ergodicity of markov channels a markov channel is a discrete information channel that includes as special cases the finite state channels and finite state codes of information theory kieffer and rahe proved that one sided and two sided markov channels have the following property if the input source to a markov channel is asymptotically mean stationary ams then so is the resulting input output process and hence the ergodic theorem and the shannon mcmillan breiman theorem hold for the input output process kieffer and rahe also provided a sufficient condition for any ams ergodic source to yield an ams ergodic input output process new conditions for a markov channel to have this ergodicity property are presented and discussed here several relations are developed among various classes of channels including weakly ergodic indecomposable and strongly mixing channels some connections between markov channels and the theory of nonhomogeneous markov chains are also discussed

a fitting algorithm for markov modulated poisson processes having two arrival rates abstract point processes with fluctuating arrival rates arise in many current applications of queueing theory notably in communications modeling markov modulated poisson processes mmpp have been used to describe such processes because they incorporate a mechanism to account for the temporal inhomogeneity of the arrival rates yet yield analytically tractable queueing results an iterative statistical procedure is developed for fitting mmpp having two arrival rates to observational data the procedure is largely numerical experimental and is motivated by maximum likelihood estimation

the generalized distributive law we discuss a general message passing algorithm which we call the generalized distributive law gdl the gdl is a synthesis of the work of many authors in information theory digital communications signal processing statistics and artificial intelligence it includes as special cases the baum welch algorithm the fast fourier transform fft on any finite abelian group the gallager tanner wiberg decoding algorithm viterbi s algorithm the bcjr algorithm pearl s belief propagation algorithm the shafer shenoy probability propagation algorithm and the turbo decoding algorithm although this algorithm is guaranteed to give exact answers only in certain cases the junction tree condition unfortunately not including the cases of gtw with cycles or turbo decoding there is much experimental evidence and a few theorems suggesting that it often works approximately even when it is not supposed to

a two state markov mixture model for a time series of epileptic seizure counts this paper discusses a model for a time series of epileptic seizure counts in which the mean of a poisson distribution changes according to an underlying two state markov chain the em algorithm dempster laird and rubin 1977 journal of the royal statistical society series b 39 1 38 is used to compute maximum likelihood estimators for the parameters of this two state mixture model and extensions are made allowing for nonstationarity the model is illustrated using daily seizure counts for patients with intractable epilepsy and results are compared with a simple poisson distribution and poisson regressions some simulation results are also presented to demonstrate the feasibility of this model

asymptotically optimal classification for multiple tests with empirically observed statistics the decision problem of testing m hypotheses when the source is kth order markov and there are m or fewer training sequences of length n and a single test sequence of length n is considered k m n n are all given it is shown what the requirements are on m n n to achieve vanishing exponential error probabilities and how to determine or bound the exponent a likelihood ratio test that is allowed to produce a no match decision is shown to provide asymptotically optimal error probabilities and minimum no match decisions as an important serial case the binary hypotheses problem without rejection is discussed it is shown that for this configuration only one training sequence is needed to achieve an asymptotically optimal test

mixture densities maximum likelihood and the em algorithm the problem of estimating the parameters which determine a mixture density has been the subject of a large diverse body of literature spanning nearly ninety years during the last two decades the

blind equalization of iir channels using hidden markov models and extended least squares in this paper we present a blind equalization algorithm for noisy iir channels when the channel input is a finite state markov chain the algorithm yields estimates of the iir channel coefficients channel noise variance transition probabilities and state of the markov chain unlike the optimal maximum likelihood estimator which is computationally infeasible since the computing cost increases exponentially with data length our algorithm is computationally inexpensive our algorithm is based on combining a recursive hidden markov model hmm estimator with a relaxed spr strictly positive real extended least squares els scheme in simulation studies we show that the algorithm yields satisfactory estimates even in low snr we also compare the performance of our scheme with a truncated fir scheme and the constant modulus algorithm cma which is currently a popular algorithm in blind equalization

asymptotic normality of the maximum likelihood estimator for general hidden markov models hidden markov models hmms have during the last decade become a widespread tool for modeling sequences of dependent random variables inference for such models is usually based on the maximum likelihood estimator mle and consistency of the mle for general hmms was recently proved by leroux in this paper we show that under mild conditions the mle is also asymptotically normal and prove that the observed information matrix is a consistent estimator of the fisher information

