covert communication over noisy channels a resolvability perspective we consider the situation in which a transmitter attempts to communicate reliably over a discrete memoryless channel while simultaneously ensuring covertness low probability of detection with respect to a warden who observes the signals through another discrete memoryless channel we develop a coding scheme based on the principle of channel resolvability which generalizes and extends prior work in several directions first it shows that irrespective of the quality of the channels it is possible to communicate on the order of sqrt n reliable and covert bits over n channel uses if the transmitter and the receiver share on the order of sqrt n key bits this improves upon earlier results requiring on the order of sqrt n log n key bits second it proves that if the receiver s channel is better than the warden s channel in a sense that we make precise it is possible to communicate on the order of sqrt n reliable and covert bits over n channel uses without a secret key this generalizes earlier results established for binary symmetric channels we also identify the fundamental limits of covert and secret communications in terms of the optimal asymptotic scaling of the message size and key size and we extend the analysis to gaussian channels the main technical problem that we address is how to develop concentration inequalities for low weight sequences the crux of our approach is to define suitably modified typical sets that are amenable to concentration inequalities

optimal throughput diversity delay tradeoff in mimo arq block fading channels in this paper we consider an automatic repeat request arq retransmission protocol signaling over a block fading multiple input multiple output mimo channel unlike previous work we allow for multiple fading blocks within each transmission arq round and we constrain the transmitter to fixed rate codes constructed over complex signal constellations in particular we examine the general case of average input power constrained con stellations with a fixed signaling alphabet of finite cardinality this scenario is a suitable model for practical wireless communications systems employing orthogonal frequency division multiplexing ofdm techniques over a mimo arq channel two cases of fading dynamics are considered namely short term static fading where channel fading gains change randomly for each arq round and long term static fading where channel fading gains remain constant over all arq rounds pertaining to a given message as our main result we prove that for the block fading mimo arq channel with a fixed signaling alphabet satisfying a short term power constraint the optimal signal to noise ratio snr exponent is given by a modified singleton bound relating all the system parameters to demonstrate the practical significance of the theoretical analysis we present numerical results showing that practical singleton bound achieving maximum distance separable codes achieve the optimal snr exponent

entanglement cost for sequences of arbitrary quantum states the entanglement cost of arbitrary sequences of bipartite states is shown to be expressible as the minimization of a conditional spectral entropy rate over sequences of separable extensions of the states in the sequence the expression is shown to reduce to the regularized entanglement of formation when the nth state in the sequence consists of n copies of a single bipartite state

multiterminal source channel communication over an orthogonal multiple access channel we consider the problem of multiterminal source channel communication where a number of distributed and possibly correlated sources are transmitted through an orthogonal multiple access channel to a common destination we provide a characterization of the optimal tradeoff between the transmission cost gamma and the distortion vector d as measured against individual sources our approach consists of two steps 1 a multiple letter characterization of the rate distortion region of the multiterminal source coding and 2 a source channel separation theorem ensuring that all achievable pairs of gamma d can be obtained by combining the rate distortion region and the orthogonal multiple access channel capacity region as a corollary we determine the optimal power and distortion tradeoff in a quadratic gaussian sensor network under orthogonal multiple access and show that separate source and channel coding strictly outperforms the uncoded amplify forward transmission and is in fact optimal in this case this result is in sharp contrast to the case of nonorthogonal multiple access for which separate source and channel coding is not only suboptimal but also strictly inferior to uncoded transmission

a consistent model coupling adhesion friction and unilateral contact a model considering both unilateral contact coulomb friction and adhesion is presented in the framework of continuum thermodynamics the contact zone is considered as a material boundary and the local constitutive laws are derived by choosing two specific surface potentials the free energy and the dissipation potential because of the non regular properties of these potentials convex analysis is used to derive the local behavior laws from the state and the complementary laws the adhesion is characterized by an internal variable introduced by fremond which represents the intensity of adhesion the continuous transition from a total adhesive condition to a possible pure frictional one is enforced by using elasticity coupled with damage for the interface non penetration conditions and coulomb law are strictly imposed without using any penalty the variational formulation for quasistatic problems is written as the coupling between an implicit variational inequality a variational inequality and a differential equation an increment formulation is proposed an existence result under a condition on the friction coefficient is given a numerical method is derived from the incremental formulation and various algorithms are implemented they solve a sequence of minimization problems under constraints the model is used to simulate a micro indentation experiment conducted to characterize the behavior of fiber matrix interface in a ceramic composite identification of the constitutive parameters is discussed

