a necessary and sufficient condition for the positive definiteness of interval symmetric matrices a necessary and sufficient condition for the positive definiteness of interval symmetric matrices is obtained and a useful application is shown

extensions of the i mmse relationship to gaussian channels with feedback and memory unveiling a fundamental link between information theory and estimation theory the i mmse relationship by guo et al together with its numerous extensions has great theoretical significance and various practical applications on the other hand its influences to date have been restricted to channels without feedback or memory due to the absence of its extensions to such channels in this paper we propose the extensions of the i mmse relationship to discrete time and continuous time gaussian channels with feedback and or memory our approach is based on a very simple observation which can be applied to other scenarios such as a simple and direct proof of the classical de bruijn s identity

a sufficient condition for stability of a polytope of matrices abstract in this paper we study the stability of interval dynamical systems a sufficient condition for the stability of a polytope of matrices which is shown to be necessary and sufficient for a certain class of matrices is obtained the results developed can also be applied to the stability of a positive cone of matrices and sufficient conditions for the stability of interval dynamical systems are obtained a relationship between real parts of eigenvalues and matrix measures is also presented

stability of interval matrices in this paper new sufficient conditions for stability and complete instability of an interval matrix jv p q are presented they include the corresponding results derived by heinen 1984 and xu daoyi 1985 as particular cases secondly we present the concept of composite type for stability and simple criteria for this type

mutual information and conditional mean estimation in poisson channels following the discovery of a fundamental connection between information measures and estimation measures in gaussian channels this paper explores the counterpart of those results in poisson channels in the continuous time setting the received signal is a doubly stochastic poisson point process whose rate is equal to the input signal plus a dark current it is found that regardless of the statistics of the input the derivative of the input output mutual information with respect to the intensity of the additive dark current can be expressed as the expected difference between the logarithm of the input and the logarithm of its noncausal conditional mean estimate the same holds for the derivative with respect to input scaling but with the logarithmic function replaced by x log x similar relationships hold for discrete time versions of the channel where the outputs are poisson random variables conditioned on the input symbols

an approach to robust stability of matrix polytopes through copositive homogeneous polynomials an approach to guaranteeing the stability of a polytope of matrices is proposed previous results in the literature have made the obvious connection between various robust stability problems and a test for positivity of a multivariable polynomial such results are extended in order to demonstrate that all matrices within a polytope are stable is and only if an associated homogeneous polynomial is strictly copositive the additional structure obtained by exploiting homogeneity of this multivariable polynomial leads to several computationally tractable sufficiency tests for establishing either robust stability or instability of a polytope of matrices

virtually uniserial modules and rings abstract we study the class of virtually uniserial modules and rings as a nontrivial generalization of uniserial modules and rings an r module m is virtually uniserial if for every finitely generated submodule 0 k m k rad k is virtually simple also an r module m is called virtually serial if it is a direct sum of virtually uniserial modules and a left virtually uniserial resp left virtually serial ring is a ring which is virtually uniserial resp serial as a left r module we give some useful properties of virtually uni serial modules and rings in particular it is shown that every left virtually uniserial module is uniform and bezout also we show that if r is a left virtually serial ring then r j r i 1 t m n i d i where t n 1 n t n and each d i is a principal left ideal domain as a consequence we obtain that a ring r is left virtually serial with j r 0 if and only if r i 1 t m n i d i where t n 1 n t n and each d i is a principal left ideal domain with j d i 0 also several classes of rings for which every virtually uniserial module resp ring is uniserial are given noetherian left virtually uniserial rings are characterized finally we obtain some structure theorems for commutative rings over which every finitely generated module is virtually serial

spectrally stable matrices abstract given an n n complex matrix a define the matrix polytope determined by a as p a ad d diag d 1 d n 1 d i 1 i 1 n we investigate the class of matrices a such that every eigenvalue of every member of p a is contained in the convex hull of the eigenvalues of the extreme points of p a

