worst case input output identification we consider worst case l1 identification of causal linear shift invariant systems from time series many results are given on general aspects of identification algorithm performance existence of optimal algorithms robust convergence and input experiment design the identification methodology studied here is compatible with the modelling requirements of modern robust control design

error exponents for dimension matched vector multiple access channels with additive noise we analyze a class of vector multiple access channels with additive noise where the sum of the dimensions of the transmitted signals matches that of the received signal we first focus on the case without power constraints in the poltyrev sense using point process techniques we find the poltyrev capacity region for noise processes that are independent and identically distributed over channel uses for each rate vector strictly in the poltyrev capacity region we study for each subset of the transmitters the exponent of the decay in block length of the smallest possible probability that decoding results in error for each transmitter in that subset in the case of independent and identically distributed gaussian noise with arbitrary positive definite covariance matrix we derive random coding exponents for each type of error event these are lower bounds to the true error exponents this also leads to random coding error exponents in the traditional power constrained case where the power constraint at each transmitter is defined by an arbitrary positive definite matrix

multiuser random coding techniques for mismatched decoding this paper studies multiuser random coding techniques for channel coding with a given possibly suboptimal decoding rule for the mismatched discrete memoryless multiple access channel an error exponent is obtained that is tight with respect to the ensemble average and positive within the interior of lapidoth s achievable rate region this exponent proves the ensemble tightness of the exponent of liu and hughes in the case of maximum likelihood decoding an equivalent dual form of lapidoth s achievable rate region is given and the latter is shown to immediately extend to channels with infinite and continuous alphabets in the setting of single user mismatched decoding similar analysis techniques are applied to a refined version of superposition coding which is shown to achieve rates at least as high as standard superposition coding for any set of random coding parameters

a fixed grid finite element technique for modelling phase change in steady state conduction advection problems a new fixed grid finite element technique for modelling phase change effects in steady state conduction advection problems is described the method is appropriate for materials that transform at a fixed critical temperature and is based on the assumption that the enthalpy experiences a jump discontinuity at this temperature yielding a singular specific heat this singularity is described using a dirac delta function and the appropriate finite element matrix equations are developed for isoparametric elements a simple first order upwinding scheme is used to avoid numerical oscillations in advection dominated problems the utility of the method is illustrated through the solution of a one dimensional test problem using eight node hexahedral isoparametric finite elements the technique may be applied to a wide range of finite element types and offers a number of advantages over other schemes for modelling phase change effects

optimum power control at finite blocklength this paper investigates the maximal channel coding rate achievable at a given blocklength n and error probability epsilon when the codewords are subjected to a long term i e averaged over all codeword power constraint the second order term in the large n expansion of the maximal channel coding rate is characterized both for additive white gaussian noise awgn channels and for quasi static fading channels with perfect channel state information available at both the transmitter and the receiver it is shown that in both the cases the second order term is proportional to n 1 ln n 1 2 for the quasi static fading case this second order term is achieved by truncated channel inversion namely by concatenating a dispersion optimal code for an awgn channel subject to a short term power constraint with a power controller that inverts the channel whenever the fading gain is above a certain threshold easy to evaluate approximations of the maximal channel coding rate are developed for both the awgn and the quasi static fading case

optimal sampling schedule for parameter estimation of linear models with unknown but bounded measurement errors the problem of optimal sampling design for parameter estimation when data are generated by linear models is addressed the measurements are assumed to be corrupted by an unknown but bounded additive noise the sampling design assumes that the number of samples is unconstrained and no replication is allowed two main results are shown 1 for particular classes of linear models the optimal number of measurements is equal to the number of parameters as in the statistical context 2 the uncertainty intervals of the parameter estimates are bounded from above by quantities that can be computer a priori knowing only the model and the error structure

the method of types information theory the method of types is one of the key technical tools in shannon theory and this tool is valuable also in other fields in this paper some key applications are presented in sufficient detail enabling an interested nonspecialist to gain a working knowledge of the method and a wide selection of further applications are surveyed these range from hypothesis testing and large deviations theory through error exponents for discrete memoryless channels and capacity of arbitrarily varying channels to multiuser problems while the method of types is suitable primarily for discrete memoryless models its extensions to certain models with memory are also discussed

on the stability of viscous free surface flow supported by a rotating cylinder using an adaptive finite element fe scheme developed recently by the authors we shed new light on the long standing fundamental problem of the unsteady free surface stokes flow exterior to a circular cylinder rotating about its horizontal axis in a vertical gravitational field for supportable loads we observe that the steadystate is more readily attained for near maximal fluid loads on the cylinder than for significantly sub maximal loads for the latter we investigate large time dynamics by means of a finite difference approximation to the thin film equations which is also used to validate the adaptive fe simulations applied to the full stokes equations for these significantly sub maximal loads conversely by comparing results of the two methods we assess the validity of the thin film approximation as either the load is increased or the rotation rate of the cylinder is decreased results are presented on the independent effects of gravity surface tension and initial film thickness on the decay to steady state finally new numerical simulations of load shedding are presented

space time finite element techniques for computation of fluid structure interactions we describe the space time finite element techniques we developed for computation of fluid structure interaction fsi problems among these techniques are the deforming spatial domain stabilized space time dsd sst formulation and its special version and the mesh update methods including the solid extension mesh moving technique semmt also among these techniques are the block iterative quasi direct and direct coupling methods for the solution of the fully discretized coupled fluid and structural mechanics equations we present some test computations for the mesh moving techniques described we also present numerical examples where the fluid is governed by the navier stokes equations of incompressible flows and the structure is governed by the membrane and cable equations overall we demonstrate that the techniques we have developed have increased the scope and accuracy of the methods used in computation of fsi problems 2005 elsevier b v all rights reserved