asymptotic performance of linear receivers in mimo fading channels linear receivers are an attractive low complexity alternative to optimal processing for multiple antenna multiple input multiple output mimo communications in this paper we characterize the information theoretic performance of mimo linear receivers in two different asymptotic regimes for fixed number of antennas we investigate the limit of error probability in the high signal to noise ratio snr regime in terms of the diversity multiplexing tradeoff dmt following this we characterize the error probability for fixed snr in the regime of large but finite number of antennas as far as the dmt is concerned we report a negative result we show that both linear zero forcing zf and linear minimum mean square error mmse receivers achieve the same dmt which is largely suboptimal even in the case where outer coding and deacircnot coding is performed across the antennas we also provide an apacircnot proximate quantitative analysis of the markedly different behavior of the mmse and zf receivers at finite rate and nonasymptotic snr and show that while the zf receiver achieves poor diversity at any finite rate the mmse receiver error curve slope flattens out progressively as the coding rate increases when snr is fixed and the number of antennas becomes large we show that the mutual information at the output of an mmse or zf linear receiver has fluctuations that converge in distribution to a gaussian random variable whose mean and variance can be characterized in closed form this analysis extends to the linear reacircnot ceiver case a well known result previously obtained for the optimal receiver simulations reveal that the asymptotic analysis captures accurately the outage behavior of systems even with a moderate number of antennas

on one useful inequality in testing of hypotheses a simple proof of one probabilistic inequality is presented let p and q be two given probability measures on a measurable space spl xscr spl ascr we consider testing of hypotheses p and q using one observation for an arbitrary decision rule let spl alpha and spl beta denote the two kinds of error probabilities if both error probabilities have equal costs or we want to minimize the maximum of them then it is natural to investigate the minimal possible sum inf spl alpha spl beta for the best decision rule

fixed rate transmission over fading interference channels using point to point gaussian codes this paper investigates transmission schemes for fixed rate communications over a rayleigh block fading interference channel there are two source destination pairs where each source in the presence of a short term power constraint intends to communicate with its dedicated destination at a fixed data rate it encodes its messages using a point to point gaussian codebook the two users transmissions can be conducted orthogonally or non orthogonally in the latter case each destination performs either direct decoding by treating the interference as noise or successive interference cancellation sic to recover its desired message for each scheme we seek solutions of a power control problem to efficiently assign power to the sources such that the codewords can be successfully decoded at destinations however because of the random nature of fading the power control problem for some channel realizations may not have any feasible solution and the transmission will be in outage thus for each transmission scheme we first compute a lower bound and an upper bound on the outage probability next we use these results to find an outer bound and an inner bound on the epsilon outage achievable rate region i e the rate region in which the outage probability is below a certain value epsilon

security analysis of varepsilon almost dual universal 2 hash functions smoothing of min entropy versus smoothing of renyi entropy of order 2 recently varepsilon almost dual universal2 hash functions have been proposed as a new and wider class of hash functions using this class of hash functions several efficient hash functions were proposed this paper evaluates the security performance when we apply this kind of hash functions we evaluate the security in several kinds of setting based on the l 1 distinguishability criterion and the modified mutual information criterion the obtained evaluation is based on smoothing of renyi entropy of order 2 and or min entropy we clarify the difference between these two methods

on the information rate of multiantenna systems with isotropic unitary input signals in the presence of channel estimation errors this correspondence focuses on the evaluation of the information rate conveyed by block faded pilot based multiple input multiple output mimo systems when the input signals are isotropic unitary iu distributed and imperfect e g error affected channel estimates are available at receiver and transmitter main contributions may be so summarized first we develop closed form analytical formulas for the computation of the ergodic information rate conveyed by the considered mimo systems equipped with a large number of transmit antennas second we point out that no rate gain may be accomplished by shaping the transmitted streams on the basis of possibly partial channel state information csi so that the feedback link becomes indeed useless when the system is block faded and fed by iu distributed input signals third we compare the obtained information rate with those supported by the corresponding mimo systems fed by gaussian distributed input signals for various values of the mean squared error mse impairing the available mimo channel estimates so doing we gain some insight about the operating conditions where actual implementation of a feedback link may be justified by the resulting improvement in the rate conveyed by the overall system

