the h text p version of the finite element method for domains with curved boundaries this paper analyzes the convergence of the h text p version of the finite element method for elliptic problems on curved domains it proves that when the boundary of the domain is piecewise analytic boundary conditions are piecewise analytic and the sides of the elements are analytic the h text p version has an exponential rate of convergence numerical computations are included the paper generalizes the results previously obtained by the authors the h text p version of finite element method part 1 the basic approximation results comp mech 1 1986 pp 21 41 the h text p version of finite element method part 2 general results and applications comp mech 1 1986 pp 203 220

subblock constrained codes for real time simultaneous energy and information transfer consider an energy harvesting receiver that uses the same received signal both for decoding information and for harvesting energy which is employed to power its circuitry in the scenario where the receiver has limited battery size a signal with bursty energy content may cause power outage at the receiver since the battery will drain during intervals with low signal energy in this paper we analyze subblock energy constrained codes seccs which ensure that sufficient energy is carried within every subblock duration we consider discrete memoryless channels and characterize the secc capacity and the secc error exponent and provide useful bounds for these values we also study constant subblock composition codes csccs which are a subclass of seccs where all the subblocks in every codeword have the same fixed composition and this subblock composition is chosen to maximize the rate of information transfer while meeting the energy requirement compared with constant composition codes cccs we show that csccs incur a rate loss and that the error exponent for csccs is also related to the error exponent for cccs by the same rate loss term we exploit the symmetry in csccs to obtain a necessary and sufficient condition on the subblock length for avoiding power outage at the receiver furthermore for cscc sequences we present a tight lower bound on the average energy per symbol within a sliding time window we provide numerical examples highlighting the tradeoff between the delivery of sufficient energy to the receiver and achieving high information transfer rates it is observed that the ability to use energy in real time imposes less of penalty compared with the ability to use information in real time

lower bounds on the quantum capacity and highest error exponent of general memoryless channels tradeoffs between the information rate and fidelity of quantum error correcting codes are discussed quantum channels to be considered are those subject to independent errors and modeled as tensor products of copies of a general completely positive cp linear map where the dimension of the underlying hilbert space is a prime number on such a quantum channel the highest fidelity of a quantum error correcting code of length n and rate r is proven to be lower bounded by 1 exp ne r o n for some function e r the e r is positive below some threshold r sub 0 a direct consequence of which is that r sub 0 is a lower bound on the quantum capacity this is an extension of the author s earlier result while the earlier work states the result for the depolarizing channel and a slight generalization of it pauli channels the result of this work applies to general discrete memoryless channels including channel models derived from a physical law of time evolution

a survey of the theory of source coding with a fidelity criterion the purpose of this paper is threefold 1 to acquaint the reader with the types of problems that have been considered in the area of source coding with a fidelity criterion 2 to survey results that have been obtained on these problems and 3 to outline future research trends in the area

statistical physics of random binning we consider the model of random binning and finite temperature decoding for slepian wolf codes from a statistical mechanical perspective while ordinary random channel coding is intimately related to the random energy model a statistical mechanical model of disordered magnetic materials it turns out that random binning for slepian wolf coding is analogous to another related statistical mechanical model of strong disorder which we call the random dilution model we use the latter analogy to characterize phase transitions pertaining to finite temperature slepian wolf decoding which are somewhat similar but not identical to those of finite temperature channel decoding we then provide the exact random coding exponent of the bit error rate as a function of the coding rate and the decoding temperature and discuss its properties finally a few modifications and extensions of our results are outlined and discussed

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

integer metrics for binary input symmetric output memoryless channels consider a coded communication system where antipodal signaling is used over symmetric memoryless channels a mismatch decoder employing metrics which assume values in a finite set of integers is used two performance measures for achievable rates are considered the generalized cutoff rate and the mismatch capacity two different integer metric assignments which maximize these criteria are found the optimal metric assignment holds for any binary input symmetric output memoryless channels it is calculated explicitly for the faded additive white gaussian noise channel with and without diversity an interference channel model and the additive cauchy channel the difference in terms of achievable rates between decoding using the optimal continuous metric and integer metric is calculated for these channels the degradation for fairly low number of quantization levels is found to be small e g for nine quantization levels degradation is less than 0 3 db for all analyzed channels the sensitivity of the generalized cutoff rate and the mismatch capacity to the exact location of the quantization levels is rather mild the difference between the mismatch capacity corresponding to the optimal integer quantization and the mismatch capacity obtained by the quantization which optimizes the generalized cutoff rate is found to be quite small

