maximum likelihood erasure decoding of ldpc codes pivoting algorithms and code design this paper investigates efficient maximum likelihood ml decoding of low density parity check ldpc codes over erasure channels a set of algorithms referred to as pivoting algorithms is developed the aim is to limit the average number of pivots or reference variables from which all the other erased symbols are recovered iteratively the suggested algorithms exhibit different trade offs between complexity of the pivoting phase and average number of pivots moreover a systematic procedure to design ldpc code ensembles for efficient ml decoding is proposed numerical results illustrate that the designed ldpc codes achieve a near optimum performance very close to the singleton bound at least down to a codeword error rate level 10 8 with an affordable decoding complexity for one of the presented codes and algorithms a software implementation has been developed which is capable to provide data rates above 1 5 gbps on a commercial computing platform

the numerical analysis of ordinary differential equations runge kutta and general linear methods mathematical and computational introduction the euler method and its generalizations analysis of runge kutta methods general linear methods bibliography

on a family of circulant matrices for quasi cyclic low density generator matrix codes we present a new class of sparse and easily invertible circulant matrices that can have a sparse inverse though not being permutation matrices their study is useful in the design of quasi cyclic low density generator matrix codes that are able to join the inner structure of quasi cyclic codes with sparse generator matrices so limiting the number of elementary operations needed for encoding circulant matrices of the proposed class permit to hit both targets without resorting to identity or permutation matrices that may penalize the code minimum distance and often cause significant error floors

differential variational inequalities this paper introduces and studies the class of differential variational inequalities dvis in a finite dimensional euclidean space the dvi provides a powerful modeling paradigm for many applied problems in which dynamics inequalities and discontinuities are present examples of such problems include constrained time dependent physical systems with unilateral constraints differential nash games and hybrid engineering systems with variable structures the dvi unifies several mathematical problem classes that include ordinary differential equations odes with smooth and discontinuous right hand sides differential algebraic equations daes dynamic complementarity systems and evolutionary variational inequalities conditions are presented under which the dvi can be converted either locally or globally to an equivalent ode with a lipschitz continuous right hand function for dvis that cannot be so converted we consider their numerical resolution via an euler time stepping procedure which involves the solution of a sequence of finite dimensional variational inequalities borrowing results from differential inclusions dis with upper semicontinuous closed and convex valued multifunctions we establish the convergence of such a procedure for solving initial value dvis we also present a class of dvis for which the theory of dis is not directly applicable and yet similar convergence can be established finally we extend the method to a boundary value dvi and provide conditions for the convergence of the method the results in this paper pertain exclusively to systems with index not exceeding two and which have absolutely continuous solutions

gaussian particle filtering sequential bayesian estimation for nonlinear dynamic state space models involves recursive estimation of filtering and predictive distributions of unobserved time varying signals based on noisy observations this paper introduces a new filter called the gaussian particle filter it is based on the particle filtering concept and it approximates the posterior distributions by single gaussians similar to gaussian filters like the extended kalman filter and its variants it is shown that under the gaussianity assumption the gaussian particle filter is asymptotically optimal in the number of particles and hence has much improved performance and versatility over other gaussian filters especially when nontrivial nonlinearities are present simulation results are presented to demonstrate the versatility and improved performance of the gaussian particle filter over conventional gaussian filters and the lower complexity than known particle filters

efficient erasure correcting codes we introduce a simple erasure recovery algorithm for codes derived from cascades of sparse bipartite graphs and analyze the algorithm by analyzing a corresponding discrete time random process as a result we obtain a simple criterion involving the fractions of nodes of different degrees on both sides of the graph which is necessary and sufficient for the decoding process to finish successfully with high probability by carefully designing these graphs we can construct for any given rate r and any given real number spl epsiv a family of linear codes of rate r which can be encoded in time proportional to ln 1 spl epsiv times their block length n furthermore a codeword can be recovered with high probability from a portion of its entries of length 1 spl epsiv rn or more the recovery algorithm also runs in time proportional to n ln 1 spl epsiv our algorithms have been implemented and work well in practice various implementation issues are discussed

a partially linearized sigma point filter for latent state estimation in nonlinear time series models a new technique for the latent state estimation of a wide class of nonlinear time series models is proposed in particular we develop a partially linearized sigma point filter in which random samples of possible state values are generated at the prediction step using an exact moment matching algorithm and then a linear programming based procedure is used in the update step of the state estimation the effectiveness of the new filtering procedure is assessed via a simulation example that deals with a highly nonlinear multivariate time series representing an interest rate process

extrinsic information transfer functions model and erasure channel properties extrinsic information transfer exit charts are a tool for predicting the convergence behavior of iterative processors for a variety of communication problems a model is introduced that applies to decoding problems including the iterative decoding of parallel concatenated turbo codes serially concatenated codes low density parity check ldpc codes and repeat accumulate ra codes exit functions are defined using the model and several properties of such functions are proved for erasure channels one property expresses the area under an exit function in terms of a conditional entropy a useful consequence of this result is that the design of capacity approaching codes reduces to a curve fitting problem for all the aforementioned codes a second property relates the exit function of a code to its helleseth klove levenshtein information functions and thereby to the support weights of its subcodes the relation is via a refinement of information functions called split information functions and via a refinement of support weights called split support weights split information functions are used to prove a third property that relates the exit function of a linear code to the exit function of its dual