a discrete queue based model for capturing memory and soft decision information in correlated fading channels a discrete binary input 2q ary output communication channel with memory is introduced to judiciously capture both the statistical memory and the soft decision information of a time correlated discrete fading channel dfc used with antipodal signaling and soft output quantization of resolution q the discrete channel which can be explicitly described via its binary input process and a 2q ary noise process is shown to be symmetric thus admitting a simple expression for its capacity when its noise is stationary ergodic it is observed that considerable capacity gains can be achieved due to the channel s memory and the use of as few as 2 bits for soft decision over interleaving the channel to render it memoryless and hard decision demodulation q 1 the 2q ary noise process is next modeled via a queue based qb ball sampling mechanism to produce a mathematically tractable stationary ergodic markovian noise source the dfc is fitted by the qb noise model via an iterative procedure that minimizes the kullback leibler divergence rate between the dfc and qb noise sources modeling results measured in terms of channel noise correlation function and capacity reveal a good agreement between the two channels for a broad range of fading conditions

first and second order coding theorems for mixed memoryless channels with general mixture this paper investigates the first and second order maximum achievable rates of codes with without cost constraints for mixed channels whose channel law is characterized by a general mixture of at most uncountably many stationary and memoryless discrete channels these channels are referred to as mixed memoryless channels with general mixture and include the class of mixed memoryless channels of finitely or countably memoryless channels as a special case for the mixed memoryless channels with general mixture the first order coding theorem which gives a formula for the varepsilon capacity is established and then a direct part of the second order coding theorem is provided a subclass of mixed memoryless channels whose component channels can be ordered according to their capacity is introduced and the first and second order coding theorems are established it is shown that the established formulas reduce to several known formulas for restricted scenarios

numerical analysis of a frictionless contact problem for elastic viscoplastic materials abstract we consider a mathematical model which describes the unilateral quasistatic contact of two elastic viscoplastic bodies the contact is without friction and it is modeled by the classical signorini boundary conditions the model consists of an evolution equation coupled with a time dependent variational inequality it has been shown that the variational problem of the model has a unique solution here we consider numerical approximations of the problem we use the finite element method to discretize the spatial domain spatially semi discrete and fully discrete schemes are studied for both schemes we show the existence of a unique solution and derive error estimates under appropriate regularity assumptions of the solution we have the optimal order convergence

elastic beam in adhesive contact abstract dynamic and quasistatic processes of contact with adhesion between an elastic or viscoelastic beam and a foundation are considered the contact is modeled with the signorini condition when the foundation is rigid and with normal compliance when it is deformable the adhesion is modeled by introducing the bonding function the evolution of which is described by an ordinary differential equation the existence and uniqueness of the weak solution for each of the problems is established using the theory of variational inequalities fixed point arguments and the existence and uniqueness result in commun contemp math 1 1 1999 87 123 the numerical approximations of the quasistatic problem with normal compliance are considered based on semi discrete and fully discrete schemes the convergence of the solutions of the discretized schemes is proved and error estimates for these approximate solutions are derived

on single antenna rayleigh block fading channels at finite blocklength this article concerns the maximum coding rate at which data can be transmitted over a noncoherent single antenna rayleigh block fading channel using an error correcting code of a given blocklength with a block error probability not exceeding a given value a high snr normal approximation of the maximum coding rate is presented that becomes accurate as the signal to noise ratio snr and the number of coherence intervals l over which we code tend to infinity numerical analyses suggest that the approximation is accurate at snr values above 15db and when the number of coherence intervals is 10 or more

existence results for dynamic adhesive contact of a rod the existence and uniqueness of the weak solution to the model for the dynamics of a viscoelastic rod which is in adhesive contact with an obstacle is established the model consists of a hyperbolic equation for the vibrations of the rod coupled with a nonlinear ordinary differential equation ode for the evolution of the bonding function the model allows for failure i e complete debonding in finite time the existence of the weak solution is established by using an existence result for odes and the schauder fixed point theorem the limit of an elastic rod when the viscosity vanishes is studied too

universal coding for classical quantum channel we construct a universal code for a stationary and memoryless classical quantum channel as a quantum version of the universal coding by csiszar and korner our code is constructed utilizing a combination of irreducible representations a decoder introduced through the quantum information spectrum and the packing lemma

generating random bits from an arbitrary source fundamental limits suppose we are given a random source and want to use it as a random number generator at what rate can we generate fair bits from it we address this question in an information theoretic setting by allowing for some arbitrarily small but nonzero deviation from ideal random bits we prove our results with three different measures of approximation between the ideal and the obtained probability distributions the variational distance the d bar distance and the normalized divergence two different contexts are studied fixed length and variable length random number generation the fixed length results of this paper provide an operational characterization of the inf entropy rate of a source defined in han and verdu see ibid vol 39 no 3 p 752 772 1993 and the variable length results characterize the liminf of the entropy rate thereby establishing a pleasing duality with the fundamental limits of source coding a feature of our results is that we do not restrict ourselves to ergodic or to stationary sources

