quantization based on statistical moments for signal detection design and analysis this paper addresses a signal detection problem based on a class of quantizers the known moments of the underlying noise distribution are used to index a set of quantization points that have been predetermined under an assumed noise model the fact that lower order moments are easy to obtain and that they are required in the implementation and analysis of most threshold detectors makes this approach quite appealing the performance of the resulting quantizers is shown to be relatively insensitive to variations in the underlying noise distribution and to small deviations of the presumed moments the detector s performance in the finite sample size case is investigated and the distribution resulting in the highest false alarm rate is described for both symmetric and asymmetric noise cases by setting the test threshold according to the worst distribution a lower bound on the detector s performance is guaranteed

on the support of mse optimal fixed rate scalar quantizers this paper determines how the support regions of optimal and asymptotically optimal fixed rate scalar quantizers with respect to mean squared error depend on the number of quantization points n and the probability density of the variable being quantized it shows that for asymptotic optimality it is necessary and sufficient that the support region grow fast enough that the outer or overload distortion decreases as o 1 n sup 2 formulas are derived for the minimal support of asymptotically optimal quantizers for generalized gamma densities including gaussian and laplacian interestingly these turn out to be essentially the same as for the support of optimal fixed rate uniform scalar quantizers heuristic arguments are then used to find closed form estimates for the support of truly optimal quantizers for generalized gamma densities these are found to be more accurate than the best prior estimates as computed by numerical algorithms they demonstrate that the support of an optimal quantizer is larger than the minimal asymptotically optimal support by a factor depending on the density but not n and that the outer distortion of optimal quantizers decreases as 1 n sup 3

on conditional and intrinsic autoregressions summary gaussian conditional autoregressions have been widely used in spatial statistics and bayesian image analysis where they are intended to describe interactions between random variables at fixed sites in euclidean space the main appeal of these distributions is in the markovian interpretation of their full conditionals intrinsic autoregressions are limiting forms that retain the markov property despite being improper they can have advantages over the standard autoregressions both conceptually and in practice for example they often avoid difficulties in parameter estimation without apparent loss or exhibit appealing invariances as in texture analysis however on small arrays and in nonlattice applications both forms of autoregression can lead to undesirable second order characteristics either in the variables themselves or in contrasts among them this paper discusses standard and intrinsic autoregressions and describes how the problems that arise can be alleviated using dempster s 1972 algorithm or an appropriate modification the approach represents a partial synthesis of standard geostatistical and gaussian markov random field formulations some nonspatial applications are also mentioned

fourier encoding of closed planar boundaries a circular gaussian autoregressive cgar source is used as a model for closed planar curves a class of suboptimal encoding schemes is considered which separately quantize the fourier coefficients of the boundary application of rate distortion theoretic techniques leads to parametric equations describing the optimal encoding bound interpretation of these equations establishes a sampling criterion and a computationally efficient transform encoding scheme for the suboptimal class several variants of this transform encoding scheme are suggested and compared to the encoding bound

hypothesis testing with multiterminal data compression the multiterminal hypothesis testing h xy against h xy is considered where x n x n and y n y n are separately encoded at rates r 1 and r 2 respectively the problem is to determine the minimum beta n of the second kind of error probability under the condition that the first kind of error probability alpha n leq epsilon for a prescribed 0 a good lower bound theta l r 1 r 2 on the power exponent theta r 1 r 2 epsilon lim inf n rightarrow infty 1 n log beta n is given and several interesting properties are revealed the lower bound is tighter than that of ahlswede and csiszar furthermore in the special case of testing against independence this bound turns out to coincide with that given by them the main arguments are devoted to the special case with r 2 infty corresponding to full side information for y n y n in particular the compact solution is established to the complete data compression cases which are useful in statistics from the practical point of view

erratum to persistence and spread of a species with a shifting habitat edge this is a correction to the article b li s bewick j shang and w f fagan siam j appl math 74 2014 pp 1397 1417