weighted analytic regularity in polyhedra we explain a simple strategy to establish analytic regularity for solutions of second order linear elliptic boundary value problems the abstract framework presented here helps to understand the proof of analytic regularity in polyhedral domains given in the authors paper in m costabel m dauge s nicaise analytic regularity for linear elliptic systems in polygons and polyhedra math models methods appl sci 22 8 2012 we illustrate this strategy by considering problems set in smooth domains in corner domains and in polyhedra

mixed hp finite element methods for stokes and non newtonian flow abstract we analyze the stability of hp finite elements for viscous incompressible flow for the classical velocity pressure formulation we give new estimates for the discrete inf sup constants on geometric meshes which are explicit in the polynomial degree k of the elements in particular we obtain new bounds for p elements on triangles for the three field stokes problem describing linearized non newtonian flow we estimate discrete inf sup constants explicit in both h and k for various subspace choices continuous and discontinuous for the extra stress we also give a stability analysis of the hp version of an elastic viscous split stress evss method and present elements that are stable and optimal in h and k finally we present numerical results that show the exponential convergence of the hp version for stokes flow over unsmooth domains

the optimal convergence rate of the p version of the finite element method optimal error estimates for the p version of the finite element method in two dimensions are proven for the case when u in h k omega or u has singularities induced by the corners of the domain the case of nonhomogenous essential boundary conditions is also analyzed

axisymmetric stokes equations in polygonal domains regularity and finite element approximations we study the regularity and finite element approximation of the axisymmetric stokes problem on a polygonal domain w in particular taking into account the singular coefficients in the equation and non smoothness of the domain we establish the well posedness and full regularity of the solution in new weighted sobolev spaces k m 1 m w using our a priori results we give a specific construction of graded meshes on which the taylor hood mixed method approximates singular solutions at the optimal convergence rate numerical tests are presented to confirm the theoretical results in the paper

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

capacity and decoding rules for classes of arbitrarily varying channels the capacity of an arbitrarily varying channel avc is considered for deterministic codes with the average probability of error criterion and typically subject to at state constraint first sufficient conditions are provided that enable relatively simple decoding rules such as typicality maximum mutual information and minimum distance to attain capacity then the possibly noisy or channels and group adder channels are studied in detail for the former the capacity is explicitly determined and shown to be attainable by minimum distance decoding next for a large class of addictive avcs in addition to providing an intuitively suggestive simplification of the general avc capacity formula it is proven that capacity can be attained by a universal decoding rule finally the effect of random state selections on capacity is studied the merits and limitations of a previous mutual information game approach are also discussed

ratio list decoding we extend the notion of list decoding to ratio list decoding which involves a list decoder whose list size is specified as a function of the number of messages m n and the block length n we present the necessary and sufficient conditions on m n for the existence of code sequences which enable reliable list decoding with respect to the desired list size l m n n it is shown that the ratio capacity defined as the supremum of achievable normalized logarithms of the ratio r m n n m n l m n n is equal to the shannon channel capacity c for both stochastic and deterministic encoding allowing for random list size we are able to deduce some properties of identification codes where the decoder s output can be viewed as a list of messages corresponding to decision regions that include the channel output we further address the regime of mismatched list decoding in which the list constitutes of the codewords that accumulate the highest score values jointly with the channel output according to some given function we study the case of deterministic encoding and mismatched ratio list decoding we establish similar necessary and sufficient conditions for the existence of code sequences which enable reliable mismatched list decoding with respect to the desired list size l m n n and we show that the ratio capacity with mismatched decoding is equal to the mismatch capacity focusing on the case of an exponential list size l n e n theta its comparison with ordinary mismatched decoding shows that the increase in capacity is by theta bits per channel used for all channels and decoding metrics several properties of the average error probability in the setup of mismatched list decoding with deterministic list size are provided

non conforming least squares spectral element method for stokes equations on non smooth domains abstract in this paper we present a discontinuous least squares spectral element method for stokes equations with primitive variable formulation on both smooth and non smooth domains we propose an exponentially accurate numerical scheme based on the stability estimates and implement it on different polygonal domains preconditioned conjugate gradient method is used to obtain the numerical solution