stability analysis of interval matrices another sufficient condition a sufficient condition for the stability of interval matrices is presented based on a lyapunov approach the condition while requiring the solution of a lyapunov matrix equation removes the restrictions imposed by heinen 1984 examples given illustrate the improvement of the proposed condition over the ones given by heinen and bialas 1983 and daoyi 1985

the capacity region of the gaussian multiple input multiple output broadcast channel the gaussian multiple input multiple output mimo broadcast channel bc is considered the dirty paper coding dpc rate region is shown to coincide with the capacity region to that end a new notion of an enhanced broadcast channel is introduced and is used jointly with the entropy power inequality to show that a superposition of gaussian codes is optimal for the degraded vector broadcast channel and that dpc is optimal for the nondegraded case furthermore the capacity region is characterized under a wide range of input constraints accounting as special cases for the total power and the per antenna power constraints

a necessary and sufficient condition for the stability of nonnegative interval discrete systems the stability of nonnegative discrete systems with interval uncertainty is discussed for this class of system a necessary and sufficient condition for the stability is provided when all elements of the system matrix are assumed to be specified by intervals an illustrative example is used as a guideline to demonstrate the effectiveness of the result simple computational tests are suggested and their usefulness in this framework is discussed the possible extension of this result to more general classes of systems is addressed

robust stability for linear discrete time systems with structured perturbations the robust stability problems of linear discrete time systems with structured perturbations are considered the necessary and sufficient condition of interval stability is given and the maximal bound of robust stability is presented for systems with a non negative or non positive nominal system matrix further it is shown that the given necessary and sufficient condition and the given maximal robust bound are still valid for time varying perturbations and nonlinear perturbations

independent of delay stability criteria for uncertain linear state space models new stability robustness criteria are presented for linear state space models with multiple uncertain time delays and structured parameter uncertainty using the lyapunov equation approach the proposed stability criteria are independent of the size of time delays some previous quadratic stability criteria for linear uncertain systems without time delays are included as special cases examples are used to illustrate the less conservative results of the proposed methods compared with existing ones in the literature

mmse of bad codes we examine codes over the additive gaussian noise channel designed for reliable communication at some specific signal to noise ratio snr and constrained by the permitted minimum mean square error mmse at lower snrs the maximum possible rate is below point to point capacity and hence these are nonoptimal codes alternatively referred to as bad codes we show that the maximum possible rate is the one attained by superposition codebooks moreover the mmse and mutual information behavior as a function of snr for any code attaining the maximum rate under the mmse constraint is known for all snr we also provide a lower bound on the mmse for finite length codes as a function of the error probability of the code

comments on sufficient and necessary condition for the asymptotic stability of discrete linear interval systems abstract in a recent paper by jiang 1988 a necessary and sufficient condition for asymptotic stability of the interval matrix of discrete time systems is presented in this contribution it is shown that this condition is not true in general a counter example is given and additional remarks are made

maximal unidirectional perturbation bounds for stability of polynomials and matrices abstract given a stable polynomial or matrix we consider a class of unidirectional perturbations in this note we provide a closed form for the maximal perturbation bounds under which stability is preserved the results are then used to derive a closed form for the maximal stability box around the coefficients of a nominally stable polynomial

mismatched estimation and relative entropy a random variable with distribution p is observed in gaussian noise and is estimated by a mismatched minimum mean square estimator that assumes that the distribution is q instead of p this paper shows that the integral over all signal to noise ratios snrs of the excess mean square estimation error incurred by the mismatched estimator is twice the relative entropy d p q in nats this representation of relative entropy can be generalized to nonreal valued random variables and can be particularized to give new general representations of mutual information in terms of conditional means inspired by the new representation we also propose a definition of free relative entropy which fills a gap in and is consistent with the literature on free probability