high rate vector quantization for detection we investigate high rate quantization for various detection and reconstruction loss criteria a new distortion measure is introduced which accounts for global loss in best attainable binary hypothesis testing performance the distortion criterion is related to the area under the receiver operating characteristic roc curve specifically motivated by sanov s theorem we define a performance curve as the trajectory of the pair of optimal asymptotic type i and type ii error rates of the most powerful neyman pearson test of the hypotheses the distortion measure is then defined as the difference between the area under the curve auc of the optimal pre encoded hypothesis test and the auc of the optimal post encoded hypothesis test as compared to many previously introduced distortion measures for decision making this distortion measure has the advantage of being independent of any detection thresholds or priors on the hypotheses which are generally difficult to specify in the code design process a high resolution zador gersho type of analysis is applied to characterize the point density and the inertial profile associated with the optimal high rate vector quantizer the analysis applies to a restricted class of high rate quantizers that have bounded cells with vanishing volumes the optimal point density is used to specify a lloyd type algorithm which allocates its finest resolution to regions where the gradient of the pre encoded likelihood ratio has greatest magnitude

an h likelihood method for spatial mixed linear models based on intrinsic auto regressions summary we consider sparse spatial mixed linear models particularly those described by besag and higdon and develop an h likelihood method for their statistical inference the method proposed allows for singular precision matrices as it produces estimates that coincide with those from the residual maximum likelihood based on appropriate differencing of the data and has a novel approach to estimating precision parameters by a gamma linear model furthermore we generalize the h likelihood method to include continuum spatial variations by making explicit use of scaling limit connections between gaussian intrinsic markov random fields on regular arrays and the de wijs process keeping various applications of spatial mixed linear models in mind we devise a novel sparse conjugate gradient algorithm that allows us to achieve fast matrix free statistical computations we provide two applications the first is an extensive analysis of an agricultural variety trial that brings forward various new aspects of nearest neighbour adjustment such as effects on statistical analyses to changes of scale and use of implicit continuum spatial formulation the second application concerns an analysis of a large cotton field which gives a focus to matrix free computations the paper closes with some further considerations such as applications to irregularly spaced data use of the parametric bootstrap and some generalizations to the gaussian matern mixed effect models

statistical analysis of field experiments using neighbouring plots the paper describes and provides examples of four different applications of the use of neighbouring plot values in the analysis of agricultural field experiments the topics include the use of check plots to control environmental variation in large unreplicated variety trials spatial models based on first differences to accommodate fertility effects in trials that have some degree of replication adjustment for interplot competition using a simultaneous equations formulation and the analysis of trials in which plot values are affected by the particular treatments on neighbouring plots

high rate vector quantization for the neyman pearson detection of correlated processes this paper investigates the effect of quantization on the performance of the neyman pearson test it is assumed that a sensing unit observes samples of a correlated stationary ergodic multivariate process each sample is passed through an n point quantizer and transmitted to a decision device which performs a binary hypothesis test for any false alarm level it is shown that the miss probability of the neyman pearson test converges to zero exponentially as the number of samples tends to infinity assuming that the observed process satisfies certain mixing conditions the main contribution of this paper is to provide a compact closed form expression of the error exponent in the high rate regime i e when the number n of quantization levels tends to infinity generalizing previous results of gupta and hero to the case of nonindependent observations if d represents the dimension of one sample it is proved that the error exponent converges at rate n2 d to the one obtained in the absence of quantization as an application relevant high rate quantization strategies which lead to a large error exponent are determined numerical results indicate that the proposed quantization rule can yield better performance than existing ones in terms of detection error