a recursive approach to low complexity codes a method is described for constructing long error correcting codes from one or more shorter error correcting codes referred to as subcodes and a bipartite graph a graph is shown which specifies carefully chosen subsets of the digits of the new codes that must be codewords in one of the shorter subcodes lower bounds to the rate and the minimum distance of the new code are derived in terms of the parameters of the graph and the subeodes both the encoders and decoders proposed are shown to take advantage of the code s explicit decomposition into subcodes to decompose and simplify the associated computational processes bounds on the performance of two specific decoding algorithms are established and the asymptotic growth of the complexity of decoding for two types of codes and decoders is analyzed the proposed decoders are able to make effective use of probabilistic information supplied by the channel receiver e g reliability information without greatly increasing the number of computations required it is shown that choosing a transmission order for the digits that is appropriate for the graph and the subcodes can give the code excellent burst error correction abilities the construction principles

different approaches for state filtering in nonlinear systems with uncertain observations this paper addresses the least squares filtering problem for nonlinear systems with uncertain observations when random interruptions in the observation process are modelled by a sequence of independent bernoulli random variables we propose four filtering algorithms which are based on different approximations of the first and second order statistics of a nonlinear transformation of random vectors perturbed by additive and multiplicative noises these algorithms generalize the extended and unscented kalman filters to the case in which there is a positive probability that the observation in each time consists of noise alone and hence does not contain the signal to be estimated the accuracy of the different approximations is also analyzed and the performance of the proposed algorithms is compared in a numerical simulation example

convergence analysis of the extended kalman filter used as an observer for nonlinear deterministic discrete time systems in this paper convergence analysis of the extended kalman filter ekf when used as an observer for nonlinear deterministic discrete time systems is presented based on a new formulation of the first order linearization technique sufficient conditions to ensure local asymptotic convergence are established furthermore it is shown that the design of the arbitrary matrix plays an important role in enlarging the domain of attraction and then improving the convergence of the modified ekf significantly the efficiency of this approach compared to the classical version of the ekf is shown through a nonlinear identification problem as well as a state and parameter estimation of nonlinear discrete time systems

gaussian filters for nonlinear filtering problems we develop and analyze real time and accurate filters for nonlinear filtering problems based on the gaussian distributions we present the systematic formulation of gaussian filters and develop efficient and accurate numerical integration of the optimal filter we also discuss the mixed gaussian filters in which the conditional probability density is approximated by the sum of gaussian distributions a new update rule of weights for gaussian sum filters is proposed our numerical tests demonstrate that new filters significantly improve the extended kalman filter with no additional cost and the new gaussian sum filter has a nearly optimal performance

degree distribution design for ldpc codes a derivative matching approach a deterministic method to design degree distributions for low density parity check codes over the binary erasure channel is proposed this method consists of matching the first and high order derivatives of the extrinsic information transfer exit function of the variable node set to the corresponding derivatives of the inverse exit function of the check node set in order to reduce the gap between the two curves in the exit chart a sufficient condition for a check concentrated distribution to achieve derivative matching up to some order is first obtained and then a deterministic design algorithm enabled by the fourier budan theorem is developed exploiting this sufficient condition a comparison with other deterministic design techniques is also provided revealing the potential of the proposed algorithm

simple capacity achieving ensembles of rateless erasure correcting codes this paper is concerned with a simple binary erasure recovery coding scheme that falls into the family of so called semi random low density parity check sr ldpc codes based on a constrained random scrambling technique the proposed coding scheme is systematic rateless and capacity achieving we provide simulation examples comparing the new scheme with the well known luby transform lt and raptor codes it is shown that the new scheme has advantages in complexity and performance over its counterparts especially in channels with a relatively low erasure rate

bandwidth efficient modulation codes based on nonbinary irregular repeat accumulate codes using nonbinary low density parity check ldpc codes with random coset mapping bennatan and burshtein constructed bandwidth efficient modulation codes with remarkable performance under belief propagation bp decoding however due to the random nature of ldpc codes most of the good ldpc codes found in the literature do not have a simple encoding structure thus the encoding complexity of those ldpc codes can be as high as o n 2 where n is the codeword length to reduce the encoding complexity in this paper nonbinary irregular repeat accumulate ira codes with time varying characteristic and random coset mapping are proposed for bandwidth efficient modulation schemes the time varying characteristic and random coset mapping result in both permutation invariance and symmetry properties respectively in the densities of decoder messages the permutation invariance and symmetry properties of the proposed codes enable the approximations of densities of decoder messages using gaussian distributions under the gaussian approximation extrinsic information transfer exit charts for nonbinary ira codes are developed and several codes of different spectral efficiencies are designed based on exit charts in addition by proper selection of nonuniform signal constellations the constructed codes are inherently capable of obtaining shaping gains even without separate shaping codes simulation results indicate that the proposed codes not only have simple encoding schemes but also have remarkable performance that is even better than that constructed using nonbinary ldpc codes

efficient encoding of low density parity check codes low density parity check ldpc codes can be considered serious competitors to turbo codes in terms of performance and complexity and they are based on a similar philosophy constrained random code ensembles and iterative decoding algorithms we consider the encoding problem for ldpc codes more generally we consider the encoding problem for codes specified by sparse parity check matrices we show how to exploit the sparseness of the parity check matrix to obtain efficient encoders for the 3 6 regular ldpc code for example the complexity of encoding is essentially quadratic in the block length however we show that the associated coefficient can be made quite small so that encoding codes even of length n spl sime 100000 is still quite practical more importantly we show that optimized codes actually admit linear time encoding