on the relations between modeling approaches for speech recognition some relations among approaches that have been applied to estimating models for acoustic signals in speech recognition systems are examined in particular the modeling approaches based on maximum likelihood ml maximum mutual information mmi and minimum discrimination information mdi are studied it is shown that all three approaches can be formulated uniformly as mdi modeling approaches for simultaneous estimation of the acoustic models for all words in the vocabulary and that none of the approaches requires any model correctness assumption the three approaches differ in the effective source being modeled and in the probability distribution attributed to this source

asymptotic normality of the maximum likelihood estimator in state space models state space models is a very general class of time series models capable of modelling dependent observations in a natural and interpretable way inference in such models has been studied by bickel ritov and ryden who consider hidden markov models which are special kinds of state space models and prove that the maximum likelihood estimator is asymptotically normal under mild regularity conditions in this paper we generalize the results of bickel ritov and ryden to state space models where the latent process is a continuous state markov chain satisfying regularity conditions which are fulfilled if the latent process takes values in a compact space

generalized design of low complexity block diagonalization type precoding algorithms for multiuser mimo systems block diagonalization bd based precoding techniques are well known linear transmit strategies for multiuser mimo mu mimo systems by employing bd type precoding algorithms at the transmit side the mu mimo broadcast channel is decomposed into multiple independent parallel single user mimo su mimo channels and achieves the maximum diversity order at high data rates the main computational complexity of bd type precoding algorithms comes from two singular value decomposition svd operations which depend on the number of users and the dimensions of each user s channel matrix in this work low complexity precoding algorithms are proposed to reduce the computational complexity and improve the performance of bd type precoding algorithms we devise a strategy based on a common channel inversion technique qr decompositions and lattice reductions to decouple the mu mimo channel into equivalent su mimo channels analytical and simulation results show that the proposed precoding algorithms can achieve a comparable sum rate performance as bd type precoding algorithms substantial bit error rate ber performance gains and a simplified receiver structure while requiring a much lower complexity

maximum likelihood estimation for multivariate observations of markov sources parameter estimation for multivariate functions of markov chains a class of versatile statistical models for vector random processes is discussed the model regards an ordered sequence of vectors as noisy multivariate observations of a markov chain mixture distributions are a special case the foundations of the theory presented here were established by baum petrie soules and weiss a powerful representation theorem by fan is employed to generalize the analysis of baum em et al to a larger class of distributions

new finite dimensional filters and smoothers for noisily observed markov chains new finite dimensional filters and smoothers that are related to the wonham filter of a noisily observed markov chain are obtained in particular finite dimensional recursive filters and smoothers are given for the number of jumps from state i to state j for the occupation time of state i and for a stochastic integral related to the drift in the observations these filters allow easy application of the em algorithm for the estimation of the parameters of the markov chain and observation process

partially hidden markov models partially hidden markov models phmm are introduced they differ from the ordinary hmms in that both the transition probabilities of the hidden states and the output probabilities are conditioned on past observations as an illustration they are applied to black and white image compression where the hidden variables may be interpreted as representing noncausal pixels

universal classification for hidden markov models binary hypotheses testing using empirically observed statistics is studied in the neyman pearson formulation for the hidden markov model hmm an asymptotically optimal decision rule is proposed and compared to the generalized likelihood ratio test glrt which has been shown in earlier studies to be asymptotically optimal for simpler parametric families the proof of the main theorem is provided the result can be applied to several types of hmms commonly used in speech recognition and communication applications several applications are demonstrated

remarks on linear and nonlinear filtering this communication tries to give some insight into relationships existing between viterbi and the forward backward algorithm used in the context of hidden markov models on the one hand and kalman filtering and rauch tung striebel smoothing on the other we give a unifying view which shows how those algorithms are related and give an example of a nonlinear hybrid system that can be filtered through a mixed algorithm

non gaussian state space modeling of nonstationary time series abstract a non gaussian state space approach to the modeling of nonstationary time series is shown the model is expressed in state space form where the system noise and the observational noise are not necessarily gaussian recursive formulas of prediction filtering and smoothing for the state estimation and identification of the non gaussian state space model are given also given is a numerical method based on piecewise linear approximation to the density functions for realizing these formulas significant merits of non gaussian modeling and the wide range of applicability of the method are illustrated by some numerical examples a typical application of this non gaussian modeling is the smoothing of a time series that has mean value function with both abrupt and gradual changes simple gaussian state space modeling is not adequate for this situation here the model with small system noise variance cannot detect jump whereas the one with large system noise variance yields unfavorable wiggle to work