buckling and postbuckling analysis of rectangular plates resting on elastic foundations with the use of the spectral method abstract buckling and contact effects for a von karman s plate unilaterally connected with a nonlinear elastic tensionless foundation are investigated the foundation is modeled as nonlinear elastic winkler type and shear deformable pasternak type medium compressive and tensile loading forces along the edges of the plate are considered the spectral method is developed for the discretization of the boundary value problems a parametric analysis of compressive and tensile loadings is given bifurcation phenomena of the solution of the equations are explored the iterative scheme with the path following algorithm is employed to solve the resulting system of nonlinear algebraic equations numerical results are presented

simulation of random processes and rate distortion theory we study the randomness necessary for the simulation of a random process with given distributions on terms of the finite precision resolvability of the process finite precision resolvability is defined as the minimal random bit rate required by the simulator as a function of the accuracy with which the distributions are replicated the accuracy is quantified by means of various measures variational distance divergence orstein 1973 prohorov 1956 and related measures of distance between the distributions of random process in the case of ornstein prohorov and other distances of the kantorovich vasershtein type we show that the finite precision resolvability is equal to the rate distortion function with a fidelity criterion derived from the accuracy measure this connection leads to new results on nonstationary rate distortion theory in the case of variational distance the resolvability of stationary ergodic processes is shown to equal entropy rate regardless of the allowed accuracy in the case of normalized divergence explicit expressions for finite precision resolvability are obtained in many cases of interest and connections with data compression with minimum probability of block error are shown

new nonasymptotic channel coding theorems for structured codes new nonasymptotic random coding theorems with error probability epsilon and finite block length n based on gallager parity check ensemble and general parity check ensembles are derived in this paper the resulting nonasymptotic achievability bounds when combined with nonasymptotic equipartition properties developed in this paper can be easily computed analytically these nonasymptotic achievability bounds are shown to be asymptotically tight up to the second order of the coding rate as n goes to infinity with either constant or subexponentially decreasing epsilon in the case of gallager parity check ensemble and to imply that low density parity check ldpc codes be capacity achieving in the case of ldpc ensembles numerically they are also compared favorably for finite n and epsilon of practical interest with existing nonasymptotic achievability bounds in the literature

the operational meaning of min and max entropy in this paper we show that the conditional min entropy h min a b of a bipartite state rhoab is directly related to the maximum achievable overlap with a maximally entangled state if only local actions on the b part of rhoab are allowed in the special case where a is classical this overlap corresponds to the probability of guessing a given b in a similar vein we connect the conditional max entropy h max a b to the maximum fidelity of rhoab with a product state that is completely mixed on a in the case where a is classical this corresponds to the security of a when used as a secret key in the presence of an adversary holding b because min and max entropies are known to characterize information processing tasks such as randomness extraction and state merging our results establish a direct connection between these tasks and basic operational problems for example they imply that the logarithm of the probability of guessing a given b is a lower bound on the number of uniform secret bits that can be extracted from a relative to an adversary holding b

two families of mixed finite elements for second order elliptic problems two families of mixed finite elements one based on triangles and the other on rectangles are introduced as alternatives to the usual raviart thomas nedelec spaces error estimates inl 2 andh 5 are derived for these elements a hybrid version of the mixed method is also considered and some superconvergence phenomena are discussed

on a markov lemma and typical sequences for polish alphabets in this paper we consider a new definition of typicality based on the weak topology that is applicable to polish alphabets which includes mathbb r n this notion is a generalization of strong typicality in the sense that it degenerates to strong typicality in the finite alphabet case and can also be applied to mixed and continuous distributions furthermore it is strong enough to prove a markov lemma and thus can be used to directly prove a more general class of results than entropy or weak typicality we provide two example applications of this technique first using the markov lemma we directly prove a coding result for gel fand pinsker channels with an average input constraint for a large class of alphabets and channels without first proving a finite alphabet result and then resorting to delicate quantization arguments this class of alphabets includes for example real and complex inputs subject to a peak amplitude restriction while this large class does not directly allow for gaussian distributions with average power constraints it is shown to be straightforward to recover this case by considering a sequence of truncated gaussian distributions as a second example we consider a problem of coordinated actions i e empirical distributions for a two node network where we derive necessary and sufficient conditions for a given desired coordination