design of irregular ldpc codes with optimized performance complexity tradeoff the optimal performance complexity tradeoff for error correcting codes at rates strictly below the shannon limit is a central question in coding theory this paper proposes a numerical approach for the minimization of decoding complexity for long block length irregular low density parity check ldpc codes the proposed design methodology is applicable to any binary input memoryless symmetric channel and any iterative message passing decoding algorithm with a parallel update schedule a key feature of the proposed optimization method is a new complexity measure that incorporates both the number of operations required to carry out a single decoding iteration and the number of iterations required for convergence this paper shows that the proposed complexity measure can be accurately estimated from a density evolution and extrinsic information transfer chart analysis of the code a sufficient condition is presented for convexity of the complexity measure in the variable edge degree distribution when it is not satisfied numerical experiments nevertheless suggest that the local minimum is unique the results presented herein show that when the decoding complexity is constrained the complexity optimized codes significantly outperform threshold optimized codes at long block lengths within the ensemble of irregular codes

least squares νth order polynomial estimation of signals from observations affected by non independent uncertainty abstract the least squares th order polynomial filtering and fixed point smoothing problems of uncertainly observed discrete time signals are considered when the variables describing the uncertainty in the observations are non independent by defining suitable augmented signal and observation vectors the polynomial estimation problem of the signal is reduced to the linear estimation problem of the augmented signal the proposed estimators do not require the knowledge of the state space model generating the signal but only the probability that the signal exists in the observations the 2 2 element of the conditional probability matrices of the sequence describing the uncertainty and the moments up to the 2 th ones of the signal and the observation noise

a new algorithm for latent state estimation in non linear time series models we consider the problem of optimal state estimation for a wide class of non linear time series models a modified sigma point filter is proposed which uses a new procedure for generating sigma points unlike the existing sigma point generation methodologies in engineering where negative probability weights may occur we develop an algorithm capable of generating sample points that always form a valid probability distribution while still allowing the user to sample using a random number generator the effectiveness of the new filtering procedure is assessed through simulation examples

brief paper derivative free estimation methods new results and performance analysis the derivative free nonlinear estimation methods exploiting the stirling s interpolation and the unscented transformation for discrete time nonlinear stochastic systems are treated the divided difference and unscented filters smoothers and predictors based on the methods are introduced in the unified framework the new relations among the first order stirling s interpolation the second order stirling s interpolation and the unscented transformation are derived and their impact on the covariance matrices of the state estimates of the corresponding filters is analysed the theoretical results are illustrated and used for the explanation of the unexpected behaviour of the sigma point gaussian sum filters given as a mixture of the derivative free filters

contact analysis of cable networks by using second order cone programming a method based on mathematical programming is proposed for large deformation and contact analysis of cable networks by explicitly considering these nonsmooth behaviors we formulate the linear complementarity problems over symmetric cones under some practically acceptable assumptions we also present the equivalent second order cone programming socp problems which can be regarded as the minimization problem of total potential energy and complementary energy with the subsidiary constraints on the displacements and contact forces respectively by solving the presented socp problems by using the primal dual interior point method the equilibrium configurations and internal forces of several cable networks are obtained without any assumptions on stress states and contact conditions

low density graph codes that are optimal for binning and coding with side information in this paper we describe and analyze the source and channel coding properties of a class of sparse graphical codes based on compounding a low density generator matrix ldgm code with a low density parity check ldpc code our first pair of theorems establishes that there exist codes from this ensemble with all degrees remaining bounded independently of block length that are simultaneously optimal for both channel coding and source coding with binary data when encoding and decoding are performed optimally more precisely in the context of lossy compression we prove that finite degree constructions can achieve any pair r d on the rate distortion curve of the binary symmetric source in the context of channel coding we prove that the same finite degree codes can achieve any pair c p on the capacity noise curve of the binary symmetric channel bsc next we show that our compound construction has a nested structure that can be exploited to achieve the wyner ziv bound for source coding with side information scsi as well as the gelfand pinsker bound for channel coding with side information ccsi although the results described here are based on optimal encoding and decoding the proposed graphical codes have sparse structure and high girth that renders them well suited to message passing and other efficient decoding procedures

accumulate repeat accumulate codes capacity achieving ensembles of systematic codes for the erasure channel with bounded complexity this paper introduces ensembles of systematic accumulate repeat accumulate ara codes which asymptotically achieve capacity on the binary erasure channel bec with bounded complexity per information bit of encoding and decoding it also introduces symmetry properties which play a central role in the construction of new capacity achieving ensembles for the bec the results here improve on the tradeoff between performance and complexity provided by previous constructions of capacity achieving code ensembles defined on graphs the superiority of ara codes with moderate to large block length is exemplified by computer simulations which compare their performance with those of previously reported capacity achieving ensembles of low density parity check ldpc and irregular repeat accumulate ira codes ara codes also have the advantage of being systematic