highly efficient oscillation free solution of the transport equation over long times and large spaces transport problems with sharp transitions or high convection often stress even the most advanced computational methods beyond feasibility limits one promising line of attack involves transforming problems to a moving deforming coordinate system mdcs using mdcs as recently developed one may concentrate computational attention when and where it is most appropriate also possibly greatly reducing the effective magnitude of terms which cause trouble in principle mdcs may be used with finite difference finite element or other numerical methods according to preference in the particular finite element system advanced here mesh movement may be variable in time and space so that physically fixed boundaries may remain fixed in the transformed coordinate system a simple finite difference system is used in time when the method is applied to the standard transport equation test case great efficiency and accuracy are obtained in early time even very steep fronts may be represented well with no oscillations using space and time step sizes well beyond conventional peclet courant number constraints more important problems are solved involving transport over much longer times and larger spaces when diffusion has some chance to operate and hence a parabolic model is more warranted the same accuracy and stability are achieved as during early time using no more nodes and time steps overall than during early time runs this constitutes orders of magnitude savings in effort over what the application of conventional constraints would require relative efficiency from application of mdcs to other problems would depend on the particulars of each case

mesh independent spectra in the moving finite element equations we derive the moving finite element mfe equations for the solution of a scalar evolutionary equation in d space dimensions d geqq 1 and introduce the elementwise approach to mfe this approa

optimal estimation theory for dynamic systems with set membership uncertainty an overview in many problems such as linear and nonlinear regressions parameter and state estimation of dynamic systems state space and time series prediction interpolation smoothing and functions approximation one has to evaluate some unknown variable using available data the data are always associated with some uncertainty and it is necessary to evaluate how this uncertainty affects the estimated variables typically the problem is approached assuming a probabilistic description of uncertainty and applying statistical estimation theory an interesting alternative approach referred to as set membership or unknown but bounded ubb error description has been investigated since the late 1960s in this approach uncertainty is described by an additive noise which is known only to have given integral typically l2 of l1 or componentwise l bounds in this paper we review the main results of this theory with special attention to the most recent advances obtained in the case of componentwise bounds

boundary integral equation solution of moving boundary phase change problems boundary integral equation methods are presented for the solution of some two dimensional phase change problems convection may enter through boundary conditions but cannot be considered within phase boundaries a general formulation based on space time green s functions is developed using the complete heat equation followed by a simpler formulation using the laplace equation the latter is pursued and applied in detail an elementary noniterative system is constructed featuring linear interpolation over elements on a polygonal boundary nodal values of the temperature gradient normal to a phase change boundary are produced directly in the numerical solution the system performs well against basic analytical solutions using these values in the interphase jump condition with the simplest formulation of the surface normal at boundary vertices because the discretized surface changes automatically to fit the scale of the problem the method appears to offer many of the advantages of moving mesh finite element methods however it only requires the manipulation of a surface mesh and solution for surface variables in some applications coarse meshes and very large time steps may be used relative to those which would be required by fixed grid domain methods computations are also compared to original lab data describing two dimensional soil freezing with a time dependent boundary condition agreement between simulated and measured histories is good

temporal derivatives in the finite element method on continuously deforming grids when solving certain time dependent partial differential equations using a finite element technique on a deforming grid it is shown that there is a need to differentiate the trial solution with respect to the position of each of the moveable node points a result is presented which enables these nonstandard derivatives to be expressed in terms of the standard spatial derivatives of the trial functions provided that certain conditions are satisfied these conditions are investigated and shown to be satisfied for a large class of trial spaces even when the necessary conditions are not satisfied by all of the trial functions being used the result is shown to be still of great use in evaluating these awkward nodal derivatives 1 u x t y u x t a u

coded modulation with mismatched csit over mimo block fading channels reliable communication over delay constrained multiple input multiple output mimo block fading channels with discrete inputs and mismatched imperfect channel state information at the transmitter csit is studied the csit mismatch is modeled as gaussian random variables whose variances decay as a power of the signal to noise ratio snr a special focus is placed on the large snr decay of the error and outage probabilities when power control with long term power constraints is used without explicitly characterizing the corresponding power allocation algorithms we derive the outage exponent as a function of the system parameters including the csit noise variance exponent and the exponent of the peak power constraint it is shown that csit even if noisy is always beneficial and leads to important gains in terms of exponents

a best approximation property of the moving finite element method the moving finite element method mfe for the solution of time dependent partial differential equations pdes is a numerical solution scheme which allows the automatic adaption of the finite element approximation space with time an analysis of how this method models the steady solutions of a general class of parabolic linear source equations is presented it is shown that under certain conditions the steady solutions of the mfe problem can correspond to best free knot spline approximations to the true steady solution of the differential equation when using the natural norm associated with the problem hence a quantitative measure of the advantages of the mfe method over the usual fixed grid galerkin method is produced for these equations a number of numerical examples are included to illustrate these results

bounds on the decoding error probability of binary linear codes via their spectra bounds on the error probability of maximum likelihood decoding of a binary linear code are considered the bounds derived use the weight spectrum of the code and they are tighter than the conventional union bound in the case of large noise in the channel the bounds derived are applied to a code with an average spectrum and the result is compared to the random coding exponent the author shows that the bound considered for the binary symmetrical channel case coincides asymptotically with the random coding bound for the case of awgn channel the author shows that berlekamp s 1980 tangential bound can be improved but even this improved bound does not coincide with the random coding bound although it can be very close to it