a priori error estimates for mixed finite element approximations of the acoustic wave equation in this paper we derive optimal a priori l infty l 2 error estimates for mixed finite element displacement formulations of the acoustic wave equation the computational complexity of this approach is equivalent to the traditional mixed finite element formulations of the second order hyperbolic equations in which the primary unknowns are pressure and the gradient of pressure however the displacement formulations with the physical variables of interest displacement and pressure requires less regularity on the displacement

unequal message protection asymptotic and non asymptotic tradeoffs we study a form of unequal error protection that we term unequal message protection ump the message set of a ump code is a union of m disjoint message classes each class has its own error protection requirement with some classes needing better error protection than others we analyze the tradeoff between rates of message classes and the levels of error protection our analysis reveals new tradeoffs which were not captured by prior works on ump codes to obtain our results we generalize finite block length achievability and converse bounds due to polyanskiy poor verdu we evaluate our bounds for the binary symmetric and binary erasure channels and analyze the asymptotic characteristic of the bounds in the fixed error and moderate deviations regimes in addition we consider two questions related to the practical construction of ump codes first we study a header construction that prefixes the message class into a header followed by data protection using a standard homogeneous classical code we show that in general this construction is not optimal at finite block lengths we further demonstrate that our main ump achievability bound can be obtained using coset codes which suggests a path to implementation of tractable ump codes

a membrane in adhesive contact a model for the process of quasi static evolution of an elastic membrane in adhesive contact with a rigid obstacle is developed analyzed and numerically simulated the model consists of an elliptic variational inequality for the membrane displacements and a nonlinear ordinary differential equation for the evolution of the adhesion field by using regularity results from the theory of elliptic variational inequalities and a fixed point argument the system is shown to have a unique weak solution a fully discrete algorithm is described and shown to converge and its error estimates are derived in this process we make critical use of the regularity properties of the solution finally the results of numerical simulations based on the fully discrete algorithm are presented

strong secrecy from channel resolvability we analyze physical layer security based on the premise that the coding mechanism for secrecy over noisy channels is tied to the notion of channel resolvability instead of considering capacity based constructions which associate to each message a subcode that operates just below the capacity of the eavesdropper s channel we consider channel resolvability based constructions which associate to each message a subcode that operates just above the resolvability of the eavesdropper s channel building upon the work of csiszar and hayashi we provide further evidence that channel resolvability is a powerful and versatile coding mechanism for secrecy by developing results that hold for strong secrecy metrics and arbitrary channels specifically we show that at least for symmetric wiretap channels random capacity based constructions fail to achieve the strong secrecy capacity while channel resolvability based constructions achieve it we then leverage channel resolvability to establish the secrecy capacity region of arbitrary broadcast channels with confidential messages and a cost constraint for strong secrecy metrics finally we specialize our results to study the secrecy capacity of wireless channels with perfect channel state information csi mixed channels and compound channels with receiver csi as well as the secret key capacity of source models for secret key agreement by tying secrecy to channel resolvability we obtain achievable rates for strong secrecy metrics with simple proofs

one shot classical quantum capacity and hypothesis testing the one shot classical capacity of a quantum channel quantifies the amount of classical information that can be transmitted through a single use of the channel such that the error probability is below a certain threshold in this work we show that this capacity is well approximated by a relative entropy type measure defined via hypothesis testing combined with a quantum version of stein s lemma our results give a conceptually simple proof of the well known holevo schumacher westmoreland theorem for the capacity of memoryless channels more generally we obtain tight capacity formulas for arbitrary not necessarily memoryless channels

variational and numerical analysis of a dynamic frictionless contact problem with adhesion we study a dynamic frictionless contact problem between a viscoelastic body and an obstacle the so called foundation the contact is subjected to an adhesion effect whose evolution is described by an ordinary differential equation for the variational formulation of the contact problem we present and prove an existence and uniqueness result a fully discrete scheme is introduced to solve the problem under certain solution regularity assumptions we derive an optimal order error estimate some numerical examples are included to show the performance of the method

variable rate channel capacity this paper introduces the notions of variable to fixed and fixed to variable channel capacity without feedback for channels that satisfy the strong converse these notions coincide with the conventional shannon capacity for channels that do not behave ergodically the conventional fixed rate shannon capacity only depends on least favorable channel conditions while the variable rate capacity notions are able to capture the whole range of channel states and their likelihood even in the absence of any side information about channel state at the transmitter particular emphasis is placed on memoryless channels that are governed by finitely valued states we show that single user variable to fixed channel capacity is intimately connected to the capacity region of broadcast channels with degraded message sets and we give an expression for the fixed to variable capacity