parity check density versus performance of binary linear block codes over memoryless symmetric channels we derive lower bounds on the density of parity check matrices of binary linear codes which are used over memoryless binary input output symmetric mbios channels the bounds are expressed in terms of the gap between the rate of these codes for which reliable communications is achievable and the channel capacity they are valid for every sequence of binary linear block codes if there exists a decoding algorithm under which the average bit error probability vanishes for every mbios channel we construct a sequence of ensembles of regular low density parity check ldpc codes so that an upper bound on the asymptotic density of their parity check matrices scales similarly to the lower bound the tightness of the lower bound is demonstrated for the binary erasure channel by analyzing a sequence of ensembles of right regular ldpc codes which was introduced by shokrollahi and which is known to achieve the capacity of this channel under iterative message passing decoding we show that this sequence of ensembles is asymptotically optimal in a sense to be defined in this paper strengthening a result of shokrollahi finally we derive lower bounds on the bit error probability and on the gap to capacity for binary linear block codes which are represented by bipartite graphs and study their performance limitations over mbios channels the latter bounds provide a quantitative measure for the number of cycles of bipartite graphs which represent good error correction codes

new sequences of capacity achieving ldpc code ensembles over the binary erasure channel in this paper new sequences n n of capacity achieving low density parity check ldpc code ensembles over the binary erasure channel bec is introduced these sequences include the existing sequences by shokrollahi et al as a special case for a fixed code rate r in the set of proposed sequences shokrollahi s sequences are superior to the rest of the set in that for any given value of n their threshold is closer to the capacity upper bound 1 r for any given 0 n0 the sequence n n requires a smaller maximum variable node degree as well as a smaller number of constituent variable node degrees to achieve a threshold within neighborhood of the capacity upper bound 1 r moreover it is proven that the check regular subset of the proposed sequences are asymptotically quasi optimal i e their decoding complexity increases only logarithmically with the relative increase of the threshold a stronger result on asymptotic optimality of some of the proposed sequences is also established

tree structure expectation propagation for ldpc decoding over the bec we present the tree structure expectation propagation tree ep algorithm to decode low density parity check ldpc codes over discrete memoryless channels dmcs expectation propagation generalizes belief propagation bp in two ways first it can be used with any exponential family distribution over the cliques in the graph second it can impose additional constraints on the marginal distributions we use this second property to impose pairwise marginal constraints over pairs of variables connected to a check node of the ldpc code s tanner graph thanks to these additional constraints the tree ep marginal estimates for each variable in the graph are more accurate than those provided by bp we also reformulate the tree ep algorithm for the binary erasure channel bec as a peeling type algorithm tep and we show that the algorithm has the same computational complexity as bp and it decodes a higher fraction of errors we describe the tep decoding process by a set of differential equations that represents the expected residual graph evolution as a function of the code parameters the solution of these equations is used to predict the tep decoder performance in both the asymptotic regime and the finite length regimes over the bec while the asymptotic threshold of the tep decoder is the same as the bp decoder for regular and optimized codes we propose a scaling law for finite length ldpc codes which accurately approximates the tep improved performance and facilitates its optimization

capacity achieving codes with bounded graphical complexity and maximum likelihood decoding in this paper the existence of capacity achieving codes for memoryless binary input output symmetric mbios channels under maximum likelihood ml decoding with bounded graphical complexity is investigated graphical complexity of a code is defined as the number of edges in the graphical representation of the code per information bit and is proportional to the decoding complexity per information bit per iteration under iterative decoding irregular repeat accumulate ira codes are studied first utilizing the asymptotic average weight distribution aawd of these codes and invoking divsalar s bound on the binary input additive white gaussian noise biawgn channel it is shown that simple nonsystematic ira ensembles outperform systematic ira and regular low density parity check ldpc ensembles with the same graphical complexity and are at most 0 124 db away from the shannon limit however a conclusive result as to whether these nonsystematic ira codes can really achieve capacity cannot be reached motivated by this inconclusive result a new family of codes is proposed called low density parity check and generator matrix ldpc gm codes which are serially concatenated codes with an outer ldpc code and an inner low density generator matrix ldgm code it is shown that these codes can achieve capacity on any mbios channel using ml decoding and also achieve capacity on any bec using belief propagation bp decoding both with bounded graphical complexity moreover it is shown that under certain conditions these capacity achieving codes have linearly increasing minimum distances and achieve the asymptotic gilbert varshamov bound for all rates

on universal properties of capacity approaching ldpc code ensembles this paper is focused on the derivation of some universal properties of capacity approaching low density parity check ldpc code ensembles whose transmission takes place over memoryless binary input output symmetric mbios channels properties of the degree distributions graphical complexity and the number of fundamental cycles in the bipartite graphs are considered via the derivation of information theoretic bounds these bounds are expressed in terms of the target block bit error probability and the gap in rate to capacity most of the bounds are general for any decoding algorithm and some others are proved under belief propagation bp decoding proving these bounds under a certain decoding algorithm validates them automatically also under any suboptimal decoding algorithm a proper modification of these bounds makes them universal for the set of all mbios channels which exhibit a given capacity bounds on the degree distributions and graphical complexity apply to finite length ldpc codes and to the asymptotic case of an infinite block length the bounds are compared with capacity approaching ldpc code ensembles under bp decoding and they are shown to be informative and are easy to calculate finally some interesting open problems are considered

