design of capacity approaching irregular low density parity check codes we design low density parity check ldpc codes that perform at rates extremely close to the shannon capacity the codes are built from highly irregular bipartite graphs with carefully chosen degree patterns on both sides our theoretical analysis of the codes is based on the work of richardson and urbanke see ibid vol 47 no 2 p 599 618 2000 assuming that the underlying communication channel is symmetric we prove that the probability densities at the message nodes of the graph possess a certain symmetry using this symmetry property we then show that under the assumption of no cycles the message densities always converge as the number of iterations tends to infinity furthermore we prove a stability condition which implies an upper bound on the fraction of errors that a belief propagation decoder can correct when applied to a code induced from a bipartite graph with a given degree distribution our codes are found by optimizing the degree structure of the underlying graphs we develop several strategies to perform this optimization we also present some simulation results for the codes found which show that the performance of the codes is very close to the asymptotic theoretical bounds

optimal estimation of a general regression function let e be a convex subset of rd and for each 0 e e let f 0 dt be a probability on the line for any vector an an an2 ann where anl e e let xn1 xnn be independent observations the distribution of xn being f an dt the main results give a method of estimating the unknown regression function an based on a minimum distance recipe under regularity assumptions the proposed estimators are shown in an appropriate framework to be asymptotically normal locally asymptotically minimax and robust the abstract results are illustrated by application to the linear model and to exponential response models in general nothing at all is assumed about the form of the regression function accordingly this forces the limiting normal distributions of the proposed estimators to be located on infinite dimensional linear spaces

mixed h2 h control of markovian jump time delay systems with uncertain transition probabilities this study addresses the robust stability problem of markovian jump time delay systems with mixed h2 and h control and uncertain transition probabilities in the discrete time domain the transition probabilities are considered to be uncertain but bounded by proposing a new lyapunov functional and applying the free weighting matrix technique we design the mode dependent mixed h2 h controller such that the resultant closed loop systems possess stochastic stability and are prescribed with h performance indices these results generalize several results reported in previous literature which consider the markovian transition probabilities to be known a priori or partially unknown transition probabilities numerical examples and a practical motion control system are presented to illustrate the effectiveness of this technique

contraction conditions for average and α discount optimality in countable state markov games with unbounded rewards the goal of this paper is to provide a theory of n person markov games with unbounded cost for a countable state space and compact action spaces we investigate both the finite and infinite horizon problems for the latter we consider the discounted cost as well as the expected average cost we present conditions for the infinite horizon problems for which equilibrium policies exist for all players within the stationary policies and show that the costs in equilibrium policies exist for all players within the stationary policies and show that the costs in equilibrium satisfy the optimality equations similar results are obtained for the finite horizon costs for which equilibrium policies are shown to exist for all players within the markov policies as special case of n person games we investigate the zero sum 2 players game for which we establish the convergence of the value iteration algorithm we conclude by studying an application of a zero sum markov game in a queueing model

n person nonzero sum games for continuous time jump processes with varying discount factors this paper is concerned with the first passage discounted payoff criterion for continuous time n person nonzero sum stochastic games in countable states and borel action spaces where the discount factor is nonconstant for the game with unbounded reward functions and transition rates the optimality is over the set of all randomized history dependent policies after showing the uniqueness of the solution to the shapley equation we give some suitable conditions imposed on the primitive data for the existence of nash equilibria then a financial system is introduced to illustrate the applications of the main result here

optimal power control for ldpc codes in block fading channels we study the error probability of ldpc codes in delay limited block fading channels with channel state information csi at the transmitter and the receiver we derive the optimal power allocation algorithms for ldpc codes with specific degree distributions using multi edge type density evolution error boundaries the resulting performance approaches the outage probability for a number of power constraints furthermore we adapt the algorithm for finite length codes and show that the proposed algorithm enables gains larger than 10 db over uniform power allocation the method is valid for general possibly correlated fading distributions this represents the first analysis of specific ldpc codes over block fading channels with full csi