optimum estimation via gradients of partition functions and information measures a statistical mechanical perspective in continuation to a recent work on the statistical mechanical analysis of minimum mean square error mmse estimation in gaussian noise via its relation to the mutual information the i mmse relation here we propose a simple and more direct relationship between optimum estimation and certain information measures e g the information density and the fisher information which can be viewed as partition functions and hence are amenable to analysis using statistical mechanical techniques the proposed approach has several advantages most notably its applicability to general sources and channels as opposed to the i mmse relation and its variants which hold only for certain classes of channels e g additive white gaussian noise channels we then demonstrate the derivation of the conditional mean estimator and the mmse in a few examples two of these examples turn out to be generalizable to a fairly wide class of sources and channels for this class the proposed approach is shown to yield an approximate conditional mean estimator and an mmse formula that has the flavor of a single letter expression we also show how our approach can easily be generalized to situations of mismatched estimation

error exponents for hypothesis testing of the general source in this correspondence we consider the simple hypothesis testing problems for general sources in the sense of han and verdu recently han established a compact formula for the supremum of achievable exponents for the second kind of error probability under the asymptotic constraint of the form mun e nr n rarr infin on the first kind of error probability mun where r is a given positive number we investigate the same hypothesis testing problems studied by han the aim of the correspondence is to give a new expression for the supremum of achievable error exponents our formula is expressed in terms of the divergences and given in quite different forms from han s expression

variational and numerical analysis of a quasistatic viscoelastic contact problem with adhesion a model for the adhesive quasistatic and frictionless contact between a viscoelastic body and a deformable foundation is described the adhesion process is modelled by a bonding field on the contact surface and contact is described by a modified normal compliance condition the problem is formulated as a coupled system of a variational equality for the displacements and a differential equation for the bonding field the existence of a unique weak solution for the problem and its continuous dependence on the adhesion parameters are established then the numerical analysis of the problem is conducted for the fully discrete approximation the convergence of the scheme is established and error estimates derived finally representative numerical simulations are presented depicting the evolution of the state of the system and in particular the evolution of the bonding field

two grid methods for maxwell eigenvalue problems two new two grid algorithms are proposed for solving the maxwell eigenvalue problem the new methods are based on the two grid methodology recently proposed by xu and zhou math comp 70 2001 pp 17 25 and further developed by hu and cheng math comp 80 2011 pp 1287 1301 for elliptic eigenvalue problems the new two grid schemes reduce the solution of the maxwell eigenvalue problem on a fine grid to one linear indefinite maxwell equation on the same fine grid and an original eigenvalue problem on a much coarser grid the new schemes therefore save total computational cost the error estimates reveals that the two grid methods maintain asymptotically optimal accuracy and the numerical experiments presented confirm the theoretical results

superconvergence analysis of a two grid method for nonlinear hyperbolic equations abstract in this paper the superconvergence analysis of a second order fully discrete scheme with two grid method tgm is studied for the two dimensional nonlinear hyperbolic equations by the bilinear finite element the existence and uniqueness of the solution for the scheme are proved rigorously by use of the combination technique of the interpolation and ritz projection the superclose results in h 1 norm are obtained and the global superconvergence is derived through the interpolated postprocessing approach finally some numerical results are provided to verify the theoretical predictions and show the efficiency of the proposed tgm

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

multicasting multiple correlated sources to multiple sinks over a noisy channel network the problem of network coding for multicasting a single source to multiple sinks has first been studied by ahlswede cai li and yeung in 2000 in which they have established the celebrated max flow min cut theorem on nonphysical information flow over a network of independent channels on the other hand in 1980 han has studied the case with multiple correlated sources and a single sink from the viewpoint of polymatroidal functions in which a necessary and sufficient condition has been demonstrated for reliable transmission over the network this paper presents an attempt to unify both cases which leads to establish a necessary and sufficient condition for reliable transmission over a network for multicasting multiple correlated sources to multiple sinks here the problem of separation of source coding and network coding is also discussed

mismatched decoding revisited general alphabets channels with memory and the wide band limit the mismatch capacity of a channel is the highest rate at which reliable communication is possible over the channel with a given possibly suboptimal decoding rule this quantity has been studied extensively for single letter decoding rules over discrete memoryless channels dmcs here we extend the study to memoryless channels with general alphabets and to channels with memory with possibly non single letter decoding rules we also study the wide band limit and in particular the mismatch capacity per unit cost and the achievable rates on an additive noise spread spectrum system with single letter decoding and binary signaling