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

not all possibly random sequences are created equal the need to assess the randomness of a single sequence especially a finite sequence is ubiquitous yet is unaddressed by axiomatic probability theory here we assess randomness via approximate entropy apen a computable measure of sequential irregularity applicable to single sequences of both even very short finite and infinite length we indicate the novelty and facility of the multidimensional viewpoint taken by apen in contrast to classical measures furthermore and notably for finite length finite state sequences one can identify maximally irregular sequences and then apply apen to quantify the extent to which given sequences differ from maximal irregularity via a set of deficit defm functions the utility of these defm functions which we show allows one to considerably refine the notions of probabilistic independence and normality is featured in several studies including i digits of e 2 and 3 both in base 2 and in base 10 and ii sequences given by fractional parts of multiples of irrationals we prove companion analytic results which also feature in a discussion of the role and validity of the almost sure properties from axiomatic probability theory insofar as they apply to specified sequences and sets of sequences in the physical world we conclude by relating the present results and perspective to both previous and subsequent studies

on the design of an optimal quantizer the problem of designing an optimal quantizer with a fixed number of levels for a wide class of error weighting functions and an arbitrary distribution function is discussed the existence of an optimal quantizer is proved and a two stage algorithm for its design is suggested in this algorithm at the first stage lloyd s iterative method i is applied for reducing the region where at the second stage the search for an optimal quantizer is performed using a hybrid of the dynamic programming algorithm and the lloyd max algorithm which achieves the absolute optimality of dynamic programming with much less computational effort for a continuous distribution with log concave density and an increasing convex weighting function of the absolute quantization error a reliable method is presented to compute the parameters of the optimal quantizer with a known precision using a generalization either of lloyd s method i or of the lloyd max algorithm

traveling waves in integro difference equations with a shifting habitat abstract we study an integro difference equation that describes the spatial dynamics of a species in a shifting habitat the growth function is nondecreasing in density and space for a given time and shifts at a constant speed c the spreading speeds for the model were previously studied the contribution of the current paper is to provide sharp conditions for existence of forced traveling waves with speed c we show the existence of traveling waves with zero value at or for c in different value ranges determined by the spreading speeds we also show the existence of a traveling wave with any speed c for the case that the species can grow everywhere our results demonstrate the existence of different types of traveling waves with the same speed

encoding of correlated observations an important class of engineering problems involves sensing an environment and making estimates based on the phenomena sensed in the traditional model of this problem the sensors observations are available to the estimator without alteration there is growing interest in em distributed sensing systems in which several observations are communicated to the estimator over channels of limited capacity the observations must be separately encoded so that the target can be estimated with minimum distortion two questions are addressed for a special case of this problem wherein there are two sensors which observe noisy data and communicate with a single estimator 1 if the encoder is unlimited in complexity what communication rates and distortions can be achieved 2 if the encoder must be a quantizer a mapping of a single observation sample into a digital output how can it be designed for good performance the first question is treated by the techniques of information theory it is proved that a given combination of rates and distortion is achievable if there exist degraded versions of the observations that satisfy certain formulas the second question is treated by two approaches in the first the outputs of the quantizers undergo a second stage of encoding which exploits their correlation to reduce the output rate algorithms which design the second stage are presented and tested the second approach is based on the em distributional distance a measure of dissimilarity between two probability distributions an algorithm to modify a quantizer for increased distributional distance is derived and tested

a note on the computation of optimal minimum mean square error quantizers this paper considers the problems associated with computing optimal minimum mean square error quantizers most computational methods in current use are iterative these iterative schemes are extremely sensitive to initial conditions various methods of obtaining good initial conditions are presented and discussed

a parametric approach to suboptimal signal detection in alpha stable noise this paper deals with the detection of a known deterministic signal embedded in alpha stable noise the implementation of the optimal receiver requires the explicit expression of the probability density function pdf of the noise unfortunately since there exists no closed form for the pdf of alpha stable distributed random variables numerical integrations are required to avoid such numerical approximations we suggest a low complexity parametric suboptimal detector well matched to essential properties of alpha stable noises this receiver does not require the explicit expression of the noise pdf in addition parameter optimization is fast for several optimization criteria and the selected receiver allows retrieval of the optimal gaussian detector matched filter as well as the locally optimal detector in the cauchy context the performance of the detector is studied and a comparison with the optimal solution along with a variety of classical detectors is given the robustness of the detector against the signal amplitude and the stability index alpha of the noise is discussed

