feedback capacity of a class of symmetric finite state markov channels we consider the feedback capacity of a class of symmetric finite state markov channels here symmetry termed quasi symmetry is defined as a generalized version of the symmetry defined for discrete memoryless channels the symmetry yields the existence of a hidden markov noise process that depends on the channel s state process and facilitates the channel description as a function of input and noise where the function satisfies a desirable invertibility property we show that feedback does not increase capacity for such class of finite state channels and that both their nonfeedback and feedback capacities are achieved by an independent and uniformly distributed i u d input as a result the channel capacity is explicitly given as a difference of output and noise entropy rates where the output is driven by the i u d input

the information lost in erasures we consider sources and channels with memory observed through erasure channels in particular we examine the impact of sporadic erasures on the fundamental limits of lossless data compression lossy data compression channel coding and denoising we define the erasure entropy of a collection of random variables as the sum of entropies of the individual variables conditioned on all the rest the erasure entropy measures the information content carried by each symbol knowing its context the erasure entropy rate is shown to be the minimal amount of bits per erasure required to recover the lost information in the limit of small erasure probability when we allow recovery of the erased symbols within a prescribed degree of distortion the fundamental tradeoff is described by the erasure rate distortion function which we characterize we show that in the regime of sporadic erasures knowledge at the encoder of the erasure locations does not lower the rate required to achieve a given distortion when no additional encoded information is available the erased information is reconstructed solely on the basis of its context by a denoiser connections between erasure entropy and discrete denoising are developed the decrease of the capacity of channels with memory due to sporadic memoryless erasures is also characterized in wide generality

robust state estimation for uncertain systems with averaged integral quadratic constraints this paper considers a robust state estimation problem for a new class of uncertain systems the new uncertainty class introduced in the paper involves structured uncertainties which are required to satisfy a certain averaged integral quadratic constraint this uncertainty class combines aspects of norm bounded and stochastic uncertainty descriptions the solution to the robust state estimation problem is obtained by solving a parametrized riccati differential equation of the game type

robust stability analysis of time varying systems using time varying quadratic forms abstract we consider the robust stability of time varying linear systems subject to structured time varying uncertainty we provide an alternate proof of the result that robust stability holds if and only if a scaled small gain condition holds asymptotically the new proof employs an extension of the so called s procedure losslessness theorem to time varying quadratic forms which is of independent interest

h output feedback control for linear discrete time varying systems via the bounded real lemma in this paper we develop a solution to the discrete time output feedback control problem for linear time varying ltv systems the solution is developed along the strategy set up by doyle et al in 1989 and the main ingredient in its derivation is the extension of the well known bounded real lemma to a discrete time varying context developed by van der veen and verhaegen in 1995 this approach contributes to the conceptual simplicity and hence to the accessibility of the solution apart from that we treat the infinite horizon case for ltv system of non uniform state dimension and varying input and output dimension both situations can easily occur in practice for example in multirate sampled data control systems the algorithm that can be derived from the solution presented in then applied to the output feedback of a dynamical system changing from one operation point in its operation envelope to another

robustness of trajectories with finite time extent the problem of estimating perturbation bounds of finite trajectories is considered the trajectory is assumed to be generated by a linear system with uncertainty characterized in terms of integral quadratic constraints it is shown that such perturbation bounds can be obtained as the solution to a nonconvex quadratic optimization problem which can be addressed using lagrange relaxation the result can be used in robustness analysis of hybrid systems and switched dynamical systems

model validation a connection between robust control and identification the gap between the models used in control synthesis and those obtained from identification experiments is considered by investigating the connection between uncertain models and data the model validation problem addressed is given experimental data and a model with both additive noise and norm bounded perturbations is it possible that the model could produce the observed input output data this problem is studied for the standard h sub infinity mu framework models a necessary condition for such a model to describe an experimental datum is obtained for a large class of models in the robust control framework this condition is computable as the solution of a quadratic optimization problem