robust estimation via minimum distance methods given a fixed parametric family p it is desired to estimate however due to contaminations of various sorts the data actually collected by the statistician follow a distribution that is close to but possibly distinct from thep s it is proved that under these conditions and in an appropriate asymptotic framework the minimum distance estimators of the cramer von mises type are robust specification of a cramer von mises weight functionh defines a notion of distance each such choice ofh then delineates the kind of contamination possible and leads to an estimator which defends optimally against it when the theory is specialized to location models various choices ofh lead to estimators asymptotically equivalent to such familiar ones as trimmed mean median hodges lehmann estimator and so forth the framework developed herein provides some guidelines for choosing among the possible estimators and suggests that the standard cramer von mises estimator of location is probably as good a robust estimator as any

a generalization of the product limit estimator with an application to censored regression the product limit estimator ple and weighted empirical processes are two important ingredients of almost any censored regression analysis a link between them is provided by the generalized ples introduced in this paper these generalized ples are the product limit integrals of the empirical cumulative hazard function estimators in which weighted empirical processes are used to replace the standard empirical processes the weak convergence and some large sample approximations of the generalized ples are established as an application these generalized ples are used to define some minimum distance estimators which are shown to be asymptotically normal these estimators are qualitatively robust in some submodels an optimal choice of the weight matrix is the covariate matrix and some of these estimators are quite efficient at a few common survival distributions to implement these estimators some computational aspects are discussed and an algorithm is given from a real data example and some preliminary simulation results these estimators seem to be very competitive to and more robust than some more traditional estimators such as the buckley james estimator

low density graph codes for coded cooperation on slow fading relay channels we study low density parity check ldpc codes with iterative decoding on block fading bf relay channels we consider two users that employ coded cooperation a variant of decode and forward with a smaller outage probability than the latter an outage probability analysis for discrete constellations shows that full diversity can be achieved only when the coding rate does not exceed a maximum value that depends on the level of cooperation we derive a new code structure by extending the previously published full diversity root ldpc code designed for the bf point to point channel to exhibit a rate compatibility property which is necessary for coded cooperation we estimate the asymptotic performance through a new density evolution analysis and the word error rate performance is determined for finite length codes we show that our code construction exhibits near outage limit performance for all block lengths and for a range of coding rates up to 0 5 which is the highest possible coding rate for two cooperating users

first passage optimality for continuous time markov decision processes with varying discount factors and history dependent policies this paper is an attempt to study the first passage optimality criterion for continuous time markov decision processes with state dependent discount factors and history dependent policies the state space is denumerable the action space is a borel space and the transition and reward rates are unbounded under suitable conditions we show the existence of a deterministic stationary optimal policy establish the bellman optimality equation to which the value function is the unique solution and give the value and policy iteration algorithms for solving at least approximating the value function and an optimal policy furthermore we give examples about reliability and controlled birth processes with killing to illustrate the potential applications of the results obtained here and also to show the difference between the main results in this paper and those in the previous literature

edge coloring and stopping sets analysis in product codes with mds components we consider non binary product codes with mds components and their iterative row column algebraic decoding on the erasure channel both independent and block erasures are considered in this paper a compact graph representation is introduced on which we define double diversity edge colorings via the rootcheck concept an upper bound of the number of decoding iterations is given as a function of the graph size and the color palette size m then we propose a differential evolution edge coloring algorithm that produces colorings with a large population of minimal rootcheck order symbols the complexity of this algorithm per iteration is o m aleph for a given differential evolution parameter aleph where m aleph itself is small with respect to the huge cardinality of the coloring ensemble stopping sets of a product code are defined in the context of mds components and a relationship is established with the graph representation a full characterization of these stopping sets is given up to a size d 1 2 where d is the minimum hamming distance of the mds component code the performance of mds based product codes with and without double diversity coloring is analyzed in presence of both the block and the independent erasures in the latter case ml and iterative decoding are proven to coincide at small channel erasure probability furthermore numerical results show excellent performance in presence of unequal erasure probability due to double diversity colorings