consistent and asymptotically normal parameter estimates for hidden markov models hidden markov models are today widespread for modeling of various phenomena it has recently been shown by leroux that the maximum likelihood estimate mle of the parameters of a such a model is consistent and local asymptotic normality has been proved by bickel and ritov in this paper we propose a new clans of estimates which are consistent asymptoti cally normal and almost as good an the mle

on kalman smoothing with random packet loss this correspondence studies the performance of kalman fixed lag smoothers with random packet losses and its comparison with the kalman filter with packet loss in terms of estimator stability via boundedness of the expectation of the error covariance we show that smoothing does not provide any benefit over filtering on the other hand it is demonstrated that using a probabilistic notion of performance smoothing can provide significant gains when compared to kalman filtering an analysis of kalman filtering using two simple retransmission schemes and its comparison with kalman smoothing is also made

on classification with empirically observed statistics and universal data compression classification with empirically observed statistics is studied for finite alphabet sources efficient universal discriminant functions are described and shown to be related to universal data compression it is demonstrated that if one of the probability measure of the two classes is not known it is still possible to define a universal discrimination function which performs as the optimal likelihood ratio discriminant function which can be evaluated only if the probability measures of the two classes are available if both of the probability measures are not available but training vectors from at least one of the two classes are available it is demonstrated that no discriminant function can perform efficiency of the length of the training vectors does not grow at least linearly with the length of the classified vector a universal discriminant function is introduced and shown to perform efficiently when the length of the training vectors grows linearly with the length of the classified sequence in the sense that it yields an error exponent that is arbitrarily close to that of the optimal discriminant function

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

bayesian estimation of switching arma models abstract switching arma processes have recently appeared as an efficient modelling to nonlinear time series models because they can represent multiple or heterogeneous dynamics through simple components the levels of dependence between the observations are double at a first level the parameters of the model are selected by a markovian procedure at a second level the next observation is generated according to a standard time series model when the model involves a moving average structure the complexity of the resulting likelihood function is such that simulation techniques like those proposed by shephard 1994 biometrika 81 115 131 and billio and monfort 1998 journal of statistical planning and inference 68 65 103 are necessary to derive an inference on the parameters of the model we propose in this paper a bayesian approach with a non informative prior distribution developed in mengersen and robert 1996 bayesian statistics 5 oxford university press oxford pp 255 276 and robert and titterington 1998 statistics and computing 8 2 145 158 in the setup of mixtures of distributions and hidden markov models respectively the computation of the bayes estimates relies on mcmc techniques which iteratively simulate missing states innovations and parameters until convergence the performances of the method are illustrated on several simulated examples this work also extends the papers by chib and greenberg 1994 journal of econometrics 64 183 206 and chib 1996 journal of econometrics 75 1 79 97 which deal with arma and hidden markov models respectively

a filtered em algorithm for joint hidden markov model and sinusoidal parameter estimation derives finite dimensional discrete time filters for estimating the parameters of discrete time finite state markov chains imbedded in a mixture of gaussian white noise and deterministic signals of known functional form with unknown parameters the filters that are derived estimate quantities used in the expectation maximization em algorithm for maximum likelihood ml estimation of the markov chain parameters transition probabilities and state levels as well as the parameters of the deterministic interference two types of deterministic signals are considered periodic or almost periodic signals with unknown frequency components amplitudes and phases and polynomial drift in the states of the markov process with the coefficients of the polynomial unknown the filter based em algorithm has negligible memory requirements in comparison implementing the em algorithm using smoothed variables forward backward variables requires memory proportional to the number of observations in addition the filters are suitable for multiprocessor implementation unlike the forward backward algorithm

on the parameters estimation of continuous time arma processes from noisy observations recently an iterative algorithm has been presented for estimating the parameters of partially observed continuous time processes 1 in this note we concentrate on continuous time arma processes observed in white noise a maximum a posteriori map estimator is defined for the trajectory of the parameters random process this approach enables the map estimation of randomly slowly varying parameters and extends the conventional treatment of time invariant parameters the iterative algorithm derived for the map estimation increases the posterior probability of the parameters in each iteration and converges to a stationary point of the posterior probability functional each iteration involves a standard linear smoother followed by a finite dimensional linear system and thus is easily implemented