on gaussian channels with feedback under expected power constraints and with non vanishing error probabilities in this paper we consider single and multi user gaussian channels with feedback under expected power constraints and with non vanishing error probabilities in the first of two contributions we study asymptotic expansions for the additive white gaussian noise awgn channel with feedback under the average error probability formalism by drawing ideas from gallager and nakiboglu s work for the direct part and the meta converse for the converse part we establish the varepsilon capacity and show that it depends on varepsilon in general and so the strong converse fails to hold furthermore we provide bounds on the second order term in the asymptotic expansion we show that for any positive integer l the second order term is bounded between a term proportional to ln l n where ln l cdot is the l fold nested logarithm function and a term proportional to n ln n 1 2 where n is the blocklength the lower bound on the second order term shows that feedback does provide an improvement in the maximal achievable rate over the case where no feedback is available in our second contribution we establish the varepsilon capacity region for the awgn multiple access channel with feedback under the expected power constraint by combining ideas from hypothesis testing information spectrum analysis ozarow s coding scheme and power control

feedback does not increase the capacity of discrete channels with additive noise we consider discrete time finite alphabet channels with additive random noise we show that output feedback does not increase the capacity of such channels this result holds in the most general case i e for arbitrary additive noise processes

sampled data h optimal control of time varying systems the sampled data h optimal control problem is studied for time varying systems the problem consists of finding all sampled data controllers with a piece wise constant control signal for which the l2 induced norm from the continuous time disturbance to the continuous time output is less than a specified bound a game theoretic approach is used to obtain a complete solution to the problem in the finite horizon time varying case the solution involves a mixed discrete continuous riccati equation and a variable transformation which takes the problem to a standard discrete finite dimensional h filtering problem

an uncertainty averaging approach to optimal guaranteed cost control of uncertain systems with structured uncertainty this paper presents an optimal state feedback guaranteed cost control result for a class of uncertain linear time varying systems with structured uncertainty the cost function considered is a quadratic cost function defined over a finite time interval the solution of the optimal control problem is obtained by solving a parametrized riccati differential equation of the game type

robust reduced order nonstrictly proper state estimation via the optimal projection equations with guaranteed cost bounds a state estimation design problem involving parametric plant uncertainties is considered an estimation error bound suggested by multiplicative white noise modeling is utilized for guaranteeing robust estimation over a specified range of parameter uncertainties necessary conditions that generalize the optimal projection equations for reduced order state estimation are used to characterize the estimator that minimizes the error bound the design equations thus effectively serve as sufficient conditions for synthesizing robust estimators additional features include the presence of a static estimation gain in conjunction with the dynamic kalman estimator to obtain a nonstrictly proper estimator

denoising via mcmc based lossy compression it has been established in the literature in various theoretical and asymptotic senses that universal lossy compression followed by some simple postprocessing results in universal denoising for the setting of a stationary ergodic source corrupted by additive white noise however this interesting theoretical result has not yet been tested in practice in denoising simulated or real data in this paper we employ a recently developed mcmc based universal lossy compressor to build a universal compression based denoising algorithm we show that applying this iterative lossy compression algorithm with appropriately chosen distortion measure and distortion level followed by a simple derandomization operation results in a family of denoisers that compares favorably both theoretically and in practice with other mcmc based schemes and with the discrete universal denoiser dude

an asymptotic expansion for a class of biorthogonal polynomials with respect to a measure on the unit circle abstract we consider the system of biorthogonal polynomials p n q n n 0 with respect to a complex valued measure supported on the unit circle and give a uniform compound asymptotic expansion formula consisting of the sum of two inverse factorial series giving the explicit expression of the terms and including error bounds as a consequence we prove that the set of accumulation points of the zeros these polynomials is included in the unit circle some numerical experiments are included

a game theoretic approach to h control for time varying systems a representation formula for all controllers that satisfy an mathcal l infty type constraint is derived for time varying systems it is now known that a formula based on two indefinite algebraic riccati equations may be found for time invariant systems over an infinite time support see j c doyle et al ieee trans automat control ac 34 1989 pp 831 847 k glover and j c doyle systems control lett 11 1988 pp 167 172 k glover et al siam j control optim 29 1991 pp 283 324 m green et al siam j control optim 28 1990 pp 1350 1371 d j n limebeer et al in proc ieee conf on decision and control austin tx 1988 g tadmor math control systems signal processing 3 1990 pp 301 324 in the time varying case two indefinite riccati differential equations are required a solution to the design problem exists if these equations have a solution on the optimization interval the derivation of the representation formula illustrated in this paper mak