coded modulation in the block fading channel coding theorems and code construction we consider coded modulation schemes for the block fading channel in the setting where a codeword spans a finite number n of fading degrees of freedom we show that coded modulations of rate r bit per complex dimension over a finite signal set spl chi spl sube spl copf of size 2 sup m achieve the optimal rate diversity tradeoff given by the singleton bound spl delta n m r 1 spl lfloor n 1 r m spl rfloor for r spl isin 0 m spl rfloor furthermore we show also that the popular bit interleaved coded modulation achieves the same optimal rate diversity tradeoff we present a novel coded modulation construction based on blockwise concatenation that systematically yields singleton bound achieving turbo like codes defined over an arbitrary signal set spl chi spl sub spl copf the proposed blockwise concatenation significantly outperforms conventional serial and parallel turbo codes in the block fading channel we analyze the ensemble average performance under maximum likelihood ml decoding of the proposed codes by means of upper bounds and tight approximations we show that differently from the additive white gaussian noise awgn and fully interleaved fading cases belief propagation iterative decoding performs very close to ml on the block fading channel for any signal to noise ratio snr and even for relatively short block lengths we also show that at constant decoding complexity per information bit the proposed codes perform close to the information outage probability for any block length while standard block codes e g obtained by trellis termination of convolutional codes have a gap from outage that increases with the block length this is a different and more subtle manifestation of the so called interleaving gain of turbo codes

discounted continuous time markov decision processes with constraints unbounded transition and loss rates this paper deals with denumerable continuous time markov decision processes mdp with constraints the optimality criterion to be minimized is expected discounted loss while several constraints of the same type are imposed the transition rates may be unbounded the loss rates are allowed to be unbounded as well from above and from below and the policies may be history dependent and randomized based on kolmogorov s forward equation and dynkin s formula we remind the reader about the bellman equation introduce and study occupation measures reformulate the optimization problem as a primary linear program provide the form of optimal policies for a constrained optimization problem here and establish the duality between the convex analytic approach and dynamic programming finally a series of examples is given to illustrate all of our results

minimum distance estimators for location and goodness of fit abstract a weighted cramer von mises distance between the empirical distribution function and the assumed model f0 x is minimized to produce estimators n that are asymptotically normal if the weight function is taken proportional to ln f 0 f 0 then n is asymptotically efficient and the minimized distance has the appropriate loss of one degree of freedom special attention is focused on the limiting distribution of this latter goodness of fit statistic in both null and alternative situations

design of ldpc codes based on multipath emd strategies for progressive edge growth low density parity check ldpc codes are capable of achieving excellent performance and provide a useful alternative for the high performance applications however at medium to high signal to noise ratios an observable error floor arises from the loss of independence of messages passed under iterative graph based decoding in this paper the error floor performance of the short block length codes is improved by the use of a novel candidate selection metric in code graph construction the proposed multipath extrinsic message degree emd approach avoids harmful structures in the graph by evaluating certain properties of the cycles introduced in each edge placement we present multipath emd based designs for several structured ldpc codes including quasi cyclic and the irregular repeat accumulate codes in addition an extended class of the diversity achieving codes on the challenging block fading channel is proposed and considered with the multipath emd design this combined approach is demonstrated to provide the gains in decoder convergence and error rate performance a simulation study evaluates the performance of the proposed and existing state of the art methods

a quadraticity limit theorem useful in linear models this paper proves an asymptotic uniform quadraticity of certain statistics based on randomly weighted residual empirical processes under fairly general conditions this result is useful in many statistical inference problems pertaining to linear models including the correlation and autoregression models some applications to the goodness of fit tests and minimum distance estimation in linear models are given

robust finite time estimation of markovian jumping systems with bounded transition probabilities this paper studies the finite time state estimation and h filter design problem for a class of uncertain markovian jumping systems mjss with bounded transition probabilities based on the selected lyapunov krasovskii functional the finite time h filter is constructed to derive a sufficient condition such that the filtering error dynamic mjss are finite time bounded and satisfies a prescribed level of h disturbance attenuation in a finite time interval then in terms of linear matrix inequalities lmis techniques the sufficient condition on the existence of finite time h filter is presented and proved the filter matrices can be solved directly by using the existing lmis optimization techniques finally two numerical examples are given to illustrate the effectiveness of the proposed design approach

semiparametric inference in the proportional odds regression model abstract for fitting the proportional odds regression model with right censored survival times we introduce some weighted empirical odds functions these functions are solutions of some self consistency equations and have a nice martingale representation from these functions several classes of new regression estimators such as the pseudo maximum likelihood estimator martingale residual based estimators and minimum distance estimators are derived these estimators have desirable properties such as easy computation asymptotic normality via a martingale analysis and reliable asymptotic covariance estimation in closed form extensive numerical studies show that the minimum l 2 distance estimators have very good finite sample behaviors compared to existing methods results of some simulation studies and applications to a real dataset are given the weighted odds function based approach also provides inference on the baseline odds function and some measures for lack of fit analysis