on the support of fixed rate minimum mean squared error scalar quantizers for a laplacian source this correspondence shows that the support growth of a fixed rate optimum minimum mean squared error scalar quantizer for a laplacian density is logarithmic with the number of quantization points specifically it is shown that for a unit variance laplacian density the ratio of the support determining threshold of an optimum quantizer to 3 spl radic 2lnn 2 converges to 1 as the number n of quantization points grows also derived is a limiting upper bound that says that the support determining threshold cannot exceed the logarithmic growth by more than a small constant e g 0 0669 these results confirm the logarithmic growth of the optimum support that has previously been derived heuristically

robust control for fuzzy dynamical systems uniform ultimate boundedness and optimality we propose a new approach for the control design of fuzzy dynamical systems the system may contain uncertainty which includes unknown parameter and input disturbance the uncertainty lies within a prescribed fuzzy set the control structure is deterministic and hence not if then rule based the desired controlled system performance includes uniform boundedness and uniform ultimate boundedness in addition we propose a quadratic cost index which reflects the fuzzy system performance we then formulate a control parameter design problem as a constrained optimization problem it is proven that the global solution to this problem always exists and is unique the closed form solution and the closed form minimum cost are derived

one hundred years of the design of experiments on and off the pages of biometrika the earliest important papers on planned experiments in biometrika appeared within a year of each other in 1917 and 1918 roughly speaking one was concerned with design optimality and industrial experiments the other with agricultural trials and blocking we find this approximate division of the subject into two parts helpful in describing its development and growth as a result of the hostility between fisher and karl pearson much of the development of designs for agriculture in the 1920s and 1930s occurred off the pages of biometrika despite this we are able to trace a coherent history of the development of the subject from field trials and response surface methods to clinical trials and bayesian versions of design optimality

fine quantization in signal detection and estimation the performance lost to data quantization in signal detection and estimation procedures is considered the performance is measured by f divergences which are useful indices of discrimination information between statistical hypotheses some properties of the f divergences are briefly discussed and a general result for the loss in divergence due to uniform data quantization is obtained several applications of this result in specific problems of signal detection and estimation being developed and some numerical results that illustrate the asymptotic behavior of the divergence in these applications are given the divergence lost to finite nonuniform quantization through the use of a companding model is considered and the asymptotically optimum nonuniform quantizer within this class is derived some interesting problems that remain open are discussed

intrinsic autoregressions and related models on the two dimensional lattice summary stationary autoregressions on a two dimensional lattice are generalized to intrinsic models where only increments are assumed to be stationary prediction formulae and the asymptotic behaviour of the semivariogram are derived for parameter estimation we propose an approximate maximum likelihood estimator a generalization of whittle s estimator it is derived also for general intrinsic models

performance of ds ssma communications in impulsive channels part i linear correlation receivers the performance of digital linear correlation receivers is studied in a multiuser environment there are assumed to be two types of sources interfering with data transmission multiple access interference and additive channel noise which is attributed to impulsive noise sources in the environment the contribution of multiple access interference is examined by considering k asynchronous users transmitting simultaneously over a linear channel using the binary psk direct sequence spreadspectrum multiple access ds ssma technique alternatively the effects of the non gaussian impulsive channel in such a system are studied by modeling the samples of noise after front end filtering errorprobability performance under these conditions is compared to that for additive white gaussian noise awgn channels due to computational complexity exact analysis is limited here to systems utilizing short spreading sequences computationally simple methods are proposed for approximating the average error probability when the length of the signature sequences is large furthermore some asymptotic results are obtained for the case of infinitely long sequences in all cases performance variation is examined as the shape of the noise density varies with snr held constant the results of this analysis indicate that the presence of impulsive noise can cause significant performance degradation over that predicted from an awgn model even when the total noise power does not increase