coding for parallel channels gallager bounds and applications to turbo like codes the transmission of coded communication systems is widely modeled to take place over a set of parallel channels this model is used for transmission over block fading channels rate compatible puncturing of turbo like codes multicarrier signaling multilevel coding etc new upper bounds on the maximum likelihood ml decoding error probability are derived in the parallel channel setting we focus on the generalization of the gallager type bounds and discuss the connections between some versions of these bounds the tightness of these bounds for parallel channels is exemplified for structured ensembles of turbo codes repeat accumulate ra codes and some of their recent variations e g punctured accumulate repeat accumulate codes the bounds on the decoding error probability of an ml decoder are compared to computer simulations of iterative decoding the new bounds show a remarkable improvement over the union bound and some other previously reported bounds for independent parallel channels this improvement is exemplified for relatively short block lengths and it is pronounced when the block length is increased in the asymptotic case where we let the block length tend to infinity inner bounds on the attainable channel regions of modern coding techniques under ml decoding are obtained based solely on the asymptotic growth rates of the average distance spectra of these code ensembles

linear estimation for discrete time systems in the presence of time correlated disturbances and uncertain observations this note considers optimum linear recursive estimation for linear discrete time systems with uncertain observations in cases where state and measurement noises are correlated the different kinds of estimation problems treated include one stage prediction and filtering

bounds on the number of iterations for turbo like ensembles over the binary erasure channel this paper provides simple lower bounds on the number of iterations which is required for successful message passing decoding of some important families of graph based code ensembles including low density parity check ldpc codes and variations of repeat accumulate codes the transmission of the code ensembles is assumed to take place over a binary erasure channel and the bounds refer to the asymptotic case where we let the block length tend to infinity the simplicity of the bounds derived in this paper stems from the fact that they are easily evaluated and are expressed in terms of some basic parameters of the ensemble which include the fraction of degree 2 variable nodes the target bit erasure probability and the gap between the channel capacity and the design rate of the ensemble this paper demonstrates that the number of iterations which is required for successful message passing decoding scales at least like the inverse of the gap in rate to capacity provided that the fraction of degree 2 variable nodes of these turbo like ensembles does not vanish hence the number of iterations becomes unbounded as the gap to capacity vanishes

recursive bayesian estimation using piece wise constant approximations abstract in bayesian estimation the objective is to calculate the complete density function for an unknown quantity conditioned on noisy observations of that quantity this work considers recursive estimation of a nonlinear discrete time system state using successive observations the formal recursion for the density function is easily written but generally there is no closed form solution the numerical solution proposed here is obtained by modifying the recursion and using a simple piece wise constant approximation to the density functions the approach also allows detailed analysis of error propagation through the algorithm yielding a bound on the maximum error growth and a characterization of the situations with potential for large errors the stability of the algorithm is demonstrated by comparing its long term performance to a kalman filter for a linear system with gaussian noises comparison to the point mass algorithm shows improved estimation accuracy and for moderately dense grids faster computation as an example the algorithm is applied to a system identification problem and the results compared to a popular second order minimum variance estimator the optimal estimate derived from the approximate density is seen to be far superior

differential mixed variational inequalities in finite dimensional spaces in this paper a differential vector variational inequality is introduced and studied in finite dimensional euclidean spaces the existence of a caratheodory weak solution for the differential vector variational inequality is presented under some suitable conditions furthermore the upper semicontinuity and the lower semicontinuity of the solution sets for the differential variational inequality are established when both the mapping and the constraint set are perturbed by two different parameters

performance evaluation of ukf based nonlinear filtering the performance of the modified unscented kalman filter ukf for nonlinear stochastic discrete time system with linear measurement equation is investigated it is proved that under certain conditions the estimation error of the ukf remains bounded furthermore it is shown that the design of noise covariance matrix plays an important role in improving the stability of the algorithm error behavior of the ukf is then derived in terms of mean square error mse and the cramer rao lower bound crlb is introduced as a performance measure the modified ukf is found to approach the crlb if the difference between the real noise covariance matrix and the selected one is small enough these results are verified by using monte carlo simulations on two example systems

dissipative control for state saturated discrete time varying systems with randomly occurring nonlinearities and missing measurements in this paper the dissipative control problem is investigated for a class of discrete time varying systems with simultaneous presence of state saturations randomly occurring nonlinearities as well as multiple missing measurements in order to render more practical significance of the system model some bernoulli distributed white sequences with known conditional probabilities are adopted to describe the phenomena of the randomly occurring nonlinearities and the multiple missing measurements the purpose of the addressed problem is to design a time varying output feedback controller such that the dissipativity performance index is guaranteed over a given finite horizon by introducing a free matrix with its infinity norm less than or equal to 1 the system state is bounded by a convex hull so that some sufficient conditions can be obtained in the form of recursive nonlinear matrix inequalities a novel controller design algorithm is then developed to deal with the recursive nonlinear matrix inequalities

posterior cramer rao bounds for discrete time nonlinear filtering a mean square error lower bound for the discrete time nonlinear filtering problem is derived based on the van trees 1968 posterior version of the cramer rao inequality this lower bound is applicable to multidimensional nonlinear possibly non gaussian dynamical systems and is more general than the previous bounds in the literature the case of singular conditional distribution of the one step ahead state vector given the present state is considered the bound is evaluated for three important examples the recursive estimation of slowly varying parameters of an autoregressive process tracking a slowly varying frequency of a single cisoid in noise and tracking parameters of a sinusoidal frequency with sinusoidal phase modulation