on the first passage g mean variance optimality for discounted continuous time markov decision processes this paper considers the discounted continuous time markov decision processes mdps in borel spaces and with unbounded transition rates the discount factors are allowed to depend on states and actions main attention is concentrated on the set f g of stationary policies attaining a given mean performance g up to the first passage of the continuous time mdp to an arbitrarily fixed target set under suitable conditions we prove the existence of a g mean variance optimal policy that minimizes the first passage variance over the set f g using a transformation technique and also give the value iteration and policy iteration algorithms for computing the g variance value function and a g mean variance optimal policy respectively two examples are analytically solved to demonstrate the application of our results

zero sum stochastic games in borel spaces average payoff criteria this paper is concerned with two person zero sum dynamic stochastic games in borel spaces with possibly unbounded payoff function and several average or ergodic payoff criteria we give conditions under which the long run expected average payoff criterion the sample path average criterion the existence of solutions to the average payoff shapley equations and a certain martingale condition are all equivalent

algorithms for joint phase estimation and decoding for mimo systems in the presence of phase noise and quasi static fading channels in this paper we derive the maximum a posteriori map symbol detector for a multiple input multiple output system in the presence of wiener phase noise due to noisy local oscillators and quasi static fading channels as in single antenna systems the computation of the optimum receiver is an analytically intractable problem and is unimplementable in practice in this purview we propose three suboptimal low complexity algorithms for approximately implementing the map symbol detector which involve joint phase noise estimation and data detection our first algorithm is obtained by means of the sum product algorithm where we use the multivariate tikhonov canonical distribution approach in our next algorithm we derive an approximate map symbol detector based on the smoother detector framework wherein the detector is properly designed by incorporating the phase noise statistics from the smoother the third algorithm is derived based on the variational bayesian framework by simulations we evaluate the performance of the proposed algorithms for both uncoded and coded data transmissions and observe that the proposed techniques significantly outperform the other important algorithms from prior works which are considered herein

finite length analysis of low density parity check codes on the binary erasure channel in this paper we are concerned with the finite length analysis of low density parity check ldpc codes when used over the binary erasure channel bec the main result is an expression for the exact average bit and block erasure probability for a given regular ensemble of ldpc codes when decoded iteratively we also give expressions for upper bounds on the average bit and block erasure probability for regular ldpc ensembles and the standard random ensemble under maximum likelihood ml decoding finally we present what we consider to be the most important open problems in this area

censored median regression using weighted empirical survival and hazard functions abstract for median regression models that regress the median of the survival time or a transform thereof on the covariates some semi parametric estimators that include the intercept component are introduced when the survival time may be censored these new median regression estimators do not require estimating the censoring distributions they can be viewed as an extension of the sample median to the censored regression model these estimators are based on some weighted empirical survival and hazard functions and are shown to be consistent and asymptotically normal they performed very well in various numerical studies the proposed procedures are illustrated in some real data examples

common information based markov perfect equilibria for stochastic games with asymmetric information finite games a model of stochastic games where multiple controllers jointly control the evolution of the state of a dynamic system but have access to different information about the state and action processes is considered the asymmetry of information among the controllers makes it difficult to compute or characterize nash equilibria using the common information among the controllers the game with asymmetric information is used to construct another game with symmetric information such that the equilibria of the new game can be transformed to equilibria of the original game further under certain conditions a markov state is identified for the new symmetric information game and its markov perfect equilibria are characterized this characterization provides a backward induction algorithm to find nash equilibria of the original game with asymmetric information in pure or behavioral strategies each step of this algorithm involves finding bayesian nash equilibria of a one stage bayesian game the class of nash equilibria of the original game that can be characterized in this backward manner are named common information based markov perfect equilibria