stability and convergence of fully discrete galerkin fems for the nonlinear thermistor equations in a nonconvex polygon in this paper we establish the unconditional stability and optimal error estimates of a linearized backward euler galerkin finite element method fem for the time dependent nonlinear thermistor equations in a two dimensional nonconvex polygon due to the nonlinearity of the equations and the non smoothness of the solution in a nonconvex polygon the analysis is not straightforward while most previous efforts for problems in nonconvex polygons mainly focused on linear models our theoretical analysis is based on an error splitting proposed in 30 31 together with rigorous regularity analysis of the nonlinear thermistor equations and the corresponding iterated time discrete elliptic system in a nonconvex polygon with the proved regularity we establish the stability in l infty l infty l l and the convergence in l infty l 2 l l2 for the fully discrete finite element solution without any restriction on the time step size the approach used in this paper may also be applied to other nonlinear parabolic systems in nonconvex polygons numerical results confirm our theoretical analysis and show clearly that no time step condition is needed

improved source coding exponents via witsenhausen s rate we provide a novel upper bound on witsenhausen s rate the rate required in the zero error analogue of the slepian wolf problem our bound is given in terms of a new information theoretic functional defined on a certain graph and is derived by upper bounding complementary graph entropy we use the functional along with graph entropy to give a single letter lower bound on the error exponent for the slepian wolf problem under the vanishing error probability criterion where the decoder has full i e unencoded side information we demonstrate that our error exponent can beat the expurgated source coding exponent of csiszar and korner for some sources that have zeroes in the channel matrix connecting the source with the side information an extension of our scheme to the lossy case i e wyner ziv is given for the case in which the side information is a deterministic function of the source the exponent of our improved scheme agrees with the sphere packing bound exactly thus determining the reliability function an application of our functional to zero error channel capacity is also given

multiterminal source coding achievable rates and reliability some open problems concerning classical multiterminal configuration in which two correlated sources x and y are encoded separately and decoded by common decoder with respect to a fidelity criterion for messages of both sources are resolved the results of berger and yeung 1989 are expanded in two directions first we determine the rate distortion region r spl delta of achievable rates r sub x r sub y for a given spl delta spl delta sub x spl delta sub y with spl delta sub x the permissible distortion level for reproduction of x and spl delta sub y for y thus we give a full solution of the problem noted by kaspi and berger 1982 they constructed the inner bound for r spl delta and solved by berger and yeung for the case of one distortion second we introduce the notion of rate reliability distortion region for the multiterminal source encoding problem more precisely the region of admissible rates of codes ensuring exponential decrease with a given exponent e 0 of the probability of exceeding the distortion levels spl delta sub x or spl delta sub y the inner and outer bounds for this region r e spl delta are constructed the analytical representation obtained for r spl delta proved to be somewhat simpler than that considered by kaspi and berger and by berger and yeung ours uses only variables pertaining to the problem statement with no auxiliary ones

universal coding for the slepian wolf data compression system and the strong converse theorem universal coding for the slepian wolf 1973 data compression system is considered we shall demonstrate based on a simple observation that the error exponent given by csiszar and korner 1980 for the universal coding system can strictly be sharpened in general for a region of relatively higher rates this kind of observation can be carried over also to the case of lower rates outside the slepian wolf region which establishes the strong converse along with the optimal exponent

weighted finite element method for the stokes problem with corner singularity abstract in this paper we introduce the notion of r generalized solution to the stokes problem with singularity in a non convex polygonal domain with one reentrant corner of 3 2 on its boundary the weighted analogue of the ladyzhenskaya babuska brezzi condition is proved a new weighted finite element method is constructed results of numerical experiments have shown the efficiency of the method

regularity estimates and optimal finite element methods in wp1 on polygonal domains abstract consider the poisson equation with the dirichlet boundary condition on a bounded convex polygonal domain r 2 we investigate the finite element approximation of singular solutions that are due to the non smoothness of the domain in the w p 1 norm 1 p in particular with analysis in weighted sobolev spaces and weighted holder spaces we provide regularity requirements on the given data and specific parameter selection criteria for graded meshes such that the resulting numerical approximation achieves the optimal convergence rate in w p 1 sample results from various numerical tests are provided to confirm the theory

integral averages and oscillation criteria for half linear partial differential equation the technique of weighted integral averages known in the oscillation theory of ordinary differential equations is extended to the half linear partial differential equation e div email protected email protected p email protected u c x u p 2u 0 p 1 this technique is used to obtain new oscillation criteria for e on the unbounded domains