when is a self injective semiperfect ring quasi frobenius abstract it is shown that a right self injective semiperfect ring r is quasi frobenius if and only if every uniform submodule of any projective right r module is contained in a finitely generated submodule

positive definiteness of hermitian interval matrices abstract we present a new necessary and sufficient criterion to check the positive definiteness of hermitian interval matrices it is shown that an n n hermitian interval matrix is positive definite if and only if its 4 n 1 n 1 specially chosen hermitian vertex matrices are positive definite

counter example to a recent result on the stability of interval matrices by s bialas abstract in bialas 1983 a condition is given which is supposedly necessary and sufficient for the stability of interval matrices we demonstrate via a counter example that the condition given is in fact not sufficient

on mmse crossing properties and implications in parallel vector gaussian channels the scalar additive gaussian noise channel has the single crossing point property between the minimum mean square error mmse in the estimation of the input given the channel output assuming a gaussian input to the channel and the mmse assuming an arbitrary input this paper extends the result to the parallel vector additive gaussian channel in three phases the channel matrix is the identity matrix and we limit the gaussian input to a vector of gaussian i i d elements the single crossing point property is with respect to the signal to noise ratio as in the scalar case the channel matrix is arbitrary and the gaussian input is limited to an independent gaussian input a single crossing point property is derived for each diagonal element of the mmse matrix the gaussian input is allowed to be an arbitrary gaussian random vector a single crossing point property is derived for each eigenvalue of the difference matrix between the two mmse matrices these three extensions are then translated to new information theoretic properties on the mutual information using the i mmse relationship a fundamental relationship between estimation theory and information theory revealed by guo and coworkers the results of the last phase are also translated to a new property of fisher information finally the applicability of all three extensions on information theoretic problems is demonstrated through a proof of a special case of shannon s vector entropy power inequality a converse proof of the capacity region of the parallel degraded broadcast channel bc under an input per antenna power constraint and under an input covariance constraint and a converse proof of the capacity region of the compound parallel degraded bc under an input covariance constraint

comments on a necessary and sufficient condition for the positive definiteness of interval symmetric matrices shi and gao 1986 gave a necessary and sufficient condition for the positive definiteness of interval symmetric matrices we point out that their result is not new and the assumptions can be less restrictive

estimation in gaussian noise properties of the minimum mean square error consider the minimum mean square error mmse of estimating an arbitrary random variable from its observation contaminated by gaussian noise the mmse can be regarded as a function of the signal to noise ratio snr as well as a functional of the input distribution of the random variable to be estimated it is shown that the mmse is concave in the input distribution at any given snr for a given input distribution the mmse is found to be infinitely differentiable at all positive snr and in fact a real analytic function in snr under mild conditions the key to these regularity results is that the posterior distribution conditioned on the observation through gaussian channels always decays at least as quickly as some gaussian density furthermore simple expressions for the first three derivatives of the mmse with respect to the snr are obtained it is also shown that as functions of the snr the curves for the mmse of a gaussian input and that of a non gaussian input cross at most once over all snrs these properties lead to simple proofs of the facts that gaussian inputs achieve both the secrecy capacity of scalar gaussian wiretap channels and the capacity of scalar gaussian broadcast channels as well as a simple proof of the entropy power inequality in the special case where one of the variables is gaussian

design optimization for dynamic response of vibration mechanical system with uncertain parameters using convex model the concept of uncertainty plays an important role in the design of practical mechanical system the most common methods for solving uncertainty problems are to model the parameters as a random vector a natural way to handle the randomness is to admit that a given probability density function represents the uncertainty distribution however the drawback of this approach is that the probability distribution is difficult to obtain in this paper we use the non probabilistic convex model to deal with the uncertain parameters in which there is no need for probability density functions using the convex model theory a new method to optimize the dynamic response of mechanical system with uncertain parameters is derived because the uncertain parameters can be selected as the optimization parameters the present method can provide more information about the optimization results than those obtained by the deterministic optimization the present method is implemented for a torsional vibration system the numerical results show that the method is effective