nearest neighbor decoding in mimo block fading channels with imperfect csir this paper studies communication outages in multiple input multiple output mimo block fading channels with imperfect channel state information at the receiver csir using mismatched decoding error exponents we prove the achievability of the generalized outage probability the probability that the generalized mutual information gmi is less than the data rate and show that this probability is the fundamental limit for independent and identically distributed i i d codebooks then using nearest neighbor decoding we study the generalized outage probability in the high signal to noise ratio snr regime for random codes with gaussian and discrete signal constellations in particular we study the snr exponent which is defined as the high snr slope of the error probability curve on a logarithmic logarithmic scale we show that the maximum achievable snr exponent of the imperfect csir case is given by the snr exponent of the perfect csir case times the minimum of one and the channel estimation error diversity random codes with gaussian constellations achieve the optimal snr exponent with finite block length as long as the block length is larger than a threshold on the other hand random codes with discrete constellations achieve the optimal snr exponent with block length growing with the logarithm of the snr the results hold for many fading distributions including rayleigh rician nakagami nakagami and weibull as well as for optical wireless scintillation distributions such as lognormal rice and gamma gamma

a general formula for channel capacity a formula for the capacity of arbitrary single user channels without feedback not necessarily information stable stationary etc is proved capacity is shown to equal the supremum over all input processes of the input output inf information rate defined as the liminf in probability of the normalized information density the key to this result is a new converse approach based on a simple new lower bound on the error probability of m ary hypothesis tests among equiprobable hypotheses a necessary and sufficient condition for the validity of the strong converse is given as well as general expressions for spl epsiv capacity

coding in the block erasure channel in this correspondence we study an m ary block erasure channel with b blocks where with probability epsi a block of l coded symbols is erased the behavior of the error probability of coded systems over such channels is studied and we show that if the code is diversity wise maximum distance separable its word error probability is equal to the outage probability which admits a very simple expression this correspondence is intended to complement the error probability analysis in previous work by lapidoth and shed some light on the design of coding schemes for nonergodic channels

explicit causal recursive estimators for continuous time bivariate markov chains a bivariate markov chain comprises a pair of random processes which are jointly markov in this paper both processes are assumed to be continuous time with finite state space one of the two processes is observable while the other is an underlying process which affects the statistical properties of the observable process neither the observable nor the underlying process is required to be a markov chain examples of bivariate markov chains include the markov modulated markov process mmmp the markov modulated poisson process mmpp and the batch markovian arrival process bmap we develop explicit causal recursions for estimating the number of jumps from one state to another and the total sojourn time in each state of a general bivariate markov chain explicit causal recursions of these statistics were previously developed for the mmmp and the mmpp using the transformation of measure approach we argue that this approach cannot be extended to a general bivariate markov chain instead we modify the approach developed by ryden for noncausal estimation of the same statistics of an mmpp and use the state augmentation approach of zeitouni and dembo and a matrix recursion from stiller and radons to derive the causal recursions the new recursions do not require any numerical integration or sampling scheme of the continuous time bivariate markov chain

on the lqg game with nonclassical information pattern using a direct solution method a two sided simultaneous optimization technique is presented for the two player linear quadratic gaussian multistage game this direct solution method naturally decomposes the solution into separate deterministic and stochastic terms which provides insight into the optimal control strategies we use the optimal governing equations to derive a compact expression for the optimal performance index value we prove that this two sided linear solution is indeed optimal out of all possible strategies linear and nonlinear by way of a saddle point proof in addition we provide some numerical results to show how system noises affect the optimal control strategies and optimal performance index value

low density parity check codes for nonergodic block fading channels we design powerful low density parity check ldpc codes with iterative decoding for the block fading channel we first study the case of maximum likelihood decoding and show that the design criterion is rather straightforward since optimal constructions for maximum likelihood decoding do not perform well under iterative decoding we introduce a new family of full diversity ldpc codes that exhibit near outage limit performance under iterative decoding for all block lengths this family competes favorably with multiplexed parallel turbo codes for nonergodic channels

evaluating the performance of convolutional codes over block fading channels this correspondence considers union upper bound techniques for error control codes with limited interleaving over block fading rician channels a modified bounding technique is presented that relies on limiting the conditional union bound before averaging over the fading process this technique although analytically not very attractive provides tight and hence useful numerical results

subgame perfect equilibria for stochastic games for an n person stochastic game with borel state space s and compact metric action sets a1 a2 an sufficient conditions are given for the existence of subgame perfect equilibria one result is that such equilibria exist if the law of motion q s a is for fixed s continuous in a a1 a2 an for the total variation norm and the payoff functions f1 f2 fn are bounded borel measurable functions of the sequence of states s1 s2 sn and in addition are continuous when sn is given the product of discrete topologies on s