formulation and comparison of algorithms for frictional contact problems this paper presents two algorithms for solving the discrete quasi static small displacement linear elastic contact problem with coulomb friction the algorithms are adoptions of a newton method for solving b differentiable equations and an interior point method for solving smooth constrained equations for the application of the former method the contact problem is formulated as a system of b differentiable equations involving the projection operator onto sets with simple structure for the application of the latter method the contact problem is formulated as a system of smooth equations involving complementarity conditions and with the non negativity of variables treated as constraints the two algorithms are numerically tested for two dimensional problems containing up to 100 contact nodes and up to 100 time increments results show that at the present stage of development the newton method is superior both in robustness and speed additional comparison is made with a commercial finite element code

non binary ldpc erasure codes with separated low degree variable nodes the code design of non binary low density parity check codes for the erasure channel under maximum a posteriori decoding is addressed in particular a partially structured ensemble of codes characterized by a careful control of the amount and of the connectivity of the variable nodes of small degrees is proposed the identified ensemble of codes is analyzed in terms of asymptotic thresholds and weight distribution and it is shown that codes from the ensemble provide a remarkable trade off between waterfall performance error floor and decoding complexity as an example the performance curve of a short 256 128 code on the memoryless 16 ary erasure channel tightly approaches the singleton bound at least down to a codeword error rate of 10 9 at low decoding complexity

accumulate repeat accumulate codes in this paper we propose an innovative channel coding scheme called accumulate repeat accumulate ara codes this class of codes can be viewed as serial turbo like codes or as a subclass of low density parity check ldpc codes and they have a projected graph or protograph representation this allows for high speed iterative decoding implementation using belief propagation an ara code can be viewed as precoded repeat accumulate ra code with puncturing or as precoded irregular repeat accumulate ira code where simply an accumulator is chosen as the precoder the amount of performance improvement due to the precoder will be called precoding gain using density evolution on their associated protographs we find some rate 1 2 ara codes with a maximum variable node degree of 5 for which a minimum bit snr as low as 0 08 db from channel capacity threshold is achieved as the block size goes to infinity such a low threshold cannot be achieved by ra ira or unstructured irregular ldpc codes with the same constraint on the maximum variable node degree furthermore by puncturing the inner accumulator we can construct families of higher rate ara codes with thresholds that stay close to their respective channel capacity thresholds uniformly iterative decoding simulation results are provided and compared with turbo codes in addition to iterative decoding analysis we analyzed the performance of ara codes with maximum likelihood ml decoding by obtaining the weight distribution of these codes and through existing tightest bounds we have shown that the ml snr threshold of ara codes also approaches very closely to that of random codes these codes have better interleaving gain than turbo codes

polynomial extended kalman filter this work presents a polynomial version of the well known extended kalman filter ekf for the state estimation of nonlinear discrete time stochastic systems the proposed filter denoted polynomial ekf pekf consists in the application of the optimal polynomial filter of a chosen degree spl mu to the carleman approximation of a nonlinear system when spl mu 1 the pekf algorithm coincides with the standard ekf for the filter implementation the moments of the state and output noises up to order 2 spl mu are required numerical simulations compare the performances of the pekf with those of some other existing filters showing significant improvements

successive maximization for systematic design of universally capacity approaching rate compatible sequences of ldpc code ensembles over binary input output symmetric memoryless channels a systematic construction of capacity achieving low density parity check ldpc code ensemble sequences over the binary erasure channel bec has been proposed by saeedi et al based on a method here referred to as successive maximization sm in sm the fraction of degree i nodes are successively maximized starting from i 2 with the constraint that the ensemble remains convergent over the channel in this paper we propose sm to design universally capacity approaching rate compatible ldpc code ensemble sequences over the general class of binary input output symmetric memoryless biosm channels this is achieved by first generalizing the sm method to other biosm channels to design a sequence of capacity approaching ensembles called the parent sequence the sm principle is then applied to each ensemble within the parent sequence this time to design rate compatible puncturing schemes as part of our results we extend the stability condition which was previously derived for degree 2 variable nodes to other variable node degrees as well as to the case of rate compatible codes consequently we prove that using the sm principle one is able to design universally capacity achieving rate compatible ldpc code ensemble sequences over the bec unlike the previous results in the literature the proposed sm approach is naturally extendable to other biosm channels the performance of the rate compatible schemes designed based on our method is comparable to those designed by optimization

higher order sigma point filter a new heuristic for nonlinear time series filtering in this paper we present some new results related to the higher order sigma point filter hospof introduced in 1 for filtering nonlinear multivariate time series this paper makes two distinct contributions firstly we propose a new algorithm to generate a discrete statistical distribution to match exactly a specified mean vector a specified covariance matrix the average of specified marginal skewness and the average of specified marginal kurtosis both the sigma points and the probability weights are given in closed form and no numerical optimization is required combined with hospof this random sigma point generation algorithm provides a new method for generating proposal density which propagates the information about higher order moments a numerical example on nonlinear multivariate time series involving real financial market data demonstrates the utility of this new algorithm secondly we show that hospof achieves a higher order estimation accuracy as compared to ukf for smooth scalar nonlinearities we believe that this new filter provides a new and powerful alternative heuristic to existing filtering algorithms and is useful especially in econometrics and in engineering applications

a new method for the nonlinear transformation of means and covariances in filters and estimators this paper describes a new approach for generalizing the kalman filter to nonlinear systems a set of samples are used to parametrize the mean and covariance of a not necessarily gaussian probability distribution the method yields a filter that is more accurate than an extended kalman filter ekf and easier to implement than an ekf or a gauss second order filter its effectiveness is demonstrated using an example