flair fluz line segment model for advection and interface reconstruction abstract a computational technique for solving fluid problems with free surfaces and interfaces is presented the conventional cell volume fraction approach is employed for tracking the interfaces however for surface advection and its reconstruction a new and more accurate flair flux line segment model for advection and interface reconstruction algorithm is developed the surface is approximated by a set of line segments fitted at the boundary of every two neighboring computational cells a criterion is developed for identifying the line segment orientation by inspecting the cell volume fractions the new cell volume fraction field is obtained by integrating the advected area underneath the interface line segment as an example this technique is applied to the capillary driven viscous flow of an initially elliptic two dimensional fluid zone the problem is posed mathematically as a solution of the navier stokes equations with moving free surface boundary conditions the damping motion of the fluid zone is observed through transport of the free surface which is related to the instantaneous internal velocity field under the influence of surface tension and viscous forces

amplify and forward two way relay networks error exponents and resource allocation in a two way relay network two terminals exchange information over a shared wireless half duplex channel with the help of a relay due to its fundamental and practical importance there has been an increasing interest in this channel however there has been little work that characterizes the fundamental tradeoff between the communication reliability and transmission rate across all signal to noise ratios in this paper we consider amplify and forward af two way relaying due to its simplicity we first derive the random coding error exponent for the link in each direction from the exponent expression the capacity and cutoff rate for each link are also deduced we then put forth the notion of bottleneck error exponent which is the worst exponent decay between the two links to give us insight into the fundamental tradeoff between the rate pair and information exchange reliability in the two way relay network as applications of the error exponent analysis to design a reliable af two way relay network we present two optimization framework to maximize the bottleneck error exponent namely i the optimal rate allocation under a sum rate constraint and its closed form quasi optimal solution that requires only knowledge of the capacity and cutoff rate of each link and ii the optimal power allocation under a total power constraint and perfect global channel state information which is shown equivalently to a quasi convex optimization problem numerical results verify our analysis and the effectiveness of the optimal rate and power allocations in maximizing the bottleneck error exponent i e the network information exchange reliability

experiment design in a bounded error context comparison with d optimality abstract the problem of optimal experiment design for linear regression models is addressed the measurement errors are supposed to be bounded with no other hypothesis on their distribution contrary to the classical statistical approach an experiment is considered here as optimal if it minimizes the volume of the set of all parameters that are consistent with the data the model structure and the noise bounds this new design policy is compared to the classical d optimal design used in a statistical context when the number of measurements is equal to the number of parameters to be estimated the new optimality criterion although relying on quite different hypotheses on the noise distribution is shown to lead to the same optimal policy as a d optimality criterion this is no longer true when more measurements are to be made depending on the shape of the admissible experimental domain it is sometimes possible to design optimal experiments without any calculations an algorithmic procedure is suggested to be used when this is not so

on the value of information in system identification bounded noise case assuming instantaneous bounds on the noise system parameter identification is formulated as membership set estimation problem sequential algorithms are constructed to estimate the membership sets of the parameters which are consistent with the measurements and the noise constraints the important new feature of the proposed algorithms is their ability to ignore redundant data the efficient data extraction property of the new algorithms is achieved with small computational effort and with improved performance when compared to the least square algorithm the convergence properties and the notion of identifiability in the set theoretic context are also studied

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

on the reliability function of the discrete memoryless relay channel bounds on the reliability function for the discrete memoryless relay channel are derived using the method of types two achievable error exponents are derived based on partial decode forward and compress forward which are well known superposition block markov coding schemes the derivations require combinations of the techniques involved in the proofs of csiszar korner marton s packing lemma for the error exponent of channel coding and marton s type covering lemma for the error exponent of source coding with a fidelity criterion the decode forward error exponent is evaluated on sato s relay channel from this example it is noted that to obtain the fastest possible decay in the error probability for a fixed effective coding rate one ought to optimize the number of blocks in the block markov coding scheme assuming the blocklength within each block is large an upper bound on the reliability function is also derived using ideas from haroutunian s lower bound on the error probability for point to point channel coding with feedback

identification and application of bounded parameter models abstract the place of parameter bounding algorithms in identification methodology is discussed such algorithms provide a radical alternative to the computation of parameter point estimates and covariances instead of p d f or mean and covariance for the noise and prior parameter estimates they require bounds in an essentially deterministic model formulation the paper is a preliminary review of some standard tasks namely experiment design testing for outliers toleranced prediction and worst case control design in the context of parameter bounding identification computational requirements of these tasks are examined and the limitations of existing parameter bounding algorithms are noted

moving boundary moving mesh analysis of phase change using finite elements with transfinite mappings two dimensional heat conduction phase change problems are solved using a moving boundary moving mesh approach a transfinite mapping technique successfully controls interior mesh motion and numerical results compare well with analytical solutions calculations also agree well with two dimensional laboratory data for cases featuring time dependent boundary conditions

equidistributing principles in moving finite element methods abstract recently miller and his co workers proposed a moving finite element method based on a least squares principle this was followed by a similar method by the present authors using a petrov galerkin approach in this paper the two methods are compared in particular it is shown that both methods move their nodes according to an approximate equidistributing principle this observation leads to a criterion for the placement of the nodes it is also shown that the penalty function designed by miller may also be used with the petrov galerkin method finally numerical examples are given illustrating the performance of the two methods

moving finite element methods for evolutionary problems i theory abstract in this paper the first of two on the subject we present a unified approach to moving and fixed finite element methods for evolutionary problems in terms of projections the central theoretical results are concerned with moving finite elements for one dimensional scalar problems particularly hyperbolic equations with shocks but the viewpoint extends to general systems in any number of dimensions