error exponent for multiple access channels upper bounds the problem of bounding the reliability function of a multiple access channel mac is studied two new upper bounds on the error exponent of a two user discrete memoryless dm mac are derived the first bound sphere packing is an upper bound on the exponent of the average probability of error and is the first bound of this type that is zero outside the capacity region and thus results in a tighter sphere packing exponent when compared with the tightest known exponent derived by haroutunian the second bound minimum distance is an upper bound on the exponent of the maximal as opposed to average probability of error to obtain this bound first an upper bound on the minimum bhattacharyya distance between codeword pairs is derived for a certain class of two user dm macs an upper bound on the exponent of maximal probability of error is derived as a consequence of the upper bound on the minimum bhattacharyya distance we analytically evaluate the sphere packing bound for uniform composition codes for an additive and nonsymmetric channel and show that it is tight near the boundary of the capacity region i e equal to the random coding lower bound

oscillation of the half linear pde in general exterior domains the variational approach abstract in the paper a variational technique is used to show how to derive new oscillation criteria for the half linear partial differential equation via the oscillation criteria for the ordinary half linear differential equation in contrast to the results usually found in the literature general types of unbounded domains can be considered

large deviations behavior of the logarithmic error probability of random codes this work studies the deviations of the error exponent of the constant composition code ensemble around its expectation known as the error exponent of the typical random code trc in particular it is shown that the probability of randomly drawing a codebook whose error exponent is smaller than the trc exponent is exponentially small upper and lower bounds for this exponent are given which coincide in some cases in addition the probability of randomly drawing a codebook whose error exponent is larger than the trc exponent is shown to be double exponentially small upper and lower bounds to the double exponential exponent are given the results suggest that codebooks whose error exponent is larger than the error exponent of the trc are extremely rare the key ingredient in the proofs is a new large deviations result of type class enumerators with dependent variables

universal wyner ziv coding for distortion constrained general side information we investigate the wyner ziv coding in which the statistics of the principal source is known but the statistics of the channel generating the side information is unknown except that it is in a certain class the class consists of channels such that the distortion between the principal source and side information is smaller than a threshold but channels may be neither stationary nor ergodic in this situation we define a new rate distortion function as the minimum rate such that there exists a wyner ziv code that is universal for every channel in the class then we show an upper bound and a lower bound on the rate distortion function and derive a matching condition such that the upper and lower bounds coincide the relation between the new rate distortion function and rate distortion function of the heegard berger problem is also discussed

some properties of sequential predictors for binary markov sources universal predictions of the next outcome of a binary sequence drawn from a markov source with unknown parameters is considered for a given source the predictability is defined as the least attainable expected fraction of prediction errors a lower bound is derived on the maximum rate at which the predictability is asymptotically approached uniformly over all sources in the markov class this bound is achieved by a simple majority predictor for bernoulli sources bounds on the large deviations performance are investigated a lower bound is derived for the probability that the fraction of errors will exceed the predictability by a prescribed amount delta 0 this bound is achieved by the same predictor if delta is sufficiently small

exponential convergence in h 1 of hp fem for gevrey regularity with isotropic singularities for functions u in h 1 omega in a bounded polytope omega subset mathbb r d d 1 2 3 with plane sides for d 2 3 which are gevrey regular in overline omega backslash mathscr s with point singularities concentrated at a set mathscr s subset overline omega consisting of a finite number of points in overline omega we prove exponential rates of convergence of hp version continuous galerkin finite element methods on affine families of regular simplicial meshes in omega the simplicial meshes are geometrically refined towards mathscr s but are otherwise unstructured

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

a block decodable 1 8 runlength limited rate 8 12 code describes a d k 1 8 runlength limited rll rate 8 12 code with fixed codeword length 12 the code is block decodable a codeword can be decoded without knowledge of preceding or succeeding codewords the code belongs to the class of bounded delay block decodable bdb codes with one symbol 8 bits look ahead due to its format this code is particularly attractive for use in combination with error correcting codes such as reed solomon codes over the finite field gf 2 sup 8

exact random coding error exponents of optimal bin index decoding we consider ensembles of channel codes that are partitioned into bins and focus on analysis of exact random coding error exponents associated with optimum decoding of the index of the bin to which the transmitted codeword belongs two main conclusions arise from this analysis i for independent random selection of codewords within a given type class the random coding exponent of optimal bin index decoding is given by the ordinary random coding exponent function computed at the rate of the entire code independently of the exponential rate of the size of the bin ii for this ensemble of codes sub optimal bin index decoding that is based on ordinary maximum likelihood ml decoding is as good as the optimal bin index decoding in terms of the random coding error exponent achieved finally for the sake of completeness we also outline how our analysis of exact random coding exponents extends to the hierarchical ensemble that correspond to superposition coding and optimal decoding where for each bin first a cloud center is drawn at random and then the codewords of this bin are drawn conditionally independently given the cloud center for this ensemble conclusions i and ii mentioned above no longer hold necessarily in general

an optimal order multigrid method for p1 nonconforming finite elements etude d une methode multigrille d ordre optimal pour la resolution des problemes aux limites elliptiques du second ordre a l aide d elements finis non conformes