a higher order correlation unscented kalman filter abstract many nonlinear extensions of the kalman filter e g the extended and the unscented kalman filter reduce the state densities to gaussian densities this approximation gives sufficient results in many cases however these filters only estimate states that are correlated with the observation therefore sequential estimation of diffusion parameters e g volatility which are not correlated with the observations is not possible while other filters overcome this problem with simulations we extend the measurement update of the gaussian two moment filters by a higher order correlation measurement update we explicitly state formulas for a higher order unscented kalman filter within a continuous discrete state space we demonstrate the filter in the context of parameter estimation of an ornstein uhlenbeck process

an interval kalman filtering with minimal conservatism abstract the interval kalman filtering ikf can handle parametric interval uncertainties of the system matrices and it computes the lower and upper boundaries of the estimated states in this paper we propose an alternative form of interval kalman filtering to reduce the conservatism inherent to the existing interval kalman filtering first we address why the existing interval kalman filtering scheme induces conservatism in the boundary estimation then to remove the conservatism we derive noise covariance matrices taking into account of interval uncertainties as well as process and measurement noises following the typical derivation process of the standard kalman filtering a new recursive form of interval kalman filtering is derived through numerical simulations the superiority of the new algorithm over existing ikf is illustrated

a tutorial on particle filters for online nonlinear non gaussian bayesian tracking increasingly for many application areas it is becoming important to include elements of nonlinearity and non gaussianity in order to model accurately the underlying dynamics of a physical system moreover it is typically crucial to process data on line as it arrives both from the point of view of storage costs as well as for rapid adaptation to changing signal characteristics in this paper we review both optimal and suboptimal bayesian algorithms for nonlinear non gaussian tracking problems with a focus on particle filters particle filters are sequential monte carlo methods based on point mass or particle representations of probability densities which can be applied to any state space model and which generalize the traditional kalman filtering methods several variants of the particle filter such as sir asir and rpf are introduced within a generic framework of the sequential importance sampling sis algorithm these are discussed and compared with the standard ekf through an illustrative example

recursive filtering with random parameter matrices multiple fading measurements and correlated noises this paper is concerned with the recursive filtering problem for a class of discrete time nonlinear stochastic systems with random parameter matrices multiple fading measurements and correlated noises the phenomenon of measurement fading occurs in a random way and the fading probability for each sensor is governed by an individual random variable obeying a certain probability distribution over the known interval b k c k such a probability distribution could be any commonly used discrete distribution over the interval b k c k that covers the bernoulli distribution as a special case the process noise and the measurement noise are one step autocorrelated respectively the process noise and the measurement noise are two step cross correlated the purpose of the addressed filtering problem is to design an unbiased and recursive filter for the random parameter matrices stochastic nonlinearity and multiple fading measurements as well as correlated noises intensive stochastic analysis is carried out to obtain the filter gain characterized by the solution to a recursive matrix equation the proposed scheme is of a form suitable for recursive computation in online applications a simulation example is given to illustrate the effectiveness of the proposed filter design scheme

an extended kalman filter frequency tracker for high noise environments the problem of constructing a frequency tracker for weak narrowband signals with slowly varying frequency is considered an extended kalman filter is proposed that uses prior knowledge of the nature of the signal to overcome the difficulties presented by the inherent nonlinearity of the problem and the very low signal to noise ratios

nonlinear estimation applying an unscented transformation in systems with correlated uncertain observations an approximation to the least squares filter is proposed for discrete signals whose evolution is governed by nonlinear functions when the estimation is based on nonlinear observations with additive noise which can consist only of random noise this uncertainty in the observation process is modelled by bernoulli random variables which are correlated at consecutive time instants and are otherwise independent the proposed recursive approximation is based on the unscented principle successive applications of the unscented transformation to a suitable augmented state vector enable us to approximate the one stage state and observation predictors from the state filter at the previous time instant the performance of the proposed algorithm is compared with that of an extended algorithm in a numerical simulation example

stochastic stability of the discrete time extended kalman filter the authors analyze the error behavior for the discrete time extended kalman filter for general nonlinear systems in a stochastic framework in particular it is shown that the estimation error remains bounded if the system satisfies the nonlinear observability rank condition and the initial estimation error as well as the disturbing noise terms are small enough this result is verified by numerical simulations for an example system

an improved sphere packing bound for finite length codes over symmetric memoryless channels this paper derives an improved sphere packing isp bound for finite length error correcting codes whose transmission takes place over symmetric memoryless channels and the codes are decoded with an arbitrary list decoder we first review classical results i e the 1959 sphere packing sp59 bound of shannon for the gaussian channel and the 1967 sphere packing sp67 bound of shannon et al for discrete memoryless channels an improvement on the sp67 bound as suggested by valembois and fossorier is also discussed these concepts are used for the derivation of a new lower bound on the error probability of list decoding referred to as the isp bound which is uniformly tighter than the sp67 bound and its improved version the isp bound is applicable to symmetric memoryless channels and some of its applications are presented its tightness under maximum likelihood ml decoding is studied by comparing the isp bound to previously reported upper and lower bounds on the ml decoding error probability and also to computer simulations of iteratively decoded turbo like codes this paper also presents a technique which performs the entire calculation of the sp59 bound in the logarithmic domain thus facilitating the exact calculation of this bound for moderate to large block lengths without the need for the asymptotic approximations provided by shannon