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

on the sensitivity of continuous time noncoherent fading channel capacity the noncoherent capacity of stationary discrete time fading channels is known to be very sensitive to the fine details of the channel model more specifically the measure of the support of the fading process power spectral density psd determines if noncoherent capacity grows logarithmically with the signal to noise ratio snr or slower than logarithmically such a result is unsatisfactory from an engineering point of view as the support of the psd cannot be determined through measurements the aim of this paper is to assess whether for general continuous time rayleigh fading channels this sensitivity has a noticeable impact on capacity at snr values of practical interest to this end we consider the general class of band limited continuous time rayleigh fading channels that satisfy the wide sense stationary uncorrelated scattering wssus assumption and are in addition under spread we show that for all snr values of practical interest the noncoherent capacity of every channel in this class is close to the capacity of an additive white gaussian noise channel with the same snr and bandwidth independently of the measure of the support of the scattering function the 2 d channel psd our result is based on a lower bound on noncoherent capacity which is built on a discretization of the channel input output relation induced by projecting onto weyl heisenberg sets this approach is interesting in its own right as it yields a mathematically tractable way of dealing with the mutual information between certain continuous time random signals

a two grid method for expanded mixed finite element solution of semilinear reaction diffusion equations we present a scheme for solving two dimensional semilinear reaction diffusion equations using an expanded mixed finite element method to linearize the mixed method equations we use a two grid algorithm based on the newton iteration method the solution of a non linear system on the fine space is reduced to the solution of two small one linear and one non linear systems on the coarse space and a linear system on the fine space it is shown that the coarse grid can be much coarser than the fine grid and achieve asymptotically optimal approximation as long as the mesh sizes satisfy h o h1 3 as a result solving such a large class of non linear equation will not be much more difficult than solving one single linearized equation copyright 2003 john wiley sons ltd

uniformly superconvergent analysis of an efficient two grid method for nonlinear bi wave singular perturbation problem abstract the main aim of this paper is to present a two grid method for the fourth order nonlinear bi wave singular perturbation problem with low order nonconforming finite element based on the ciarlet raviart scheme the existence and uniqueness of the approximation solution are demonstrated through the brouwer fixed point theorem and the uniform superconvergent estimates in the broken h 1 norm and l 2 norm are obtained which are independent of the perturbation parameter some numerical results indicate that the proposed method is indeed an efficient algorithm

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

the capacity of channels with feedback in this paper we introduce a general framework for treating channels with memory and feedback first we prove a general feedback channel coding theorem based on massey s concept of directed information second we present coding results for markov channels this requires determining appropriate sufficient statistics at the encoder and decoder we give a recursive characterization of these sufficient statistics third a dynamic programming framework for computing the capacity of markov channels is presented fourth it is shown that the average cost optimality equation acoe can be viewed as an implicit single letter characterization of the capacity fifth scenarios with simple sufficient statistics are described sixth error exponents for channels with feedback are presented

discrimination on the grassmann manifold fundamental limits of subspace classifiers we derive fundamental limits on the reliable classification of linear and affine subspaces from noisy linear features drawing an analogy between discrimination among subspaces and communication over vector wireless channels we define two shannon inspired characterizations of asymptotic classifier performance first we define the classification capacity which characterizes the necessary and sufficient conditions for vanishing misclassification probability as the signal dimension the number of features and the number of subspaces to be discriminated all approach infinity second we define the diversity discrimination tradeoff which by analogy with the diversity multiplexing tradeoff of fading vector channels characterizes relationships between the number of discernible subspaces and the misclassification probability as the feature noise power approaches zero we derive upper and lower bounds on these quantities which are tight in many regimes numerical results including a face recognition application validate the results in practice

a counter example to the mismatched decoding converse for binary input discrete memoryless channels this paper studies the mismatched decoding problem for binary input discrete memoryless channels an example is provided for which an achievable rate based on superposition coding exceeds the csiszar korner hui rate thus providing a counter example to a previously reported converse result both numerical evaluations and theoretical results are used in establishing this claim

a novel two grid method for semilinear elliptic equations a new finite element discretization technique based on two coarse and fine subspaces is presented for a semilinear elliptic boundary value problem the solution of a nonlinear system on the fine space is reduced to the solution of two small one linear and one nonlinear systems on the coarse space and a linear system on the fine space it is shown both theoretically and numerically that the coarse space can be extremely coarse and still achieve asymptotically optimal approximation as a result the numerical solution of such a nonlinear equation is not significantly more expensive than the solution of one single linearized equation

the capacity of finite state markov channels with feedback we consider a class of finite state markov channels with feedback we first introduce a simplified equivalent channel model and then construct the optimal stationary and nonstationary input processes that maximize the long term directed mutual information furthermore we give a sufficient condition under which the channel s shannon capacity can be achieved by a stationary input process the corresponding converse coding theorem and direct coding theorem are proved