representation of mutual information via input estimates a relationship between information theory and estimation theory was recently shown for the gaussian channel relating the derivative of mutual information with the minimum mean square error this paper generalizes the link between information theory and estimation theory to arbitrary channels giving representations of the derivative of mutual information as a function of the conditional marginal input distributions given the outputs we illustrate the use of this representation in the efficient numerical computation of the mutual information achieved by inputs such as specific codes or natural language

stability analysis of interval matrices improved bounds new sufficient conditions for the stability of interval matrices are presented based on the lyapunov stability approach as well as on the frequency domain approach the conditions help to overcome the conservatism of the existing criteria for the stability of interval matrices based on a matrix approach several numerical examples are given to demonstrate the new conditions and to compare them with results previously reported

stability of a polytope of matrices counterexamples while there have been significant breakthroughs for the stability of a polytope of polynomials since v l kharitonov s 1978 seminal result on interval polynomials for a polytope of matrices the stability problem is considered far from completely resolved counterexamples are provided for three conjectures that are directly motivated by the results in the polynomial case these counterexamples illustrate the fundamental differences between polynomial stability and matrix stability problems and indicate that some obvious lines of attack on the matrix polytope stability problem will fail

minimax guaranteed cost control for linear continuous time systems with large parameter uncertainty abstract this paper presents a method for designing a robust controller for linear systems with structured time varying uncertainty the proposed robustness design method results in a simple linear output feedback control law which not only guarantees the asymptotic stability of the closed loop system but also minimizes the maximal performance bound over all possible parameter perturbations the problem is solved by employing a constrained optimization method using analytical gradients a comparative study of an example shows the improvements and advantages of the proposed method over previous ones

sufficient conditions for stability of interval matrices extremely simple sufficient conditions are presented for the stability of interval matrices these complement the necessary and sufficient conditions developed by bialas 1983 which become unwieldy for large matrices 4 4 and above

necessary and sufficient conditions for stability of a matrix polytope with normal vertex matrices abstract it is shown that the eigenvalue set of a matrix polytope with normal vertex matrices is a subset of the convex hull of eigenvalues of the vertex matrices

mutual information relative entropy and estimation in the poisson channel let be a nonnegative random variable and let the conditional distribution of a random variable given be poisson for a parameter we identify a natural loss function such that 1 the derivative of the mutual information between and with respect to is equal to the minimum mean loss in estimating based on regardless of the distribution of 2 when is estimated based on by a mismatched estimator that would have minimized the expected loss had the integral over all values of of the excess mean loss is equal to the relative entropy between and for a continuous time setting where is a nonnegative stochastic process and the conditional law of given is that of a non homogeneous poisson process with intensity function under the same loss function 1 the minimum mean loss in causal filtering when is equal to the expected value of the minimum mean loss in noncausal filtering smoothing achieved with a channel whose parameter is uniformly distributed between 0 and bridging the two quantities is the mutual information between and 2 this relationship between the mean losses in causal and noncausal filtering holds also in the case where the filters employed are mismatched i e optimized assuming a law on which is not the true one bridging the two quantities in this case is the sum of the mutual information and the relative entropy between the true and the mismatched distribution of thus relative entropy quantifies the excess estimation loss due to mismatch in this setting these results are parallel to those recently found for the gaussian channel the i mmse relationship of guo the relative entropy and mismatched estimation relationship of verdu and the relationship between causal and noncasual mismatched estimation of weissman

gradient of mutual information in linear vector gaussian channels this paper considers a general linear vector gaussian channel with arbitrary signaling and pursues two closely related goals i closed form expressions for the gradient of the mutual information with respect to arbitrary parameters of the system and ii fundamental connections between information theory and estimation theory generalizing the fundamental relationship recently unveiled by guo shamai and verdu spl acute we show that the gradient of the mutual information with respect to the channel matrix is equal to the product of the channel matrix and the error covariance matrix of the best estimate of the input given the output gradients and derivatives with respect to other parameters are then found via the differentiation chain rule