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

lossy joint source channel coding in the finite blocklength regime this paper finds new tight finite blocklength bounds for the best achievable lossy joint source channel code rate and demonstrates that joint source channel code design brings considerable performance advantage over a separate one in the nonasymptotic regime a joint source channel code maps a block of k source symbols onto a length n channel codeword and the fidelity of reproduction at the receiver end is measured by the probability e that the distortion exceeds a given threshold d for memoryless sources and channels it is demonstrated that the parameters of the best joint source channel code must satisfy nc kr d nv k v d q 1 e where c and v are the channel capacity and channel dispersion respectively r d and v d are the source rate distortion and rate dispersion functions and q is the standard gaussian complementary cumulative distribution function symbol by symbol uncoded transmission is known to achieve the shannon limit when the source and channel satisfy a certain probabilistic matching condition in this paper we show that even when this condition is not satisfied symbol by symbol transmission is in some cases the best known strategy in the nonasymptotic regime

channel coding rate in the finite blocklength regime this paper investigates the maximal channel coding rate achievable at a given blocklength and error probability for general classes of channels new achievability and converse bounds are given which are tighter than existing bounds for wide ranges of parameters of interest and lead to tight approximations of the maximal achievable rate for blocklengths n as short as 100 it is also shown analytically that the maximal rate achievable with error probability isclosely approximated by c v n q 1 where c is the capacity v is a characteristic of the channel referred to as channel dispersion and q is the complementary gaussian cumulative distribution function

a study on universal codes with finite block lengths based on random codes and typical set decoding an alternative proof of root and varaiya s compound channel coding theorem for linear gaussian channels is presented the performance limit of codes with finite block length under a compound channel is studied through error bounds and simulation although the theorem promises uniform convergence of the probability of error as the block length approaches infinity with short block lengths the performance can differ considerably for individual channels simulation results show that universal performance can be a practical goal as the block lengths become large

parallel finite element computations in fluid mechanics we provide an overview of the role of parallel finite element computations in fluid mechanics we emphasize the class of flow problems involving moving boundaries and interfaces some of the computationally most challenging flow problems such as fluid object and fluid structure interactions as well as free surface and two fluid flows belong to this class in the development of the methods targeting this class of problems the computational challenges involved need to be addressed in such a way that 3d computation of complex applications can be carried out efficiently on parallel computers this requirement has to be one of the key factors in designing various components of the overall solution approach such as solution techniques for the discretized equations and mesh update methods for handling the changes in the spatial domain occupied by the fluid this overview includes a description of how the computational challenges are addressed and how the computational schemes can be enhanced with special preconditioning techniques 2005 elsevier b v all rights reserved

quasi static multiple antenna fading channels at finite blocklength this paper investigates the maximal achievable rate for a given blocklength and error probability over quasi static multiple input multiple output fading channels with and without channel state information at the transmitter and or the receiver the principal finding is that outage capacity despite being an asymptotic quantity is a sharp proxy for the finite blocklength fundamental limits of slow fading channels specifically the channel dispersion is shown to be zero regardless of whether the fading realizations are available at both transmitter and receiver at only one of them or at neither of them these results follow from analytically tractable converse and achievability bounds numerical evaluation of these bounds verifies that zero dispersion may indeed imply fast convergence to the outage capacity as the blocklength increases in the example of a particular 1 times 2 single input multiple output rician fading channel the blocklength required to achieve 90 of capacity is about an order of magnitude smaller compared with the blocklength required for an awgn channel with the same capacity for this specific scenario the coding decoding schemes adopted in the lte advanced standard are benchmarked against the finite blocklength achievability and converse bounds

bounds on capacity and minimum energy per bit for awgn relay channels upper and lower bounds on the capacity and minimum energy per bit for general additive white gaussian noise awgn and frequency division awgn fd awgn relay channel models are established first the max flow min cut bound and the generalized block markov coding scheme are used to derive upper and lower bounds on capacity these bounds are never tight for the general awgn model and are tight only under certain conditions for the fd awgn model two coding schemes that do not require the relay to decode any part of the message are then investigated first it is shown that the side information coding scheme can outperform the block markov coding scheme it is also shown that the achievable rate of the side information coding scheme can be improved via time sharing in the second scheme the relaying functions are restricted to be linear the problem is reduced to a single letter nonconvex optimization problem for the fd awgn model the paper also establishes a relationship between the minimum energy per bit and capacity of the awgn relay channel this relationship together with the lower and upper bounds on capacity are used to establish corresponding lower and upper bounds on the minimum energy per bit that do not differ by more than a factor of 1 45 for the fd awgn relay channel model and 1 7 for the general awgn model

delay constrained capacity with causal feedback a block fading channel model is considered and a k block delay constraint is imposed on data transmission the key consideration is that the channel state information is fed back to the transmitter in a causal manner a general cost function spl mu x is considered in solving the delay constrained transmission problem under the short term and the long term power constraints a causal power adaptation strategy is needed to maximize the cost function hence dynamic programming is found to give the optimum solution the general cost function is then specialized to the cases of expected and outage capacities in the case of expected capacity it is observed that optimizing the transmitted power does not give much benefit at high signal to noise ratio snr but provides a substantial gain at low snr at low snr it is proved that the capacity increases by a factor of approximately log k m due to power adaptation when the channel fades according to the spl chi sub 2m sup 2 statistics in the case of outage capacity it is shown that the optimum power adaptation solution to the long term constraint problem provides a substantial snr gain at both low and high values of snr random coding bounds are derived for the outage capacity algorithms

a characteristic finite element scheme for convective dispersive transport with non equilibrium reaction a finite element method coupled with the method of characteristics is applied to the problem of convective dispersive transport with non equilibrium reaction convective terms are calculated using moving particles together with influence element meshes for particle tracking whereas dispersion terms are calculated by means of finite element techniques the contribution from the term of non equilibrium reaction is incorporated into the algebraic equations by the use of analytical solutions to the equation of non equilibrium reaction for each time step and extended simpson s numerical integrations comparison of the numerical results from the proposed procedure with analytical solutions to the simultaneous partial differential equations shows good agreement for the wide spectrum ranging from dispersion to convection dominated transport with various reaction parameters

moving finite elements i we present new and general numerical methods for dealing with problems whose solutions develop sharp transition layers or near shocks these methods allow many nodes automatically to concentrate in the critical regions and move with them for clarity of exposition we concentrate on the space of piecewise linear functions with movable nodes with burgers equation as our test equation but the generalization to much more general spaces and equations including even certain previous moving vorticity blobs of the first author and s doss for the navier stokes equations becomes clear in this paper we present the theoretical and computational details of our scheme along with computational trial runs for burgers equation showing that the nodes do concentrate sharply and move with the shocks as desired the conclusiveness of these preliminary numerical trials is marred somewhat by the fact that we never successfully debugged a newton s method for our implicit stiff ode solver and were thus limited to ver