new error bounds and optimum quantization for multisensor distributed signal detection the binary signal detection problem is considered when a distributed system of sensors operates in a decentralized fashion local processing at each sensor is performed using chernoff s large deviation theorems the author considers as a criterion the rate of convergence of the error probability to zero it is shown that the optimum quantizer of blocks of data under the above criterion is the likelihood ratio quantizer a lower bound to the error probability is also developed the question of how many coarsely quantized sensors can replace the infinitely quantized one is also answered the main result given is the structure of the optimum quantizer consisting of the calculation of the likelihood ratio concatenated by a scalar quantizer

on initialization of max s algorithm for optimum quantization two methods for initializing j max s 1960 iterative algorithm for optimum quantization for a rapid convergence of the algorithm are derived and tested the methods which are based on making an intelligent guess of the starting point perform considerably better than the existing methods for a wide class of reasonably well behaved unimodal density functions while the amount of computations involved is negligible compared with what is involved in a single iteration of max s algorithm an interesting relationship between optimum quantizers of different levels is revealed in the derivation of these methods this relationship could also be useful for scalar quantizer design

on the asymptotics of m hypothesis bayesian detection in two hypothesis detection problems with i i d observations the minimum error probability decays exponentially with the amount of data with the constant in the exponent equal to the chernoff distance between the probability distributions characterizing the hypotheses we extend this result to the general m hypothesis bayesian detection problem where zero cost is assigned to correct decisions and find that the bayesian cost function s exponential decay constant equals the minimum chernoff distance among all distinct pairs of hypothesized probability distributions

an analytic function describing the error performance of optimum quantizers corresp for optimizing or analyzing digital source coding systems a model for the mean square quantizing error as a function of the number of levels is necessary an analytic approximation function is presented which is valid for a wide range of important probability density functions

optimum quantization for detection vector quantization is a procedure widely used in communications the problem has been solved for the basic detection situation using the locally optimal procedure and with some constraints on the quantization scheme it is stated in its widest sense which consists of finding the partition of the observation space and the values associated with it in such a way that the detection performance is optimal it is solved completely with the deflection criterion and the solution introduces the concept of quantization by a likelihood ratio procedure

can pathogen spread keep pace with its host invasion we consider the fisher kpp equation in a wavelike shifting environment for which the wave profile of the environment is given by a monotonically decreasing function changing signs shifting from favorable to unfavorable environment this type of equation arises naturally from the consideration of pathogen spread in a classical susceptible infected susceptible epidemiological model of a host population where the disease impact on host mobility and mortality is negligible we conclude that there are three different ranges of the disease transmission rate where the disease spread has distinguished spatiotemporal patterns extinction spread in pace with the host invasion spread not in a wave format and slower than the host invasion we calculate the disease propagation speed when disease does spread our analysis for a related elliptic operator provides closed form expressions for two generalized eigenvalues in an unbounded domain the obtained closed forms yield unsolvability of the related elliptic equation in the critical case which relates to the open problem 4 6 in h berestycki and l rossi j eur math soc jems 8 2006 pp 195 215

statistical inference under multiterminal data compression this paper presents a survey of the literature on the information theoretic problems of statistical inference under multiterminal data compression with rate constraints significant emphasis is put on problems 1 multiterminal hypothesis testing 2 multiterminal parameter estimation and 3 multiterminal pattern classification in either case of positive rates or zero rates in addition the paper includes three new results i e the converse theorems for all problems of multiterminal hypothesis testing multiterminal parameter estimation and multiterminal pattern classification at the zero rate

quantization in multisensor random signal detection optimum detection schemes based on quantized data are of great interest in radar and sonar applications the design and properties of multisensor schemes are considered here for detection of weak random signals in additive possibly non gaussian noise signal to noise ratios are assumed unknown and the signals at the different sensors may be statistically dependent analytical expressions describing the best way to fuse the quantized observations for cases with any given observation sample size are provided the best schemes for originally quantizing the observations are also studied for the case of asymptotically large observation sample sizes these schemes are shown to minimize the mean squared error between the best weak signal test statistic based on unquantized observations and the best weak signal test statistic based on quantized observations under signal absent numerical results indicate it is sometimes best for each quantizer to use different size alphabets when a quantizer is located at each sensor