h fuzzy control for nonlinear time delay singular markovian jump systems with partly unknown transition rates abstract this paper investigates the problem of h fuzzy control for a class of nonlinear time delay singular markovian jump systems with partly unknown transition rates this class of systems under consideration is described by takagi sugeno t s fuzzy model the goal of the paper is to design fuzzy state feedback controllers such that systems with partly unknown transition rates are not only regular impulse free and stochastically stable but also satisfy a prescribed h performance for all delays no larger than a given upper bound in terms of linear matrix inequalities and systems with completely known transition rates can be viewed as a special case of the one we consider here finally numerical examples are given to illustrate the merit and usability of the approach proposed in this paper

state estimation and sliding mode control for semi markovian jump systems with mismatched uncertainties this paper is concerned with the state estimation and sliding mode control problems for phase type semi markovian jump systems using a supplementary variable technique and a plant transformation a finite phase type semi markov process has been transformed into a finite markov chain which is called its associated markov chain as a result phase type semi markovian jump systems can be equivalently expressed as its associated markovian jump systems a sliding surface is then constructed and a sliding mode controller is synthesized to ensure that the associated markovian jump systems satisfy the reaching condition moreover an observer based sliding mode control problem is investigated sufficient conditions are established for the solvability of the desired observer two numerical examples are presented to show the effectiveness of the proposed design techniques

filtering design for two dimensional markovian jump systems with state delays and deficient mode information this paper is concerned with the problem of h filtering for a class of two dimensional markovian jump linear systems described by the fornasini marchesini local state space model the systems under consideration are subject to state delays and deficient mode information in the markov chain the description of deficient mode information is comprehensive that simultaneously includes the exactly known partially unknown and uncertain transition probabilities by invoking the properties of the transition probability matrix together with the convexification of uncertain domains a new h performance analysis criterion for the filtering error system is firstly derived then via some matrix inequality linearisation procedures two approaches for the filter synthesis are proposed it is shown that both the full order and reduced order filters can be constructed by solving a set of linear matrix inequalities finally simulation studies are provided to illustrate the effectiveness of the proposed design methods

a tight lower bound to the outage probability of discrete input block fading channels in this correspondence a tight lower bound to the outage probability of discrete input nakagami m block fading channels is proposed the approach permits an efficient method for numerical evaluation of the bound providing an additional tool for system design the optimal rate diversity tradeoff for the nakagami m block fading channel is also derived and a tight upper bound is obtained for the optimal coding gain constant

minimum distance methods based on quadratic distances for transforms in simple linear regression models minimum distance estimators and test statistics based on quadratic distances for transforms are introduced in simple linear regression models asymptotic properties of quadratic distance estimators and tests for the error distributions are derived the modified quadratic distance estimator is shown to be efficient provided that the error distribution is symmetric and the derivative of the logarithm of the error density is a linear combination of the transforms

coded diversity on block fading channels this paper considers coded diversity schemes over block fading rician channels using random coding techniques two random coding upper bounds on the error probability of block codes are derived a new bound and a simpler but looser bound assuming binary input distribution also a new lower bound for any block code is derived using the strong converse to channel coding theorem the lower bound shows that the new random coding upper bound is quite tight furthermore it is shown that the maximum achievable diversity order in a block fading channel with finite interleaving depends not only on the number of subchannels l but also on the code rate r and that the performance can only marginally be improved by increasing the block length of the code the random coding upper bound and the lower bound are shown to converge to the capacity outage for large channel block lengths n demonstrating that the capacity outage can be used for estimating the error probability of coded diversity schemes

minimum distance estimation in a linear regression model this paper discusses a class of minimum distance cramer von mises type estimators of the slope parameter in a linear regression model these estimators are obtained by minimizing an integral of squared difference between weighted empiricals of the residuals and their expectations with respect to a large class of integrating measures the estimator corresponding to the weights proportional to the design variable is shown to be asymptotically efficient within the class at a given error distribution the paper also discusses the asymptotic null distribution of a class of minimum cramer von mises type goodness of fit test statistics