measurement matrix design for phase retrieval based on mutual information in phase retrieval problems a signal of interest soi is reconstructed based on the magnitude of a linear transformation of the soi observed with additive noise the linear transform is typically referred to as a measurement matrix many works on phase retrieval assume that the measurement matrix is a random gaussian matrix which in the noiseless scenario with sufficiently many measurements guarantees invertability of the transformation between the soi and the observations up to an inherent phase ambiguity however in many practical applications the measurement matrix corresponds to an underlying physical setup and is therefore deterministic possibly with structural constraints in this paper we study the design of deterministic measurement matrices based on maximizing the mutual information between the soi and the observations we characterize necessary conditions for the optimality of a measurement matrix and analytically obtain the optimal matrix in the low signal to noise ratio regime practical methods for designing general measurement matrices and masked fourier measurements are proposed simulation tests demonstrate the performance gain achieved by the suggested techniques compared to random gaussian measurements for various phase recovery algorithms

sufficient conditions for the stability of interval matrices the stability of interval dynamical systems is studied sufficient conditions for the polytope of interval matrices are examined and some of the proofs are greatly simplified more generally sufficient conditions are obtained and the approach taken in the new proofs has the potential for further generalizations of the result obtained in this paper

a necessary and sufficient condition for the stability of interval matrices consider the linear dynamical system described by the equation xdot t ax t where a is a constant real matrix with dimensions n n and the elements of matrix a are not known precisely we know only the upper and lower bounds of the intervals in which the elements of matrix a are confined in this paper there is proved a necessary and sufficient condition for the stability of solutions of eqn 1 with incomplete information about the elements of matrix a

counter examples to jiang s results abstract this note points out an important mistake in a recent paper by jiang 1988 on the asymptotic stability of discrete linear interval systems

stability analysis of interval matrices continuous and discrete systems this paper considers the stability properties of dynamical interval systems two new methods of determining an upper bound on interval perturbations are presented one of the methods is applicable to both continuous and discrete systems

stability of interval parameter matrices the stability of interval matrices has been studied by many authors in this paper the stability of interval parameter matrices is introduced and some criteria for this stability are given our results are effective for testing the stability of interval matrices and are more general than previous results furthermore criteria for the stability of time varying matrices are obtained

correspondence counter example to clockwise nature of nyquist locus of stable transfer functionsrsquo horowitz and ben adam 1989 noted that the nyquist loci of stable proper real rational functions tend to be clockwise they conjectured that these loci are always clockwise it will be shown by counter example that this conjecture is false the conjecture had been proved using theorem 1 of their paper the same counterexample can be used to show that theorem 1 is incorrect

robust positive realness of functions with dependent parameter uncertainty in numerator and denominator this paper is concerned with the robust positive realness prness and strict positive realness sprness of a family of rational functions with the numerator and denominator simultaneously dependent on the same set of parameters we show that under certain conditions only the extreme values and certain edges of the parameter bounding set are needed for testing the robust prness and sprness of the family communicated by professor h kimura

hessian and concavity of mutual information differential entropy and entropy power in linear vector gaussian channels within the framework of linear vector gaussian channels with arbitrary signaling the jacobian of the minimum mean square error and fisher information matrices with respect to arbitrary parameters of the system are calculated in this paper capitalizing on prior research where the minimum mean square error and fisher information matrices were linked to information theoretic quantities through differentiation the hessian of the mutual information and the entropy are derived these expressions are then used to assess the concavity properties of mutual information and entropy under different channel conditions and also to derive a multivariate version of an entropy power inequality due to costa