on optimum and nearly optimum data quantization for signal detection the application of companding approximation theory to the quantization of data for detection of coherent signals in a noisy environment is considered this application is twofold allowing for greater simplicity in both analysis and design of quantizers for detection systems most computational methods for designing optimum most efficient quantizers for signal detection systems are iterative and are extremely sensitive to initial conditions companding approximation theory is used here to obtain suitable initial conditions for this problem furthermore the companding approximation idea is applied to design suboptimum quantizers which are nearly as efficient as optimum quantizers when the number of levels is large in this design iteration is not needed to derive the parameters of the quantizer and the design procedure is very simple in this paper we explore this approach numerically and demonstrate its effectiveness for designing and analyzing quantizers in detection systems

adaptive learning vector quantization for online parametric estimation this paper addresses the problem of parameter estimation in a quantized and online setting a sensing unit collects random vector valued samples from the environment these samples are quantized and transmitted to a central processor which generates an online estimate of the unknown parameter this paper provides a closed form expression of the excess mean square error mse caused by quantization in the high rate regime i e when the number of quantization levels is supposed to be large next we determine the quantizers which mitigate the excess mse the optimal quantization rule unfortunately depends on the unknown parameter to circumvent this issue we introduce a novel adaptive learning vector quantization scheme which allows to simultaneously estimate the parameter of interest and select an efficient quantizer

a simple class of asymptotically optimal quantizers a simple class of quantizers is introduced which are asymptotically optimal as the number of quantization levels increases to infinity with respect to a mean r th power absolute error distortion measure these asymptotically optimal quantizers are very easy to compute their performance is evaluated for several distributions and compares favorably with the performance of the optimal quantizers in all cases for which the latter have been computed in addition their asymptotic robustness is studied under location scale and shape mismatch for several families of distributions

an algorithm for the design of generalized quantizers for detection a procedure based on the generalized lloyd algorithm approach using a sequence of independent noise samples to design m region generalized quantizers for signal detection is presented included in this case are the conventional m interval quantizer detectors the quantizer parameters for s a kassam s 1985 four region generalized quantizer detector are computed using various sample sizes for the known sequence of independent noise samples two families of densities which cover a wide spectrum of possible nongaussian densities are considered the generalized gaussian densities and the johnson s sub u family of densities the performance of the quantizer detector is compared to that of the locally optimum detector and the results are presented as the asymptotic relative efficiencies of the respective detectors the case when the noise density is not known before analysis is considered and the detection performance is examined using an estimate of the density a mean squared error distortion criterion is used in the proposed algorithm to obtain quantizers that yield maximum efficacy it is shown through numerical examples that the design procedure is simple fast and applicable to a wide range of nongaussian distributions

asymptotically optimum quantization with time invariant breakpoints for signal detection the nonlinear equations whose solution determines the locally optimum detection quantizer design are derived for a general parametric detection problem where the breakpoints are constrained to be time invariant these quantizers maximize the efficacy of a test based on quantized data some specific optimum detection quantizer problems for the case of time invariant breakpoints have been solved in the past but only for the special case when the locally optimum nonlinearity factors in a certain way examples of observation models that do not satisfy these conditions are given it is demonstrated that the locally optimum quantizer design for the time invariant breakpoint constraint is the same as that quantizer design that minimizes the time average mean square difference between the quantizer and the locally optimum time varying nonlinearity a specific result shows that the optimum quantizer is not symmetric for the quadratic detector for random signals in gaussian noise

a further investigation of max s algorithm for optimum quantization although max s algorithm is frequently thought of as a simple and adequate method for the design of scalar minimum mean squared error quantizers there are two tactical problems associated with this iterative scheme the initialization and the updating of the algorithm this paper proposes easy and efficient solutions to these problems a straightforward method for obtaining good initial conditions for three common input densities is presented also an efficient technique for updating the algorithm for a wide class of input densities is given