generalized channel inversion methods for multiuser mimo systems block diagonalization bd is a well known precoding method in multiuser multi input multi output mimo broadcast channels this scheme can be considered as a extension of the zero forcing zf channel inversion to the case where each receiver is equipped with multiple antennas one of the limitation of the bd is that the sum rate does not grow linearly with the number of users and transmit antennas at low and medium signal to noise ratio regime since the complete suppression of multi user interference is achieved at the expense of noise enhancement also it performs poorly under imperfect channel state information in this paper we propose a generalized minimum mean squared error mmse channel inversion algorithm for users with multiple antennas to overcome the drawbacks of the bd for multiuser mimo systems we first introduce a generalized zf channel inversion algorithm as a new approach of the conventional bd applying this idea to the mmse channel inversion for identifying orthonormal basis vectors of the precoder and employing the mmse criterion for finding its combining matrix the proposed scheme increases the signal to interference plus noise ratio at each user s receiver simulation results confirm that the proposed scheme exhibits a linear growth of the sum rate as opposed to the bd scheme for block fading channels with four transmit antennas the proposed scheme provides a 3 db gain over the conventional bd scheme at 1 frame error rate also we present a modified precoding method for systems with channel estimation errors and show that the proposed algorithm is robust to channel estimation errors

kalman filtering with intermittent observations motivated by navigation and tracking applications within sensor networks we consider the problem of performing kalman filtering with intermittent observations when data travel along unreliable communication channels in a large wireless multihop sensor network the effect of communication delays and loss of information in the control loop cannot be neglected we address this problem starting from the discrete kalman filtering formulation and modeling the arrival of the observation as a random process we study the statistical convergence properties of the estimation error covariance showing the existence of a critical value for the arrival rate of the observations beyond which a transition to an unbounded state error covariance occurs we also give upper and lower bounds on this expected state error covariance

hidden markov processes an overview of statistical and information theoretic aspects of hidden markov processes hmps is presented an hmp is a discrete time finite state homogeneous markov chain observed through a discrete time memoryless invariant channel in recent years the work of baum and petrie 1966 on finite state finite alphabet hmps was expanded to hmps with finite as well as continuous state spaces and a general alphabet in particular statistical properties and ergodic theorems for relative entropy densities of hmps were developed consistency and asymptotic normality of the maximum likelihood ml parameter estimator were proved under some mild conditions similar results were established for switching autoregressive processes these processes generalize hmps new algorithms were developed for estimating the state parameter and order of an hmp for universal coding and classification of hmps and for universal decoding of hidden markov channels these and other related topics are reviewed

application of the conditional population mixture model to image segmentation the problem of image segmentation is considered in the context of a mixture of probability distributions the segments fall into classes a probability distribution is associated with each class of segment parametric families of distributions are considered a set of parameter values being associated with each class with each observation is associated an unobservable label indicating from which class the observation arose segmentation algorithms are obtained by applying a method of iterated maximum likelihood to the resulting likelihood function a numerical example is given choice of the number of classes using akaike s information criterion aic for model identification is illustrated

on state estimation of a two state hidden markov model with quantization we consider quantization from the perspective of minimizing filtering error when quantized instead of continuous measurements are used as inputs to a nonlinear filter specializing to discrete time two state hidden markov models hmms with continuous range output an explicit expression for the filtering error when continuous measurements are used is presented we also propose a quantization scheme based on maximizing the mutual information between quantized observations and the hidden states of the hmm

factoring polynomials with rational coefficients in this paper we present a polynomial time algorithm to solve the following problem given a non zero polynomial fe q x in one variable with rational coefficients find the decomposition of f into irreducible factors in q x it is well known that this is equivalent to factoring primitive polynomials fez x into irreducible factors in z x here we call f z x primitive if the greatest common divisor of its coefficients the content of f is 1 our algorithm performs well in practice cf 8 its running time measured in bit operations is o nl2 n9 log fd3

the strong ergodic theorem for densities generalized shannon mcmillan breiman theorem let xi x2 be a stationary process with probability densities f x1 x2 xn with respect to lebesgue measure or with respect to a markov measure with a stationary transition measure it is shown that the sequence of relative entropy densities 1 n log f xi x2 x0 converges almost surely this long conjectured result extends the l convergence obtained by moy perez and kieffer and generalizes the shannon mcmillanbreiman theorem to nondiscrete processes the heart of the proof is a new martingale inequality which shows that logarithms of densities are l dominated