mutual information and minimum mean square error in gaussian channels this paper deals with arbitrarily distributed finite power input signals observed through an additive gaussian noise channel it shows a new formula that connects the input output mutual information and the minimum mean square error mmse achievable by optimal estimation of the input given the output that is the derivative of the mutual information nats with respect to the signal to noise ratio snr is equal to half the mmse regardless of the input statistics this relationship holds for both scalar and vector signals as well as for discrete time and continuous time noncausal mmse estimation this fundamental information theoretic result has an unexpected consequence in continuous time nonlinear estimation for any input signal with finite power the causal filtering mmse achieved at snr is equal to the average value of the noncausal smoothing mmse achieved with a channel whose snr is chosen uniformly distributed between 0 and snr

modules with chain conditions up to isomorphism abstract we study modules with chain conditions up to isomorphism in the following sense we say that a right module m is isoartinian if for every descending chain m m 1 m 2 of submodules of m there exists an index n 1 such that m n is isomorphic to m i for every i n a ring r is right isoartinian if r r is an isoartinian module similarly we define isonoetherian and isosimple modules and rings we determine a number of properties of such modules and rings giving several examples for instance we prove that a ring r is a right isoartinian semiprime right noetherian ring if and only if r is a finite direct product of matrix rings over principal right ideal domains

bridging mixture model estimation and information bounds using i mmse we derive bounds on mutual information for arbitrary estimation problems in additive noise modeled using gaussian mixtures previous work exploiting the i minimum mean squared error mmse formula to formulate a bridge between bounds on the mmse for gaussian mixture model estimation problems and bounds on the mutual information are generalized to allow arbitrary noise modeling a novel upper bound on estimation information is also developed for the general estimation case in addition limits are analyzed to develop bounds on arbitrary entropy asymptotic behavior of all bounds and bound errors with some results bridged back to the mmse domain

comments on a necessary and sufficient condition for the positive detiniteness of interval symmetric matrices the main results obtained recently by shi and gao are already known and can be strengthened

a survey of extreme point results for robustness of control systems abstract this paper surveys a subset of the body of research which was sparked by kharitonov s theorem the focal point is extreme point results for robust stability and robust performance that is we give conditions under which satisfaction of a performance specification is ascertained for a family of systems by only checking a finite subset of the extreme members of this family the results which are surveyed apply mainly to systems with structured real parametric uncertainty in addition a number of counterexamples are given to illustrate cases for which an extreme point result does not hold for such cases a solution via the so called edge theorem is often possible

fundamentals of statistical signal processing estimation theory minimum variance unbiased estimation cramer rao lower bound linear models general minimum variance unbiased estimation best linear unbiased estimators maximum likelihood estimation least squares method of moments the bayesian philosophy general bayesian estimators linear bayesian estimators kalman filters summary of estimators extension for complex data and parameters

an extremal inequality motivated by multiterminal information theoretic problems we prove a new extremal inequality motivated by the vector gaussian broadcast channel and the distributed source coding with a single quadratic distortion constraint problems as a corollary this inequality yields a generalization of the classical entropy power inequality epi as another corollary this inequality sheds insight into maximizing the differential entropy of the sum of two dependent random variables

a kharitonov like theorem for interval polynomial matrices abstract as an extension of kharitonov s theorem robust stability of interval polynomial matrices is studied here a polynomial matrix is said to be stable if its determinant has all roots with negative real parts the present paper shows that the robust stability of interval polynomial matrices is equivalent to that of the subclasses where each row column has only one element that involves kharitonov edge polynomials and all the other elements take on one of the four kharitonov vertex polynomials

artinian dimension and isoradical of modules abstract this paper is a continuation of our previous article 9 we introduce an artinian dimension of modules which allows us to study isoartinian modules and an isoradical of a module which is the analogue of the jacobson radical of a module we study the modules generated by isosimple submodules and modules of finite i length which are analogous to modules of finite composition length