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

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

short packet communications over multiple antenna rayleigh fading channels motivated by the current interest in ultra reliable low latency machine type communication systems we investigate the tradeoff between reliability throughput and latency in the transmission of information over multiple antenna rayleigh block fading channels specifically we obtain finite blocklength finite snr upper and lower bounds on the maximum coding rate achievable over such channels for a given constraint on the packet error probability numerical evidence suggests that our bounds delimit tightly the maximum coding rate already for short blocklengths packets of about 100 symbols furthermore our bounds reveal the existence of a tradeoff between the rate gain obtainable by spreading each codeword over all available time frequency spatial degrees of freedom and the rate loss caused by the need of estimating the fading coefficients over these degrees of freedom in particular our bounds allow us to determine the optimal number of transmit antennas and the optimal number of time frequency diversity branches that maximize the rate finally we show that infinite blocklength performance metrics such as the ergodic capacity and the outage capacity yield inaccurate throughput estimates

optimal asymptotic identification under bounded disturbances the intrinsic limitation of worst case identification of linear time invariant systems using data corrupted by bounded disturbances when the unknown plant is known to belong to a given model set is studied this is done by analyzing the optimal worst case asymptotic error achievable by performing experiments using any bounded input and estimating the plant using any identification algorithm it is shown that under some topological conditions on the model set there is an identification algorithm which is asymptotically optimal for any input and the optimal asymptotic error is characterized as a function of the inputs these results which hold for any error metric and disturbance norm are applied to three specific identification problems identification of stable systems in the l sub 1 norm identification of stable rational systems in the h sub infinity norm and identification of unstable rational systems in the gap metric for each of these problems the general characterization of optimal asymptotic error is used to find near optimal inputs to minimize the error

on the expected rate of slowly fading channels with quantized side information we study a multiple layer variable rate system employing quantized feedback to maximize the expected rate over a single input single output slowly fading gaussian channel the transmitter uses partial channel state information which is obtained via an optimized resolution constrained feedback link to adapt the power and to assign code layer rates subject to different power constraints to systematically design the system parameters we develop a simple iterative algorithm that successfully exploits results in the study of parallel broadcast channels we present the necessary and sufficient conditions for single layer coding to be optimal irrespective of the number of code layers that the system can afford unlike in the ergodic case even coarsely quantized feedback is shown to improve the expected rate considerably our results also indicate that with as little as one bit of feedback information the role of multilayer coding reduces significantly

communication over fading channels with delay constraints we consider a user communicating over a fading channel with perfect channel state information data are assumed to arrive from some higher layer application and are stored in a buffer until transmitted we study adapting the user s transmission rate and power based on the channel state information as well as the buffer occupancy the objectives are to regulate both the long term average transmission power and the average buffer delay incurred by the traffic two models for this situation are discussed one corresponding to fixed length variable rate codewords and one corresponding to variable length codewords the tradeoff between the average delay and the average transmission power required for reliable communication is analyzed a dynamic programming formulation is given to find all pareto optimal power delay operating points we then quantify the behavior of this tradeoff in the regime of asymptotically large delay in this regime we characterize simple buffer control policies which exhibit optimal characteristics connections to the delay limited capacity and the expected capacity of fading channels are also discussed

sphere packing bounds revisited for moderate block lengths the main reference of this paper is the sphere packing bound of 1967 sp67 derived by shannon gallager and berlekamp it offers a lower bound on the decoding error probability over a very large variety of channels if it has failed so far to provide any usable material in practical implementation of telecommunication systems it is due to an original focus on asymptotic results making it inapplicable for moderate code lengths and to the difficulty of the involved methods which makes the derivation of sp67 quite hermetic and uninspiring for further research the purpose of this paper is two fold 1 to stir up some renewed interest in the topic on which shannon concluded his career in information theory thanks to a qualitative rather than technical review of the derivation of sp67 introduced by a review of the simpler sphere packing bound derived by shannon in 1959 2 to prove the practical interest of sp67 by extending its field of application to continuous output channels and particularly the additive white gaussian noise awgn channel used with any particular modulation scheme and by improving its lower bound for the moderate code length case so that it becomes the best lower bound for most iteratively decodable codes turbo codes low density parity check ldpc codes repeat accumulate ra codes etc of usual lengths

a constrained moving finite element solution of the one dimensional oxygen diffusion with absorption problem abstract we derive an adaptive finite element method for the numerical solution of a one dimensional implicit moving boundary problem the oxygen diffusion with absorption problem of crank and gupta the method which includes a moving grid and incorporates an iteration for the velocity of the moving boundary produces good results over a range of parameters we present numerical and graphical results in one dimension and indicate an extension of the method to two dimensions