extended and unscented filtering algorithms using one step randomly delayed observations in this paper the least squares filtering problem is investigated for a class of nonlinear discrete time stochastic systems using observations with stochastic delays contaminated by additive white noise the delay is considered to be random and modelled by a binary white noise with values of zero or one these values indicate that the measurement arrives on time or that it is delayed by one sampling time using two different approximations of the first and second order statistics of a nonlinear transformation of a random vector we propose two filtering algorithms the first is based on linear approximations of the system equations and the second on approximations using the scaled unscented transformation these algorithms generalize the extended and unscented kalman filters to the case in which the arrival of measurements can be one step delayed and hence the measurement available to estimate the state may not be up to date the accuracy of the different approximations is also analyzed and the performance of the proposed algorithms is compared in a numerical simulation example

sparse graph codes for quantum error correction sparse graph codes appropriate for use in quantum error correction are presented quantum error correcting codes based on sparse graphs are of interest for three reasons first the best codes currently known for classical channels are based on sparse graphs second sparse graph codes keep the number of quantum interactions associated with the quantum error correction process small a constant number per quantum bit independent of the block length third sparse graph codes often offer great flexibility with respect to block length and rate we believe some of the codes we present are unsurpassed by previously published quantum error correcting codes

convergence of a time stepping scheme for rigid body dynamics and resolution of painleve s problem this paper gives convergence theory for a new implicit time stepping scheme for general rigid body dynamics with coulomb friction and purely inelastic collisions and shocks an important consequence of this work is the proof of existence of solutions of rigid body problems which include the famous counterexamples of painleve the mathematical basis for this work is the formulation of the rigid body problem in terms of measure differential inclusions of moreau and monteiro marques the implicit time stepping method is based on complementarity problems and is essentially a particular case of the algorithm described in anitescu potra 2 which in turn is based on the formulation in stewart trinkle 47

linear complementarity systems we introduce a new class of dynamical systems called linear complementarity systems the time evolution of these systems consists of a series of continuous phases separated by events which cause a change in dynamics and possibly a jump in the state vector the occurrence of events is governed by certain inequalities similar to those appearing in the linear complementarity problem of mathematical programming the framework we describe is suitable for certain situations in which both differential equations and inequalities play a role for instance in mechanics electrical networks piecewise linear systems and dynamic optimization we present a precise definition of the solution concept of linear complementarity systems and give sufficient conditions for existence and uniqueness of solutions

a time stepping complementarity approach for frictionless systems of rigid bodies this paper presents a time stepping complementarity approach for computing a numerical trajectory of a system of rigid bodies under frictionless contact such a system is formulated as a time dependent ordinary differential complementarity problem dcp which consists of an ordinary differential equation ode coupled with a complementarity condition the phenomenon of impact plays an essential role when modeling a mechanical system of this type within the time stepping scheme which uses a high order ode discretization we include an impact detection routine and an impact law governing the behavior of the system over the duration of an impact we report computational results for the application of the overall numerical scheme to computing the solution trajectories of several realistic mechanical systems

a strong tracking extended kalman observer for nonlinear discrete time systems the authors show how the extended kalman filter used as an observer for nonlinear discrete time systems or extended kalman observer eko becomes a useful state estimator when the arbitrary matrices namely r sub k and q sub k are adequately chosen as a first step we use the linearization technique given by boutayed et al 1997 which consists of introducing unknown diagonal matrices to take the approximation errors into account it is shown that the decreasing lyapunov function condition leads to a linear matrix inequality lmi problem which points out the connection between a good convergence behavior of the eko and the instrumental matrices r sub k and q sub k in order to satisfy the obtained lmi a particular design of q sub k is given high performances of the proposed technique are shown through numerical examples under the worst conditions

capacity achieving ensembles for the binary erasure channel with bounded complexity we present two sequences of ensembles of nonsystematic irregular repeat accumulate ira codes which asymptotically as their block length tends to infinity achieve capacity on the binary erasure channel bec with bounded complexity per information bit this is in contrast to all previous constructions of capacity achieving sequences of ensembles whose complexity grows at least like the log of the inverse of the gap in rate to capacity the new bounded complexity result is achieved by puncturing bits and allowing in this way a sufficient number of state nodes in the tanner graph representing the codes we derive an information theoretic lower bound on the decoding complexity of randomly punctured codes on graphs the bound holds for every memoryless binary input output symmetric mbios channel and is refined for the binary erasure channel

the extended kalman filter as an exponential observer for nonlinear systems we analyze the behavior of the extended kalman filter as a state estimator for nonlinear deterministic systems using the direct method of lyapunov we prove that under certain conditions the extended kalman filter is an exponential observer i e the dynamics of the estimation error is exponentially stable furthermore we discuss a generalization of the kalman filter with exponential data weighting to nonlinear systems

chandrasekhar type filter for a wide sense stationary signal from uncertain observations using covariance information in this paper the least mean squared error linear filtering problem of a wide sense stationary signal from uncertain observations perturbed by a white noise is approached by means of a chandrasekhar type recursive algorithm in comparison with a riccati type algorithm the proposed algorithm is more advantageous from a computational point of view since it reduces the number of difference equations contained in it and consequently the computation time the algorithm is derived by using covariance information without requiring that the state space model of the signal is completely known