the capacity region of the degraded multiple input multiple output compound broadcast channel the capacity region of a compound multiple antenna broadcast channel is characterized when the users exhibit a certain degradedness order the channel under consideration has two users each user has a finite set of possible realizations the transmitter transmits two messages one for each user in such a manner that regardless of the actual realizations both users will be able to decode their messages correctly an alternative view of this channel is that of a broadcast channel with two common messages each common message is intended to a different set of users the degradedness order between the two sets of realizations users is defined through an additional fictitious user whose channel is degraded with respect to all realizations users from one set while all realizations users from the other set are degraded with respect to him

convergence property of interval matrices and interval polynomials in association with robust control system design and analysis the hurwitz property of interval matrices and interval polynomials has recently been actively investigated however its discrete counterpart the convergence property has seemingly not been much discussed in this paper this property is studied in comparison with the hurwitz counterpart some conditions under which interval matrices or interval polynomials are convergent are derived

necessary and sufficient conditions for stability of a class of interval matrices in this paper some necessary and sufficient conditions for stability complete instability and composite stability type of a class of interval matrices are given

the relationship between causal and noncausal mismatched estimation in continuous time awgn channels a continuous time finite power process with distribution p is observed through an awgn channel at a given signal to noise ratio snr and is estimated by an estimator that would have minimized the mean square error if the process had distribution q we show that the causal filtering mean square error mse achieved at snr level snr is equal to the average value of the noncausal smoothing mse achieved with a channel whose snr is chosen uniformly distributed between 0 and snr emerging as the bridge for equating these two quantities are mutual information and relative entropy our result generalizes that of guo shamai and verdu 2005 from the nonmismatched case where p q to general p and q among our intermediate results is an extension of duncan s theorem that relates mutual information and causal mmse to the case of mismatched estimation some further extensions and implications are discussed key to our findings is the recent result of verdu on mismatched estimation and relative entropy

comments on a necessary and sufficient condition for the stability of interval matrices in a recent paper by bialas a new proof of a known result concerning interval polynomials was given this result is summarized here and a much stronger result is mentioned bialas main theorem on the stability of interval matrices is shown to be false

on the minimum mean p th error in gaussian noise channels and its applications the problem of estimating an arbitrary random vector from its observation corrupted by additive white gaussian noise where the cost function is taken to be the minimum mean p th error mmpe is considered the classical minimum mean square error mmse is a special case of the mmpe several bounds properties and applications of the mmpe are derived and discussed the optimal mmpe estimator is found for gaussian and binary input distributions properties of the mmpe as a function of the input distribution signal to noise ratio snr and order p are derived the single crossing point property scpp which provides an upper bound on the mmse and which together with the mutual information mmse relationship is a powerful tool in deriving converse proofs in multi user information theory is extended to the mmpe moreover a complementary bound to the scpp is derived as a first application of the mmpe a bound on the conditional differential entropy in terms of the mmpe is provided which then yields a generalization of the ozarow wyner lower bound on the mutual information achieved by a discrete input on a gaussian noise channel as a second application the mmpe is shown to improve on previous characterizations of the phase transition phenomenon that manifests in the limit as the length of the capacity achieving code goes to infinity as a discontinuity of the mmse as a function of snr as a final application the mmpe is used to show new bounds on the second derivative of mutual information or the first derivative of the mmse

stability analysis of a family of matrices the authors extend the use of the lyapunov equation method to check the stability of a family of matrices the family of interval matrices is defined as the convex hull of a finite number of matrices and is a special case where each element has independent perturbation while the stability of interval matrices cannot be inferred from the stability of its vertex matrices the authors show that the family of matrices will be stable if the symmetric matrices associated with the vertex matrices have matrix measures less than two

on sufficient conditions for the stability of interval matrices using gershgorin s diagonal dominance theorem new sufficient conditions for the stability of interval matrices are obtained the new conditions remove a restriction in heinen s 1983 analysis and are applicable to a wider class of problems than previously possible