two grid mixed finite element method for nonlinear hyperbolic equations abstract in this paper a combination method of mixed finite element method and two grid scheme is constructed for solving numerically the two dimensional nonlinear hyperbolic equations in this approach the nonlinear system is solved on a coarse mesh with width h and the linear system is solved on a fine mesh with width h h it is proved that the coarse grid can be much coarser than the fine grid the two grid methods achieve asymptotically optimal approximation as long as the mesh sizes h o h 1 2 in the first algorithm and h o h 1 4 in the second algorithm respectively error estimates are derived in detail finally two numerical examples are carried out to verify the accuracy and efficiency of the presented method

a linear program for the finite block length converse of polyanskiy poor verdu via nonsignaling codes motivated by recent work on entanglement assisted codes for sending messages over classical channels the larger easily characterized class of nonsignaling codes is defined analyzing the optimal performance of these codes yields an alternative proof of the finite block length converse of polyanskiy poor and verdu and shows that they achieve this converse this provides an explicit formulation of the converse as a linear program which has some useful features for discrete memoryless channels it is shown that nonsignaling codes attain the channel capacity with zero error probability if and only if the dispersion of the channel is zero

evolutionary variational inequalities arising in viscoelastic contact problems we consider a class of evolutionary variational inequalities arising in various frictional contact problems for viscoelastic materials under the smallness assumption of a certain coefficient we prove an existence and uniqueness result using banach s fixed point theorem we then study two numerical approximation schemes of the problem a semidiscrete scheme and a fully discrete scheme for both schemes we show the existence of a unique solution and derive error estimates finally all these results are applied to the analysis and numerical approximations of a viscoelastic frictional contact problem with the finite element method used to discretize the spatial domain

epsilon capacity of binary symmetric averaged channels we consider the channel model obtained by averaging binary symmetric channel bsc components with respect to a weighting distribution a nonempty open interval a b is called a capacity gap for this channel model if no channel component has capacity in a b and this property fails for every open interval strictly containing a b for a fixed epsi 0 suppose one wishes to compute the epsi capacity of the channel which is the maximum asymptotic rate at which the channel can be encoded via a sequence of channel codes each achieving block error probability lesepsi in 1963 parthasarathy provided a formula for epsi capacity which is valid for all but at most countably many values of epsi when the formula fails there exists a unique capacity gap a b such that the epsi capacity lies in a b but one does not know precisely where via a coding theorem and converse we establish a formula for computing epsi capacity as a function of the endpoints a b of the associated capacity gap a b the formula holds whenever the capacity gap is sufficiently narrow in width

a formula for the capacity of the general gel fand pinsker channel we consider the gel fand pinsker problem in which the channel and state are general i e possibly non stationary non memoryless and non ergodic using the information spectrum method and a non trivial modification of the piggyback coding lemma by wyner we prove that the capacity can be expressed as an optimization over the difference of a spectral inf and a spectral sup mutual information rate we consider various specializations including the case where the channel and the state are memoryless but not necessarily stationary

a lower bound on the probability of error in multihypothesis testing consider two random variables x and y where x is finitely or countably infinitely valued and where y is arbitrary let spl epsiv denote the minimum probability of error incurred in estimating x from y it is shown that spl epsiv spl ges sub 0 spl les spl alpha spl les 1 sup sup 1 spl alpha p spl pi x y spl les spl alpha where spl pi x y denotes the posterior probability of x given y this bound finds information theoretic applications in the proof of converse channel coding theorems it generalizes and strengthens previous lower bounds due to shannon and to verdu and han 1994

saddle point in the minimax converse for channel coding a minimax metaconverse has recently been proposed as a simultaneous generalization of a number of classical results and a tool for the nonasymptotic analysis in this paper it is shown that the order of optimizing the input and output distributions can be interchanged without affecting the bound in the course of the proof a number of auxiliary results of separate interest are obtained in particular it is shown that the optimization problem is convex and can be solved in many cases by the symmetry considerations as a consequence it is demonstrated that in the latter cases the multiletter input distribution in information spectrum verdu han converse bound can be taken to be a memoryless product of single letter ones a tight converse for the binary erasure channel is rederived by computing the optimal nonproduct output distribution for discrete memoryless channels a conjecture of poor and verdu regarding the tightness of the information spectrum bound on the error exponents is resolved in the negative concept of the channel symmetry group is established and relations with the definitions of symmetry by gallager and dobrushin are investigated