices the influence is described and calculated with a soft computing technique the simplified fuzzy reasoning experimental results show that such a flexible strategy significantly reduces the average distortion between the reconstructed image and the original one avoiding excess block splitting and as a result increasing the data compression rate

parallel algorithms to evaluate orthogonal polynomial series in this paper four parallel algorithms for the evaluation of finite series of orthogonal polynomials are introduced the algorithms are based on the forsythe and clenshaw sequential algorithms several tests carried out on a cray t3d are presented

differentiation of srb states abstract let f be a diffeomorphism of a manifold m and f a generalized srb state for f if supp f is a hyperbolic compact set we show that the map is differentiable in a suitable functional setup and we compute the derivative when supp f is an attractor the derivative is given by where x is the vector field this formula can be extended to time dependent situations and also at least formally to nonuniformly hyperbolic situations the above results will find their use in the study of the onsager reciprocity relations and the fluctuation dissipation formula of nonequilibrium statistical mechanics

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

continuity properties of entropy on donne une borne superieure sur le defaut en semicontinuite superieure des entropies topologiques et metriques d une auto application c r d une variete c r r 1

transform and hybrid transform dpcm coding of images using pyramid vector quantization the transform and hybrid transform dpcm methods of image coding are generalized to allow pyramid vector quantization of the transform coefficients an asymptotic mean squared error performance expression is derived for the pyramid vector quantizer and used to determine the optimum rate assignment for encoding the various transform coefficients coding simulations for two images at average rates of 0 5 1 bit pixel demonstrate a 1 3 db improvement in signal to noise ratio for the vector quantization approach in the hybrid coding with more modest improvements in signal to noise ratio in the transform coding however this improvement is quite noticeable in image quality particularly in reducing blockiness in the low bit rate encoded images

image coding using vector quantization a review a review of vector quantization techniques used for encoding digital images is presented first the concept of vector quantization is introduced then its application to digital images is explained spatial predictive transform hybrid binary and subband vector quantizers are reviewed the emphasis is on the usefulness of the vector quantization when it is combined with conventional image coding techniques or when it is used in different domains

predictive vector quantization of images the purpose of this paper is to present new image coding schemes based on a predictive vector quantization pvq approach the predictive part of the encoder is used to partially remove redundancy and the vq part further removes the residual redundancy and selects good quantization levels for the global waveform two implementations of this coding approach have been devised namely sliding block pvq and block tree pvq simulations on real images show significant improvement over the conventional dpcm and tree codes using these new techniques the strong robustness property of these coding schemes is also experimentally demonstrated

parallel evaluation of chebyshev and trigonometric series abstract in this paper we introduce a general parallel algorithm for the evaluation of chebyshev and trigonometric series the algorithm is based on a recurrence property that allows the effective implementation on partial sums that can be calculated independently several examples carried out on a cray t3d are provided comparing the forsythe and clenshaw parallel algorithms

comparison between several adaptive search vector quantization schemes and jpeg standard for image compression this paper introduces an adaptive search vector quantization vq algorithm hierarchical adaptive search vq hasvq and compares its performance against several previously proposed adaptive search image compression algorithms these algorithms are the jpeg standard adaptive tree search vector quantization atsvq multi stage adaptive search vector quantization masvq the bit rate examined is from 0 625 to 1 25 bits per pixel bpp the results indicate that hasvq outperforms all the other algorithms over the entire range of bit rates examined for higher bit rates masvq performs next to the hasvq algorithm and is in turn followed by the jpeg standard atsvq performs well at lower bit rates however its performance at higher bit rates is suppressed by not having an adequate codebook size

statistical stability and continuity of srb entropy for systems with gibbs markov structures we present conditions on families of diffeomorphisms that guarantee statistical stability and srb entropy continuity they rely on the existence of horseshoe like sets with infinitely many branches and variable return times as an application we consider the family of henon maps within the set of benedicks carleson parameters

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

next state functions for finite state vector quantization in this paper the finite state vector quantization scheme called dynamic finite state vector quantization dfsvq is investigated with regard to its subcodebook construction in dfsvq each input block is encoded by a small codebook called subcodehook which is created from a much larger codebook called supercodebook each subcodebook is constructed by selecting using a reordering procedure a set of appropriate codevectors from the supercodebook the performance of the dfsvq depends on this reordering procedure therefore several reordering procedures are introduced and their performances are evaluated in this paper the reordering procedures that are investigated are based on the conditional histogram of the codevectors index prediction vector prediction nearest neighbor design and frequency usage of the code vectors the performances of the reordering procedures are evaluated by comparing their hit ratios the number of blocks encoded by the subcodebook and their computational complexity experimental results are presented and it is found that the reordering procedure based on the vector prediction performs the best when compared with the other reordering procedures

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