a vector perturbation technique for near capacity multiantenna multiuser communication part ii perturbation recent theoretical results describing the sum capacity when using multiple antennas to communicate with multiple users in a known rich scattering environment have not yet been followed with practical transmission schemes that achieve this capacity we introduce a simple encoding algorithm that achieves near capacity at sum rates of tens of bits channel use the algorithm is a variation on channel inversion that regularizes the inverse and uses a sphere encoder to perturb the data to reduce the energy of the transmitted signal the paper is comprised of two parts in this second part we show that after the regularization of the channel inverse introduced in the first part a certain perturbation of the data using a sphere encoder can be chosen to further reduce the energy of the transmitted signal the performance difference with and without this perturbation is shown to be dramatic with the perturbation we achieve excellent performance at all signal to noise ratios the results of both uncoded and turbo coded simulations are presented

on the statistical analysis of dirty pictures may 7th 1986 professor a f m smith in the chair summary a continuous two dimensional region is partitioned into a fine rectangular array of sites or pixels each pixel having a particular colour belonging to a prescribed finite set the true colouring of the region is unknown but associated with each pixel there is a possibly multivariate record which conveys imperfect information about its colour according to a known statistical model the aim is to reconstruct the true scene with the additional knowledge that pixels close together tend to have the same or similar colours in this paper it is assumed that the local characteristics of the true scene can be represented by a nondegenerate markov random field such information can be combined with the records by bayes theorem and the true scene can be estimated according to standard criteria however the computational burden is enormous and the reconstruction may reflect undesirable largescale properties of the random field thus a simple iterative method of reconstruction is proposed which does not depend on these large scale characteristics the method is illustrated by computer simulations in which the original scene is not directly related to the assumed random field some complications including parameter estimation are discussed potential applications are mentioned briefly

zero forcing methods for downlink spatial multiplexing in multiuser mimo channels the use of space division multiple access sdma in the downlink of a multiuser multiple input multiple output mimo wireless communications network can provide a substantial gain in system throughput the challenge in such multiuser systems is designing transmit vectors while considering the co channel interference of other users typical optimization problems of interest include the capacity problem maximizing the sum information rate subject to a power constraint or the power control problem minimizing transmitted power such that a certain quality of service metric for each user is met neither of these problems possess closed form solutions for the general multiuser mimo channel but the imposition of certain constraints can lead to closed form solutions this paper presents two such constrained solutions the first referred to as block diagonalization is a generalization of channel inversion when there are multiple antennas at each receiver it is easily adapted to optimize for either maximum transmission rate or minimum power and approaches the optimal solution at high snr the second known as successive optimization is an alternative method for solving the power minimization problem one user at a time and it yields superior results in some e g low snr situations both of these algorithms are limited to cases where the transmitter has more antennas than all receive antennas combined in order to accommodate more general scenarios we also propose a framework for coordinated transmitter receiver processing that generalizes the two algorithms to cases involving more receive than transmit antennas while the proposed algorithms are suboptimal they lead to simpler transmitter and receiver structures and allow for a reasonable tradeoff between performance and complexity

adaptive reduced rank processing based on joint and iterative interpolation decimation and filtering we present an adaptive reduced rank signal processing technique for performing dimensionality reduction in general adaptive filtering problems the proposed method is based on the concept of joint and iterative interpolation decimation and filtering we describe an iterative least squares ls procedure to jointly optimize the interpolation decimation and filtering tasks for reduced rank adaptive filtering in order to design the decimation unit we present the optimal decimation scheme and also propose low complexity decimation structures we then develop low complexity least mean squares lms and recursive least squares rls algorithms for the proposed scheme along with automatic rank and branch adaptation techniques an analysis of the convergence properties and issues of the proposed algorithms is carried out and the key features of the optimization problem such as the existence of multiple solutions are discussed we consider the application of the proposed algorithms to interference suppression in code division multiple access cdma systems simulations results show that the proposed algorithms outperform the best known reduced rank schemes with lower complexity

exact filters for the estimation of the number of transitions of finite state continuous time markov processes the problem of estimating the number of transitions of finite state continuous time markov processes observed by a noisy sensor is considered a finite dimensional exact filter is derived and using the em algorithm an extension of the baum welch algorithm for the discrete time case an application is made to the problem of estimating the unknown transition matrix of a finite state continuous time markov process

a minimum discrimination information approach for hidden markov modeling an iterative approach for minimum discrimination information mdi hidden markov modeling of information sources is proposed the approach is developed for sources characterized by a given set of partial covariance matrices and for hidden markov models hmms with gaussian autoregressive output probability distributions pds the approach aims at estimating the hmm which yields the mdi with respect to all sources that could have produced the given set of partial covariance matrices each iteration of the mdi algorithm generates a new hmm as follows first a pd for the source is estimated by minimizing the discrimination information measure with respect to the old model over all pds which satisfy the given set of partial covariance matrices then a new model that decreases the discrimination information measure between the estimated pd of the source and the pd of the old model is developed the problem of estimating the pd of the source is formulated as a standard constrained minimization problem in the euclidean space the estimation of a new model given the pd of the source is done by a procedure that generalizes the baum algorithm the mdi approach is shown to be a descent algorithm for the discrimination information measure and its local convergence is proved