quadratic differentials and asymptotics of laguerre polynomials with varying complex parameters abstract in this paper we study the asymptotics as n of the sequences of laguerre polynomials with varying complex parameters depending on the degree n more precisely we assume that n n a n and lim n a n a c this study has been carried out previously only for n r but complex values of a introduce an asymmetry that makes the problem more difficult the main ingredient of the asymptotic analysis is the right choice of the contour of orthogonality which requires the analysis of the global structure of trajectories of an associated quadratic differential on the complex plane which may have an independent interest while the weak asymptotics is obtained by reduction to the theorem of gonchar rakhmanov stahl the strong asymptotic results are derived via the non commutative steepest descent analysis based on the riemann hilbert characterization of the laguerre polynomials

noise prediction for channels with side information at the transmitter the computation of channel capacity with side information at the transmitter side but not at the receiver side requires in general extension of the input alphabet to a space of strategies and is often hard we consider the special case of a discrete memoryless module additive noise channel y x z sub s where the encoder observes causally the random state s spl isin s that governs the distribution of the noise z sub s we show that the capacity of this channel is given by c log spl chi min sub t s spl rarr spl chi h z sub s t s this capacity is realized by a state independent code followed by a shift by the noise prediction t sub min s that minimizes the entropy of z sub s t s if the set of conditional noise distributions p z s s spl isin s is such that the optimum predictor t sub min spl middot is independent of the state weights then c is also the capacity for a noncausal encoder that observes the entire state sequence in advance furthermore for this case we also derive a simple formula for the capacity when the state process has memory

capacity region of the finite state multiple access channel with and without feedback the capacity region of the finite state multiple access channel fs mac with feedback that may be an arbitrary time invariant function of the channel output samples is considered we characterize both an inner and an outer bound for this region using massey s directed information these bounds are shown to coincide and hence yield the capacity region of indecomposable fs macs without feedback and of stationary and indecomposable fs macs with feedback where the state process is not affected by the inputs though multiletter in general our results yield explicit conclusions when applied to specific scenarios of interest for example our results allow us to do the following 1 identify a large class of fs macs that includes the additive mod2 noise mac where the noise may have memory for which feedback does not enlarge the capacity region 2 deduce that for a general fs mac with states that are not affected by the input if the capacity region without feedback is zero then so is the capacity region with feedback 3 deduce that the capacity region of a mac that can be decomposed into a multiplexer concatenated by a point to point channel with without or with partial feedback the capacity region is given by sigmam rm les c where c is the capacity of the point to point channel and m indexes the encoders moreover we show that for this family of channels source channel coding separation holds

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

on the existence of short trajectories of quadratic differentials related to generalized jacobi polynomials with non real varying parameters abstract the motivation of this paper is to analyze to a large degree the behavior of the jacobi p n n n polynomials when the parameters determining the polynomials are complex and depend on the degree n linearly we show that the cauchy transform of the limit weak of the root counting measures of these polynomials satisfies quadratic algebraic equation we investigate the existence of solutions to these equations as cauchy transform of compactly supported positive measures any connected curve of the support of these measures if exists coincides with a horizontal trajectory of some quadratic differential in this paper we describe the trajectories of the family of quadratic differentials 2 z a z b z 2 1 2 d z 2 and we give a necessary and sufficient condition on the complex numbers a b and for the existence of at least one finite critical trajectory

achieving the empirical capacity using feedback memoryless additive models we address the problem of universal communications over an unknown channel with an instantaneous noiseless feedback and show how rates corresponding to the empirical behavior of the channel can be attained although no rate can be guaranteed in advance first we consider a discrete modulo additive channel with alphabet x where the noise sequence zn is arbitrary and unknown and may causally depend on the transmitted and received sequences and on the encoder s message possibly in an adversarial fashion although the classical capacity of this channel is zero we show that rates approaching the empirical capacity log x h emp zn can be universally attained where h emp zn is the empirical entropy of zn for the more general setting where the channel can map its input to an output in an arbitrary unknown fashion subject only to causality we model the empirical channel actions as the modulo addition of a realized noise sequence and show that the same result applies if common randomness is available the results are proved constructively by providing a simple sequential transmission scheme approaching the empirical capacity