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

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 error exponent for the noiseless encoding of finite ergodic markov sources a new approach to the classical fixed length noiseless source coding problem is proposed for the case of finite ergodic markov sources this approach is based on simple counting arguments the central notion of markov type a set containing all the source sequences having the same transition counts from letter to letter is introduced and the cardinality of such a set is evaluated via graph theoretical tools the error exponent is shown to be a weighted average of informational divergences and the universal character of the result is stressed as a corollary the classical source coding theorem determining the achievable rates is rederived

analytic regularity of stokes flow on polygonal domains in countably weighted sobolev spaces we investigate the analytic regularity of the stokes problem in a polygonal domain r2 with straight sides and piecewise analytic data we establish a shift theorem in weighted sobolev spaces of arbitrary order with explicit control of the order dependence of the constants the shift theorem in the framework of countably weighted sobolev spaces implies in particular interior analyticity and gevrey type analytic regularity near the corners

optimum tradeoffs between the error exponent and the excess rate exponent of variable rate slepian wolf coding we analyze the optimal tradeoff between the error exponent and the excess rate exponent for variable rate slepian wolf codes in particular we first derive upper converse bounds on the optimal error and excess rate exponents and then lower achievable bounds via a simple class of variable rate codes which assign the same rate to all source blocks of the same type class then using the exponent bounds we derive bounds on the optimal rate functions namely the minimal rate assigned to each type class needed in order to achieve a given target error exponent the resulting excess rate exponent is then evaluated iterative algorithms are provided for the computation of both bounds on the optimal rate functions and their excess rate exponents the resulting slepian wolf codes bridge between the two extremes of fixed rate coding which has minimal error exponent and maximal excess rate exponent and average rate coding which has maximal error exponent and minimal excess rate exponent

on achievable rates and error exponents for channels with mismatched decoding the problem of characterizing achievable rates and error exponents for discrete memoryless channels with mismatched decoding is addressed a mismatched cognitive multiple access channel is introduced and an inner bound on its capacity region is derived using two alternative encoding methods 1 superposition coding and 2 random binning the inner bounds are derived by analyzing the average error probability of the code ensemble for both methods and by a tight characterization of the resulting error exponents random coding converse theorems are also derived a comparison of the achievable regions shows that in the matched case random binning performs as well as superposition coding i e the region achievable by random binning is equal to the capacity region the achievability results are further specialized to obtain a lower bound on the mismatch capacity of the single user channel by investigating a cognitive multiple access channel whose achievable sum rate serves as a lower bound on the single user channel s capacity while the achievable rate presented here may not improve the rate achieved by lapidoth s scheme in optimizing over the parameters of the random coding scheme it can improve the achieved rate for given parameters and thereby may reduce the computational complexity required to find a good code

a converse coding theorem for mismatched decoding at the output of binary input memoryless channels an upper bound on the maximal transmission rate over binary input memoryless channels provided that the decoding decision rule is given is derived if the decision rule is equivalent to the maximum likelihood decoding matched decoding then the bound coincides with the channel capacity otherwise mismatched decoding it coincides with a known lower bound

on the duality between slepian wolf coding and channel coding under mismatched decoding in this paper slepian wolf coding with a mismatched decoding metric is studied two different dualities between slepian wolf coding and channel coding under mismatched decoding are established these two dualities provide a systematic framework for comparing linear slepian wolf codes nonlinear slepian wolf codes and variable rate slepian wolf codes in contrast with the fact that linear codes suffice to achieve the slepian wolf limit under matched decoding the minimum rate achievable with nonlinear slepian wolf codes under mismatched decoding can be strictly lower than that achievable with linear slepian wolf codes