the consistency of the bic markov order estimator the bayesian information criterion bic estimates the order of a markov chain with finite alphabet a from observation of a sample path x 1 x 2 x n as that value k k that minimizes the sum of the negative logarithm of the kth order maximum likelihood and the penalty term a k a 1 2 log n we show that k equals the correct order of the chain eventually almost surely as n oo thereby strengthening earlier consistency results that assumed an apriori bound on the order a key tool is a strong ratio typicality result for markov sample paths we also show that the bayesian estimator or minimum description length estimator of which the bic estimator is regarded as an approximation fails to be consistent for the uniformly distributed i i d process

on universal coding for classes of composite and remote sources with memory corresp weakly minimax universal codes for composite sources whose channel analog has asymptotically decreasing input memory and anticipation adima are examined in particular weak universal codes of all rates with respect to an arbitrary distortion measure are shown to exist for adima composite sources when the switch processes belong to a bar d compact class these results are immediately applicable to universal coding for classes of remote sources

on the convergence properties of the em algorithm two convergence aspects of the em algorithm are studied i does the em algorithm find a local maximum or a stationary value of the incomplete data likelihood function ii does the sequence of parameter estimates generated by em converge several convergence results are obtained under conditions that are applicable to many practical situations two useful special cases are a if the unobserved complete data specification can be described by a curved exponential family with compact parameter space all the limit points of any em sequence are stationary points of the likelihood function b if the likelihood function is unimodal and a certain differentiability condition is satisfied then any em sequence converges to the unique maximum likelihood estimate a list of key properties of the algorithm is included

optimal simultaneous detection and estimation of filtered discrete semi markov chains an optimal algorithm for the detection of noisy filtered discrete semi markov chains is presented estimation of the underlying model parameters is also considered for a given path of the discrete semi markov chain the optimum estimates of the model parameters obtained by the maximum likelihood method are expressed as functions of the path these functions are then used to derive a single maximum a posteriori criterion for the optimal detection of the unknown single path the final optimization is carried out numerically by a combination of gradient divide and conquer and search techniques this set of techniques is referred to as the integer most likely search detector experimental results using synthetic data demonstrate the potential of the algorithm

likelihood ratio tests for hidden markov models summary we consider hidden markov models as a versatile class of models for weakly dependent random phenomena the topic of the present paper is likelihood ratio testing for hidden markov models and we show that under appropriate conditions the standard asymptotic theory of likelihood ratio tests is valid such tests are crucial in the specification of multivariate gaussian hidden markov models which we use to illustrate the applicability of our general results finally the methodology is illustrated by means of a real data set

complex lattice reduction algorithm for low complexity full diversity mimo detection recently lattice reduction aided detectors have been proposed for multiinput multioutput mimo systems to achieve performance with full diversity like the maximum likelihood receiver however these lattice reduction aided detectors are based on the traditional lenstra lenstra lovasz lll reduction algorithm that was originally introduced for reducing real lattice bases in spite of the fact that the channel matrices are inherently complex valued in this paper we introduce the complex lll algorithm for direct application to reducing the basis of a complex lattice which is naturally defined by a complex valued channel matrix we derive an upper bound on proximity factors which not only show the full diversity of complex lll reduction aided detectors but also characterize the performance gap relative to the lattice decoder our analysis reveals that the complex lll algorithm can reduce the complexity by nearly 50 compared to the traditional lll algorithm and this is confirmed by simulation interestingly our simulation results suggest that the complex lll algorithm has practically the same bit error rate performance as the traditional lll algorithm in spite of its lower complexity

exponential stability of filters and smoothers for hidden markov models we address the problem of filtering and fixed lag smoothing for discrete time and discrete state hidden markov models hmms with the intention of extending some important results in kalman filtering notably the property of exponential stability by appealing to a generalized perron frobenius result for non negative matrices we are able to demonstrate exponential forgetting for both the recursive filters and smoothers furthermore methods for deriving overbounds on the convergence rate are indicated simulation studies for a two state and two output hmm verify qualitatively some of the theoretical predictions and the observed convergence rate is shown to be bounded in accordance with the theoretical predictions