a conserving discretization for the free boundary in a two dimensional stefan problem the dissolution of a disk likeal2cuparticle is considered a characteristic property is that initially the particle has a nonsmooth boundary the mathematical model of this dissolution process contains a description of the particle interface of which the position varies in time such a model is called a stefan problem it is impossible to obtain an analytical solution for a general two dimensional stefan problem so we use the finite element method to solve this problem numerically first we apply a classical moving mesh method computations show that after some time steps the predicted particle interface becomes very unrealistic therefore we derive a new method for the displacement of the free boundary based on the balance of atoms this method leads to good results also for nonsmooth boundaries some numerical experiments are given for the dissolution of anal2cuparticle in anal cualloy

graph decomposition a new key to coding theorems a new and simple method is proposed for finding good encoders both for channels and for sources with side information this method relies on the continuous version of a graph decomposition result of lovasz the presently known best exponential error bounds for both problems follow in a unified manner with an improvement on the source coding bound the previous bounds for universal codes of the authors and marton are also improved

high order finite element methods for moving boundary problems with prescribed boundary evolution abstract we introduce a framework for the design of finite element methods for two dimensional moving boundary problems with prescribed boundary evolution that have arbitrarily high order of accuracy both in space and in time at the core of our approach is the use of a universal mesh a stationary background mesh containing the domain of interest for all times that adapts to the geometry of the immersed domain by adjusting a small number of mesh elements in the neighborhood of the moving boundary the resulting method maintains an exact representation of the prescribed moving boundary at the discrete level or an approximation of the appropriate order yet is immune to large distortions of the mesh under large deformations of the domain the framework is general making it possible to achieve any desired order of accuracy in space and time by selecting a preferred and suitable finite element space on the universal mesh for the problem at hand and a preferred and suitable time integrator for ordinary differential equations we illustrate our approach by constructing a particular class of methods and apply them to a prescribed boundary variant of the stefan problem we present numerical evidence for the order of accuracy of our schemes in one and two dimensions

feedback in the non asymptotic regime without feedback the backoff from capacity due to non asymptotic blocklength can be quite substantial for blocklengths and error probabilities of interest in many practical applications in this paper novel achievability bounds are used to demonstrate that in the non asymptotic regime the maximal achievable rate improves dramatically thanks to variable length coding and feedback for example for the binary symmetric channel with capacity 1 2 the blocklength required to achieve 90 of the capacity is smaller than 200 compared to at least 3100 for the best fixed blocklength code even with noiseless feedback virtually all the advantages of noiseless feedback are shown to be achievable even if the feedback link is used only to send a single signal informing the encoder to terminate the transmission stop feedback it is demonstrated that the non asymptotic behavior of the fundamental limit depends crucially on the particular model chosen for the end of packet control signal fixed blocklength codes and related questions concerning communicating with a guaranteed delay are discussed in which situation feedback is demonstrated to be almost useless even non asymptotically

achievable rates for gaussian degraded relay channels with non vanishing error probabilities this paper revisits the gaussian degraded relay channel where the link that carries information from the source to the destination is a physically degraded version of the link that carries information from the source to the relay the source and the relay are subject to expected power constraints the varepsilon capacity of the channel is characterized and it is strictly larger than the capacity for any varepsilon 0 which implies that the channel does not possess the strong converse property the proof of the achievability part is based on several key ideas block markov coding which is used in the classical decode forward strategy power control for gaussian channels under expected power constraints and a careful scaling between the block size and the total number of block uses the converse part is proved by first establishing two non asymptotic lower bounds on the error probability which are derived from the type ii errors of some binary hypothesis tests subsequently each lower bound is simplified by conditioning on an event related to the power of some linear combination of the codewords transmitted by the source and the relay lower and upper bounds on the second order term of the optimal coding rate are also obtained

finite element analysis of diffusion with reaction at a moving boundary abstract we consider the model problem of mass transport by diffusion with chemical reaction at a moving boundary the objective is to model the chemical process by predicting the location of the boundary as the reaction proceeds in time a finite element analysis is formulated in one dimension using moving elements to follow the boundary motion and an iterative linearization method is developed to uncouple and solve the diffusion and reaction equations the semidiscrete system for the transport process is integrated using a predictor corrector scheme and its accuracy and stability are examined in numerical experiments numerical results are compared with an analytic solution for the quasi steady case in which diffusion is very rapid in comparison to reaction and to a perturbation solution for the unsteady case other supporting numerical studies are made to examine the sensitivity of the solution and boundary motion to changes in diffusion and reaction rate for both linear and nonlinear reactions

mesh deformation using the biharmonic operator the use of the biharmonic operator for deforming a mesh in an arbitrary lagrangian eulerian simulation is investigated the biharmonic operator has the advantage that two conditions can be specified on each boundary of the mesh this allows both the position and the normal mesh spacing along a boundary to be controlled which is important for two fluid interfaces and periodic boundaries at these boundaries we can simultaneously fix the position of the boundary and ensure that the normal mesh spacing is continuous across the boundary in addition results for deforming surfaces show that greater surface deformation can be tolerated when using biharmonic equations compared to approaches using second order partial differential equations a final advantage is that with the biharmonic operator the integrity of a grid in a moving boundary layer can be preserved as the boundary moves the main disadvantage of the approach is its increased computational expense

reliability in source coding with side information we study error exponents for source coding with side information both achievable exponents and converse bounds are obtained for the following two cases lossless source coding with coded information and lossy source coding with full side information wyner ziv these results recover and extend several existing results on source coding error exponents and are tight in some circumstances our bounds have a natural interpretation as a two player game between nature and the code designer with nature seeking to minimize the exponent and the code designer seeking to maximize it in the wyner ziv problem our analysis exposes a tension in the choice of test channel with the optimal test channel balancing two competing error events the gaussian and binary erasure cases are examined in detail

a direct method for solving two dimensional one phase stefan problems abstract a new algorithm is proposed for solving the stefan problem for the case when the initial region occupied by the medium in a given phase is a starshaped two dimensional domain the evolution of this region as time increases is determined by plotting the free boundary directly at each time step this is approximated by a polygon in the interior of which the heat equation is solved with piecewise linear finite elements numerical experiments indicate that the method is stable and that convergence is to be expected under suitable assumptions on the regularity of both the boundary and initial data of the problem

unified approach to simulation on deforming elements with application to phase change problems abstract several different approaches to simulation on deforming finite elements are shown to generate the same weighted residuals formulation for the evolution of the dependent variables control of node motion by means of mesh stretching in two dimensions is illustrated in the context of phase change problems simulation of problems with large phase boundary excursions shows good agreement with analytic solutions