a new parametrization of h suboptimal controllers elementary state space concepts are used to derive a transparent solution to the h control problem on an infinite horizon the main contribution of this solution is a novel representation of suboptimal controllers in terms of a pair of parametric riccati equations with a coupling constraint unlike the classical parametrization in terms of linear fractional transformation this state space representation has a homogeneous riccati formulation which should help to make the most of the suboptimal controller diversity potential applications include the design of reduced order controllers and more generally the selection of suboptimal controllers to meet or optimize additional constraints

the capacity cost function of discrete additive noise channels with and without feedback we consider modulo q additive noise channels where the noise process is a stationary irreducible and aperiodic markov chain of order k we begin by investigating the capacity cost function c spl beta of such additive noise channels without feedback we establish a tight upper bound to c spl beta which holds for general not necessarily markovian stationary q ary noise processes this bound constitutes the counterpart of the wyner ziv lower bound to the rate distortion function of stationary sources with memory we also provide two simple lower bounds to c spl beta which along with the upper bound can be easily calculated using the blahut algorithm for the computation of channel capacity numerical results indicate that these bounds form a tight envelope on c spl beta we next examine the effect of output feedback on the capacity cost function of these channels and establish a lower bound to the capacity cost function with feedback c sub fb spl beta we show both analytically and numerically that for a particular feedback encoding strategy and a class of markov noise sources the lower bound to c sub fb spl beta is strictly greater than c spl beta this demonstrates that feedback can increase the capacity cost function of discrete channels with memory

feedback capacity of the compound channel in this work we find the capacity of a compound finite state channel fsc with time invariant deterministic feedback we consider the use of fixed length block codes over the compound channel our achievability result includes a proof of the existence of a universal decoder for the family of fscs with feedback as a consequence of our capacity result we show that feedback does not increase the capacity of the compound gilbert elliot channel additionally we show that for a stationary and uniformly ergodic markovian channel if the compound channel capacity is zero without feedback then it is zero with feedback finally we use our result on the fsc to show that the feedback capacity of the memoryless compound channel is given by infthetas maxqx i x y thetas

capacity of burst noise erasure channels with and without feedback and input cost a class of burst noise erasure channels which incorporate both errors and erasures during transmission is studied the channel whose output is explicitly expressed in terms of its input and a stationary ergodic noise erasure process is shown to have a so called quasi symmetry property under certain invertibility conditions as a result it is proved that a uniformly distributed input process maximizes the channel s block mutual information resulting in a closed form formula for its non feedback capacity in terms of the noise erasure entropy rate and the entropy rate of an auxiliary erasure process the feedback channel capacity is also characterized showing that the feedback does not increase capacity and generalizing prior related results the capacity cost function of the channel with and without feedback is next investigated a sequence of finite letter upper bounds for the capacity cost function without feedback is derived finite letter lower bonds for the capacity cost function with feedback are obtained using a specific encoding rule based on these bounds it is demonstrated both numerically and analytically that feedback can increase the capacity cost function for a class of channels with markov noise erasure processes

robust reduced order unbiased filtering for uncertain systems this paper presents a simple solution to the robust unbiased functional reduced order filtering problem in the case of uncertain systems described by integral quadratic constraint iqc the existence condition of the unbiased filter is expressed through a rank relation then the filter is designed via linear matrix inequalities coupled with an equality constraint the results obtained in this paper are applicable to unstable systems the approach is illustrated by a numerical example

a coding theorem for a class of stationary channels with feedback a coding theorem is proved for a class of stationary channels with feedback in which the output yn f xn m n zn m n is the function of the current and past m symbols from the channel input xn and the stationary ergodic channel noise zn in particular it is shown that the feedback capacity is equal to limnrarr infin supp x n y n 1 1 n i xn rarr yn where i xn rarr yn sigmai 1 n i xi yi yi 1 denotes the massey directed information from the channel input to the output and the supremum is taken over all causally conditioned distributions p xn yn 1 pii 1 n p xi xi 1 yi 1 the main ideas of the proof are a classical application of the shannon strategy for coding with side information and a new elementary coding technique for the given channel model without feedback which is in a sense dual to gallager s lossy coding of stationary ergodic sources a similar approach gives a simple alternative proof of coding theorems for finite state channels by yang kavcic tatikonda chen berger and permuter weissman goldsmith