recursive estimation of parameters in markov modulated poisson processes a hidden markov regime is a markov process that governs the time or space dependent distributions of an observed stochastic process recursive algorithms can be used to estimate parameters in mixed distributions governed by a markov regime the authors derive a recursive algorithm for estimation of parameters in a markov modulated poisson process also called a cox point process by this the authors mean a doubly stochastic poisson process with a time dependent intensity that can take on a finite number of different values the intensity switches randomly between the possible values according to a markov process the authors consider two different ways to observe the markov modulated poisson process in the first model the observations consist of the observed time intervals between events and in the second model they use the total number of events in successive intervals of fixed length they derive an algorithm for recursive estimation of the poisson intensities and the switch intensities between the two states and illustrate the algorithm in a simulation study the estimates of the switch intensities are based on the observed conditional switch probabilities

linear transmit processing in mimo communications systems we examine and compare the different types of linear transmit processing for multiple input multiple output systems where we assume that the receive filter is independent of the transmit filter contrary to the joint optimization of transmit and receive filters we can identify three filter types similar to receive processing the transmit matched filter the transmit zero forcing filter and the transmit wiener filter we show that the transmit filters are based on similar optimizations as the respective receive filters with an additional constraint for the transmit power moreover the transmit wiener filter has similar convergence properties as the receive wiener filter i e it converges to the matched filter and the zero forcing filter for low and high signal to noise ratio respectively we give closed form solutions for all transmit filters and present the fundamental result that their mean square errors are equal to the errors of the respective receive filters if the information symbols and the additive noise are uncorrelated however our simulations reveal that the bit error ratio results of the transmit filters differ from the results for the respective receive filters

lll reduction achieves the receive diversity in mimo decoding diversity order is an important measure for the performance of communication systems over multiple input multiple output mimo fading channels in this correspondence we prove that in mimo multiple access systems or mimo point to point systems with v blast transmission lattice reduction aided decoding achieves the maximum receive diversity which is equal to the number of receive antennas also we prove that the naive lattice decoding which discards the out of region decoded points achieves the maximum diversity

image classification by a two dimensional hidden markov model for block based classification an image is divided into blocks and a feature vector is formed for each block by grouping statistics extracted from the block conventional block based classification algorithms decide the class of a block by examining only the feature vector of this block and ignoring context information in order to improve classification by context an algorithm is proposed that models images by two dimensional 2 d hidden markov models hmms the hmm considers feature vectors statistically dependent through an underlying state process assumed to be a markov mesh which has transition probabilities conditioned on the states of neighboring blocks from both horizontal and vertical directions thus the dependency in two dimensions is reflected simultaneously the hmm parameters are estimated by the em algorithm to classify an image the classes with maximum a posteriori probability are searched jointly for all the blocks applications of the hmm algorithm to document and aerial image segmentation show that the algorithm outperforms cart sup tm lvq and bayes vq

fixed complexity lll algorithm a common technique to perform lattice basis reduction is the lenstra lenstra lovasz lll algorithm an implementation of this algorithm in real time systems suffers from the problem of variable run time and complexity this correspondence proposes a modification of the lll algorithm the signal flow is altered to follow a deterministic structure which promises to obtain an easier implementation as well as a fixed execution time known in advance in the case of a maximum number of iterations as it is likely in real time systems our modification clearly outperforms the original lll algorithm as far as the quality of the reduced lattice basis is concerned

a recursive algorithm for the bayes solution of the smoothing problem the optimum fixed interval smoothing problem is solved using a bayesian approach assuming that the signal is markov and is corrupted by independent noise not necessarily additive a recursive algorithm to compute the a posteriori smoothed density is obtained using this recursive algorithm the smoothed estimate of a binary markov signal corrupted by an independent noise in a nonlinear manner is determined demonstrating that the bayesian approach presented in this paper is not restricted to the gauss markov problem

an adaptive receiver for space time trellis codes based on per survivor processing an adaptive receiver based on per survivor processing is proposed for detecting space time trellis codes transmitted over time selective flat fading channels and its performance is examined through simulations results suggest that the new receiver can outperform iterative approaches based on kalman filtering and the expectation maximization algorithm at the cost of increased receiver complexity

probability of error analysis for hidden markov model filtering with random packet loss this paper studies the probability of error for maximum a posteriori map estimation of hidden markov models where measurements can be either lost or received according to another markov process analytical expressions for the error probabilities are derived for the noiseless and noisy cases some relationships between the error probability and the parameters of the loss process are demonstrated via both analysis and numerical results in the high signal to noise ratio snr regime approximate expressions which can be more easily computed than the exact analytical form for the noisy case are presented