on the snr evolution of the mmse function of codes for the gaussian broadcast and wiretap channels this paper considers the signal to noise ratio snr evolution meaning the behavior as a function of the snr of the minimum mean square error mmse function of code sequences in several multi user settings in the additive white gaussian noise regime the settings investigated in this context include the gaussian wiretap channel the gaussian broadcast channel bc and the gaussian bc with confidential messages bcc this paper shows that the specific properties of the snr evolution of the mmse and conditional mmse functions are necessary and sufficient conditions for capacity or equivocation achieving code sequences in some cases the complete snr evolution of a family of code sequences can be determined providing significant insight into the disturbance in terms of mmse such codes have on unintended receivers at other snrs moreover the effects of an additional mmse constraint on the capacity region and on the snr evolution of code sequences are considered in the bc and bcc settings such an analysis emphasizes the tradeoff between rates and limited disturbance on unintended receivers

on communication through a gaussian channel with an mmse disturbance constraint this paper considers a gaussian channel with one transmitter and two receivers the goal is to maximize the communication rate at the intended primary receiver subject to a disturbance constraint at the unintended secondary receiver the disturbance is measured in terms of the minimum mean square error mmse of the interference that the transmission to the primary receiver inflicts on the secondary receiver this paper presents a new upper bound for the problem of maximizing the mutual information subject to an mmse constraint the new bound holds for vector inputs of any length and recovers a previously known limiting when the length of the vector input tends to infinity expression from the work of bustin et al the key technical novelty is a new upper bound on the mmse this bound allows one to bound the mmse for all signal to noise ratio snr values below a certain snr at which the mmse is known which corresponds to the disturbance constraint the bound also complements the single crossing point property of the mmse that upper bounds the mmse for all snr values above a certain value at which the mmse value is known the mmse upper bound provides a refined characterization of the phase transition phenomenon which manifests in the limit as the length of the vector input goes to infinity as a discontinuity of the mmse for the problem at hand for vector inputs of size n 1 a matching lower bound to within an additive gap of order o log log 1 sf mmse where sf mmse is the disturbance constraint is shown by means of the mixed inputs technique recently introduced by dytso et al

the secrecy capacity region of the gaussian mimo multi receiver wiretap channel in this paper we consider the gaussian multiple input multiple output mimo multi receiver wiretap channel in which a transmitter wants to have confidential communication with an arbitrary number of users in the presence of an external eavesdropper we derive the secrecy capacity region of this channel for the most general case we first show that even for the single input single output siso case existing converse techniques for the gaussian scalar broadcast channel cannot be extended to this secrecy context to emphasize the need for a new proof technique our new proof technique makes use of the relationships between the minimum mean square error and the mutual information and equivalently the relationships between the fisher information and the differential entropy using the intuition gained from the converse proof of the siso channel we first prove the secrecy capacity region of the degraded mimo channel in which all receivers have the same number of antennas and the noise covariance matrices can be arranged according to a positive semi definite order we then generalize this result to the aligned case in which all receivers have the same number of antennas however there is no order among the noise covariance matrices we accomplish this task by using the channel enhancement technique finally we find the secrecy capacity region of the general mimo channel by using some limiting arguments on the secrecy capacity region of the aligned mimo channel we show that the capacity achieving coding scheme is a variant of dirty paper coding with gaussian signals

lyapunov stability robust analysis and robustness design for linear continuous time systems the linear continuous time systems to be discussed are described by state space models with structured time varying uncertainties first the explicit maximal perturbation bound for maintaining quadratic lyapunov stability of the closed loop systems is presented then a robust design method is proposed given an open loop nominal system with information of the uncertainty structure the proposed robust design method produces a linear constant output feedback control law which maximizes the perturbation bound for maintaining quadratic lyapunov stability both the optimal results for robust analysis and robustness design can be obtained by using an efficient numerical algorithm e g minimax of matlab with analytic gradients given in this paper examples are investigated in some detail to show the improvements and advantages of the proposed methods over previous ones