extremal properties of likelihood ratio quantizers m hypotheses and a random variable y with a different probability distribution under each hypothesis are considered a quantizer is applied to form a quantized random variable gamma y the extreme points of the set of possible probability distributions of gamma y as gamma ranges over all quantizers is characterized optimality properties of likelihood ratio quantizers are established for a very broad class of quantization problems including problems involving the maximization of an ali silvey 1966 distance measure and the neyman pearson variant of the decentralized detection problem

quantization for decentralized hypothesis testing under communication constraints in a decentralized hypothesis testing network several peripheral nodes observe an environment and communicate their observations to a central node for the final decision the presence of capacity constraints introduces theoretical and practical problems the following problem is addressed given that the peripheral encoders that satisfy these constraints are scalar quantizers how should they be designed in order that the central test to be performed on their output indices is most powerful the scheme is called cooperative design separate encoding since the quantizers process separate observations but have a common goal they seek to maximize a system wide performance measure the bhattacharyya distance of the joint index space as such a criterion is suggested and a design algorithm to optimize arbitrarily many quantizers cyclically is proposed a simplified version of the algorithm namely an independent design separate encoding scheme where the correlation is either absent or neglected for the sake of simplicity is outlined performances are compared through worked examples

distributed scalar quantization for computing high resolution analysis and extensions communication of quantized information is frequently followed by a computation we consider situations of distributed functional scalar quantization distributed scalar quantization of possibly correlated sources followed by centralized computation of a function under smoothness conditions on the sources and function companding scalar quantizer designs are developed to minimize mean squared error mse of the computed function as the quantizer resolution is allowed to grow striking improvements over quantizers designed without consideration of the function are possible and are larger in the entropy constrained setting than in the fixed rate setting as extensions to the basic analysis we characterize a large class of functions for which regular quantization suffices consider certain functions for which asymptotic optimality is achieved without arbitrarily fine quantization and allow limited collaboration between source encoders in the entropy constrained setting a single bit per sample communicated between encoders can have an arbitrarily large effect on functional distortion in contrast such communication has very little effect in the fixed rate setting

randomness and degrees of irregularity the fundamental question are sequential data random arises in myriad contexts often with severe data length constraints furthermore there is frequently a critical need to delineate nonrandom sequences in terms of closeness to randomness e g to evaluate the efficacy of therapy in medicine we address both these issues from a computable framework via a quantification of regularity apen approximate entropy defining maximal randomness for sequences of arbitrary length indicating the applicability to sequences as short as n 5 points an infinite sequence formulation of randomness is introduced that retains the operational and computable features of the finite case in the infinite sequence setting we indicate how the foundational definition of independence in probability theory and the definition of normality in number theory reduce to limit theorems without rates of convergence from which we utilize apen to address rates of convergence of a deficit from maximal randomness refining the aforementioned concepts in a computationally essential manner representative applications among many are indicated to assess i random number generation output ii well shuffled arrangements and iii the quality of bootstrap replicates

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

performance of ds ssma communications in impulsive channels ii hard limiting correlation receivers for pt i see ibid vol com 35 no 11 p 1179 88 1987 in part i it was demonstrated that impulsive channel noise can be a serious detriment to the performance of direct sequence spread spectrum multiple access ds ssma communications when conventional linear correlation reception is used here a hard limiting correlator as an alternative for reception of multiple access transmission in impulsive channels is considered for k asynchronous binary psk ds ssma users sharing a linear channel corrupted by impulsive noise that is modeled at the output of the front end filter of the receiver techniques are developed for analyzing bit error probabilities of this hard limiting receiver by exact computation for short spreading sequences by approximation for longer spreading sequences and by asymptotic limits for infinitely long spreading sequences performance is compared to that of the linear correlator under a variety of conditions showing that hard limiting correlation reception can offer substantial improvement over conventional systems in impulsive channels however the linear receiver is more effective against multiple access noise only and so a tradeoff emerges between rejection of impulsive noise and rejection of multiple access interference