per survivor processing and tentative decisions what is in between in per survivor processing psp the number of parameter estimators equals the number of retained hypothetical data sequences survivors the authors propose an algorithm which uses an arbitrary number of parameter estimators and compromises between the two extremes of tentative decisions one parameter estimator and psp specific applications to reduced state sequence estimation rsse and maximum likelihood sequence estimation mlse with adaptive tracking of a fading channel are considered

finding the observed information matrix when using the em algorithm a procedure is derived for extracting the observed information matrix when the em algorithm is used to find maximum likelihood estimates in incomplete data problems the technique requires computation of a complete data gradient vector or second derivative matrix but not those associated with the incomplete data likelihood in addition a method useful in speeding up the convergence of the em algorithm is developed two examples are presented

strict stationarity of generalized autoregressive processes in this paper we consider the multivariate equation x n 1 a n 1 x n b n 1 with i i d coefficients which have only a logarithmic moment we give a necessary and sufficient condition for existence of a strictly stationary solution independent of the future as an application we characterize the multivariate arma equations with general noise which have such a solution

estimation of finite mixture distributions through bayesian sampling summary a formal bayesian analysis of a mixture model usually leads to intractable calculations since the posterior distribution takes into account all the partitions of the sample we present approximation methods which evaluate the posterior distribution and bayes estimators by gibbs sampling relying on the missing data structure of the mixture model the data augmentation method is shown to converge geometrically since a duality principle transfers properties from the discrete missing data chain to the parameters the fully conditional gibbs alternative is shown to be ergodic and geometric convergence is established in the normal case we also consider non informative approximations associated with improper priors assuming that the sample corresponds exactly to a k component mixture

maximum penalized likelihood estimation for independent and markov dependent mixture models summary this paper concerns the use and implementation of maximum penalized likelihood procedures for choosing the number of mixing components and estimating the parameters in independent and markov dependent mixture models computation of the estimates is achieved via algorithms for the automatic generation of starting values for the em algorithm computation of the information matrix is also discussed poisson mixture models are applied to a sequence of counts of movements by a fetal lamb in utero obtained by ultrasound the resulting estimates are seen to provide plausible mechanisms for the physiological process the analysis of count data that are overdispersed relative to the poisson distribution i e variance mean has received considerable recent attention such data might arise in a clinical study in which overdispersion is caused by unexplained or random subject effects alternatively we might observe a time series of counts in which temporal patterns in the data suggest that a poisson model and its implied randomness are inappropriate this paper is motivated by analysis of a time series of overdispersed count data generated in a study of central nervous system development in fetal lambs our data set consists of observed movement counts in 240 consecutive 5 second intervals obtained from a single animal in analysing these data we focus on the use of poisson mixture models assuming independent observations and also markov dependent mixture models or hidden markov models these models assume that the counts follow independent poisson distributions conditional on the rates which are generated from a mixing distribution either independently or with markov dependence we believe finite mixture models are particularly attractive because they provide plausible explanations for variation in the data this paper will emphasize the following issues concerning estimation inference and application of mixture models i choosing the number of model components ii applying the em algorithm to obtain parameter estimates iii generating sufficiently many starting values to identify a global maximum of the likelihood iv avoiding numerical instability

cartesian hidden markov models with applications the author introduces the concept of a cartesian hidden markov model chmm which consists of a markov chain assuming values in the cartesian product of a finite number of elementary state sets the states are observed via a multivariable probabilistic mapping again assuming values in a cartesian product of finite sets of observables the chmm can be reduced to an ordinary i e scalar hmm by conventional nonlinear techniques the forms of the forward backward algorithm which gives the fixed interval smoothed maximum a posteriori map estimates of the states and the viterbi algorithm which gives the map fixed interval sequence are straightforward generalizations of the scalar case two applications of chmms in the area of frequency tracking are briefly indicated

approximate ml decoding of coded psk with no explicit carrier phase reference an approximate method is discussed for maximum likelihood estimation of coded psk sequences in the presence of an unknown carrier phase this method makes use of the viterbi algorithm to find an optimum path in the encoder trellis diagram phase estimation is embedded into the structure of the detection algorithm and the branch metrics in the trellis are modified with respect to those employed with known carrier phase comparisons with traditional decoding schemes show that the proposed solution has better performance in terms of acquisition time and cycle slips