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

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

non linear simulation of dendritic solidification of an undercooled melt two dimensional finite element simulations of solidification for quiescent undercooled pure metals are presented the full non linear transient heat equation is used with phase front tracking which is subject to local curvature and interfacial kinetics during early stages of the waveform instability the simulated solutions match the linear stability analysis with fidelity beyond the valid range of that analysis the numerical solution continues to demonstrate the physically observed exponential growth behaviour and characteristic spacing between fingers whereas the simulations show the sensitivity of dendritic growth to initial conditions as expected for an unstable process the overall pattern formation preserves the characteristic spacing the simulations are terminated after the onset of bifurcation thereafter the numerical model is inappropriate for physical comparison owing to the planar two dimensional limitation

an implementation of a moving finite element method abstract the moving finite element method an adaptive gridding procedure for systems of partial differential equations whose solutions contain steep gradients has been implemented in a very straightforward way accurate results can be obtained using fewer nodes than that required by fixed mesh solution methods performance of the method using some minor changes to a standard ordinary differential equation algorithm is illustrated with solutions to burger s equation

an analysis of solidification problems by the boundary element method the problem of interest in this paper is the calculation of the motion of the solid liquid interface and the time dependent temperature field during solidification of a pure metal an iterative implicit algorithm has been developed for this purpose using the boundary element method bem with time dependent green s functions and convolution integrals the bem approach requires discretization of only the surface of the solidifying body thus the numerical method closely follows the physics of the problems and is intuitively very appealing the formulation and the numerical scheme presented here are general and can be applied to a broad range of moving boundary problems emphasis is given to two dimensional problems comparison with existing semi analytical solutions and other numerical solutions from the literature reveals that the method is fast accurate and without major time step limitations

minimum volume ellipsoids containing compact sets application to parameter bounding abstract the problem of finding the minimum volume ellipsoid containing a compact set is shown to be equivalent to the determination of an optimal distribution of weights over several equivalent conditions for optimality of this distribution are obtained and used to construct algorithms guaranteed to converge to the optimum these algorithms can be used to approximate the posterior feasible set for the parameters of a model in the bounded error context linear and nonlinear illustrative examples are treated

coherent multiple antenna block fading channels at finite blocklength in this paper we consider a channel model that is often used to describe mobile wireless scenarios multiple antenna additive white gaussian noise channels subject to random fading gains with full channel state information at the receiver the dynamics of the fading process are approximated by a piecewise constant process frequency non selective isotropic block fading this paper addresses the finite blocklength fundamental limits of this channel model specifically we give a formula for the channel dispersion a quantity governing the delay required to achieve capacity the multiplicative nature of the fading disturbance leads to a number of interesting technical difficulties that required us to enhance traditional methods for finding the channel dispersion alas one difficulty remains the converse impossibility part of our result holds under an extra constraint on the growth of the peak power with blocklength our results demonstrate for example that while the capacities of n t times n r and n r times n t antenna configurations coincide under fixed received power the coding delay can be sensitive to this switch for example at the received snr of 20 db the 16 times 100 system achieves capacity with codes of length delay which is only 60 of the length required for the 100 times 16 system another interesting implication is that for the miso channel the dispersion optimal coding schemes require employing orthogonal designs such as alamouti s scheme a surprising observation considering the fact that alamouti s scheme was designed for reducing demodulation errors not improving coding rate finding these dispersion optimal coding schemes naturally gives a criteria for producing orthogonal design like inputs in dimensions where orthogonal designs do not exist

a monolithic approach to fluid structure interaction using space time finite elements abstract the paper presents a simultaneous solution procedure for fluid structure interaction problems the structural motion is described by geometrically nonlinear elastodynamics the fluid is modeled by the incompressible navier stokes equations the space time finite element method is applied to both continua leading to an almost uniform discretization in which velocity variables are used for fluid and structure in order to enforce momentum conservation and geometric continuity at the interface a weighted residual formulation of coupling conditions is introduced the discretized model equations for fluid structure and coupling conditions are formulated in a single equation system the nonlinear system and the fluid mesh movement are solved in a single iteration loop two dimensional examples of membrane flutter and vortex excited plate vibrations demonstrate the efficiency of the methodology

achievability proof of some multiuser channel coding theorems using backward decoding new and simpler achievability proofs that are based on the backward decoding technique are presented for the well known coding theorems for the multiple access channel mac with perfect feedback and the degraded relay channel a class of macs with different generalized feedback signals is also considered and achievable rate regions that are larger than those previously presented in the literature are established

the moving finite element method applications to general partial differential equations with multiple large gradients abstract the moving finite element mfe method has been reduced to practice in the automatic solution program dyla for general systems of transient partial differential equations pdes in 1 d several test examples are presented which illustrate the unique node movement and systematic control features which are intrinsic in the mfe method computational dilemmas of numerical diffusion gibbs overshooting and undershooting zone tangling and grid remap or re connection aliasing which occur frequently in conventional pde methods are essentially eliminated in the mfe method arbitrarily large gradients or shocks can be solved with extremely high resolution and accuracy for non coincident or even counterdirected propagating wavefronts boundary layers of arbitrarily small dimensions are solved with high accuracy simultaneously with the large scale structures in reactive and non reactive fluid calculations the mfe method requires a small fraction of the grid nodes which are used in conventional pde solution methods because the nodes migrate continuously and systematically to those positions where they are most needed in order to yield accurate pde solutions on entire problem domains courant friedrichs lewy time step limits are exceeded by wide margins by factors of two to several thousand finally the extension of the mfe method to 2 d is briefly discussed

near optimal finite length scaling for polar codes over large alphabets for any prime power q mori and tanaka introduced a family of q ary polar codes based on the q times q reed solomon polarization kernels for transmission over a q ary erasure channel they also derived a closed form recursion for the erasure probability of each effective channel in this paper we use that expression to analyze the finite length scaling of these codes on the q ary erasure channel with erasure probability epsilon in 0 1 our primary result is that for any gamma 0 and delta 0 there is a q 0 such that for all q geq q 0 the fraction of effective channels with erasure rate at most n gamma is at least 1 epsilon o n 1 2 delta where n q n is the blocklength since this fraction cannot be larger than 1 epsilon o n 1 2 this establishes near optimal finite length scaling for this family of codes our approach can be seen as an extension of a similar analysis for binary polar codes by hassani alishahi and urbanke a similar analysis is also considered for q ary polar codes with m times m polarizing matrices this separates the effect of the alphabet size from the effect of the matrix size if the polarizing matrix at each stage is drawn independently and uniformly from the set of invertible m times m matrices then the linear operator associated with the lyapunov function analysis can be written in the closed form to prove near optimal scaling for polar codes with fixed q as m increases however two technical obstacles remain thus we conclude by stating two concrete mathematical conjectures that if proven would imply near optimal scaling for fixed q

estimation theory and uncertainty intervals evaluation in presence of unknown but bounded errors linear families of models and estimators the problem of parameter estimation and of the evaluation of related uncertainty intervals is considered in the case that a probabilistic description of noise and errors is not available of suitable but only a bound on them is known in the present paper only linear parametrizations and estimators are considered very simple and computationally feasible algorithms are derived for evaluating two different types of uncertainty intervals estimates uncertainty intervals parameter uncertainty intervals the relationships between the eui s and the pui s are established and the solution to the problem of the minimum uncertainty intervals estimator is given the latter can be obtained by means of a simple linear programming algorithm

strong converse theorems for classes of multimessage multicast networks a renyi divergence approach this paper establishes that the strong converse holds for some classes of discrete memoryless multimessage multicast networks dm mmns whose corresponding cut set bounds are tight i e coincide with the corresponding sets of achievable rate tuples our strong converse result implies that for any dm mmn of these classes the average error probabilities of any sequence of codes operated at a rate tuple belonging to the exterior of the cut set bound must tend to one and are not simply bounded away from zero as the block length grows examples in the classes of dm mmns include wireless erasure networks dm mmns consisting of independent discrete memoryless channels dmcs as well as single destination dm mmns consisting of independent dmcs with destination feedback our elementary proof technique leverages properties of the renyi divergence

variable rate coding for slowly fading gaussian multiple access channels we consider a nonergodic multiple access gaussian block fading channel where a fixed number of independent and identically distributed i i d fading coefficients affect each codeword variable rate coding with input power constraint enforced on a per codeword basis is examined a centralized power and rate allocation policy is determined as a function of the previous and present fading coefficients the power control policy that optimizes the expected rates is obtained through dynamic programming and the average capacity region and the average capacity region per unit energy are characterized moreover we study the slope of spectral efficiency curve versus e sub b n sub 0 db and we quantify the penalty incurred by time division multiple access tdma over superposition coding in the low power regime

capacity and random coding exponents for channel coding with side information capacity formulas and random coding exponents are derived for a generalized family of gel fand pinsker coding problems these exponents yield asymptotic upper bounds on the achievable log probability of error in our model information is to be reliably transmitted through a noisy channel with finite input and output alphabets and random state sequence and the channel is selected by a hypothetical adversary partial information about the state sequence is available to the encoder adversary and decoder the design of the transmitter is subject to a cost constraint two families of channels are considered 1 compound discrete memoryless channels cdmc and 2 channels with arbitrary memory subject to an additive cost constraint or more generally to a hard constraint on the conditional type of the channel output given the input both problems are closely connected the random coding exponent is achieved using a stacked binning scheme and a maximum penalized mutual information decoder which may be thought of as an empirical generalized maximum a posteriori decoder for channels with arbitrary memory the random coding exponents are larger than their cdmc counterparts applications of this study include watermarking data hiding communication in presence of partially known interferers and problems such as broadcast channels all of which involve the fundamental idea of binning

an algorithm for the simulation of transient viscoelastic flows with free surfaces we propose a numerical procedure for solving a class of transient viscoelastic flows with free surfaces it is based on a galerkin finite element technique on deforming elements combined with a predictor corrector scheme the method is applied to the analysis of jet breakup caused by capillary forces non linear effects known to experimentalists are predicted and a detailed comparison with asymptotic results is carried out

information spectrum approach to second order coding rate in channel coding in this paper second order coding rate of channel coding is discussed for general sequence of channels the optimum second order transmission rate with a constant error constraint epsiv is obtained by using the information spectrum method we apply this result to the discrete memoryless case the discrete memoryless case with a cost constraint the additive markovian case and the gaussian channel case with an energy constraint we also clarify that the gallager bound does not give the optimum evaluation in the second order coding rate

finite element solution of maxwell s equations for hyperthermia treatment planning abstract a general galerkin formulation is given for the periodic form of maxwell s equations on a bounded inhomogeneous medium the formulation conserves energy exactly and its dispersion relation is studied solutions for test problems representative of hyperthermia applications show good agreement with analytic solutions a representative clinical example is shown

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