error exponents of typical random codes for the colored gaussian channel the error exponent of the typical random code is defined as the asymptotic normalized expectation of the logarithm of the probability of error as opposed to the traditional definition of the random coding exponent as the normalized logarithm of the expectation of the probability of error with respect to a given ensemble of codes for a certain ensemble of independent codewords with a given power spectrum and a generalized stochastic mismatched decoder we characterize the error exponent of the typical random codes trc for the colored gaussian channel with emphasis on the range of low rates where the trc error exponent differs in value from the ordinary random coding error exponent the error exponent formula which is exponentially tight at some range of low rates is presented as the maximum of a certain function with respect to one parameter only in the spirit of gallager s formulas in the case of matched decoding and two parameters in the case of mismatched decoding several aspects of the main results are discussed these include general properties a parametric representation critical rates phase transitions optimal input spectrum water pouring and comparison to the random coding exponent

linear codes for sources and source networks error exponents universal coding for slepian wolf source networks the error exponents obtained by korner marton and the author are shown to be universally attainable by linear codes also improved exponents are derived for linear codes with large rates specializing the results to simple discrete memoryless sources reveals their relationship to the random coding and expurgated bounds for channels with additive noise one corollary is that there are universal linear codes for this class of channels which attain the random coding error exponent for each channel in the class the combinatorial approach of csiszar korner marton is used in particular all results are derived from a lemma specifying good encoders in terms of purely combinatorial properties

on the convergence of the p version of the boundary element galerkin method abstract the authors consider various physical problems which may be formulated in terms of integral equations of the first kind including the two dimensional screen neumann and dirichlet problems in acoustics and crack problems in elasticity sharp regularity results for the solutions are available for these problems proven is the convergence of the p version for some galerkin boundary element schemes based on the integral equation formulations it is shown that the rate of convergence obtained by our method is twice that for the usual h version

oscillation criteria of nehari type for sturm liouville operators and elliptic differential operators of second order and the lower spectrum on etablit des criteres suffisants d oscillation de type nehari pour l equation differentielle u q t u t 0 0 t avec et sans restriction de signe sur q t on etend ces resultats aux equations de sturm liouville et aux equations elliptiques d ordre 2

the p version of the finite element method in the p version of the finite element method the triangulation is fixed and the degree p of the piecewise polynomial approximation is progressively increased until some desired level of precision is reached in this paper we first establish the basic approximation properties of some spaces of piecewise polynomials defined on a finite element triangulation these properties lead to an a priori estimate of the asymptotic rate of convergence of the p version the estimate shows that the p version gives results which are not worse than those obtained by the conventional finite element method called the h version in which h represents the maximum diameter of the elements when quasi uniform triangulations are employed and the basis for comparison is the number of degrees of freedom furthermore in the case of a singularity problem we show under conditions which are usually satisfied in practice that the rate of convergence of the p version is twice that of the h version with quasi uniform mesh inve

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 general formula for the mismatch capacity the fundamental limits of channels with mismatched decoding are addressed a general formula is established for the mismatch capacity of a general channel defined as a sequence of conditional distributions with a general decoding metrics sequence we deduce an identity between the verdu han general channel capacity formula and the mismatch capacity formula applied to maximum likelihood decoding metric furthermore several upper bounds on the capacity are provided and a simpler expression for a lower bound is derived for the case of a non negative decoding metric the general formula is specialized to the case of finite input and output alphabet channels with a type dependent metric the closely related problem of threshold mismatched decoding is also studied and a general expression for the threshold mismatch capacity is obtained as an example of threshold mismatch capacity we state a general expression for the erasures only capacity of the finite input and output alphabet channel we observe that for every channel there exists a matched threshold decoder which is capacity achieving in addition necessary and sufficient conditions are stated for a channel to have a strong converse

the effect of variable change on oscillation and disconjugacy criteria with applications to spectral theory and asymptotic theory this study of the effect of variable change on differential operators was motivated by recent papers of tipler 131 and hinton and lewis 37 which appeared in the same issue of the journal of d erential equations tipler gave a geometric proof 13 p 1671 of the following result of hawking and penrose see 29 301 let f t be a real valued continuous nonnegative function on w co such that f b 0 for some point b then there exists a pair of conjugate points on co co for the differential equation

error exponents of typical random codes we define the error exponent of the typical random code trc as the long block limit of the negative normalized expectation of the logarithm of the error probability of the random code as opposed to the traditional random coding error exponent which is the limit of the negative normalized logarithm of the expectation of the error probability for the ensemble of uniformly randomly drawn fixed composition codes we provide exact error exponents of trcs for a general discrete memoryless channel and a wide class of stochastic decoders collectively referred to as the generalized likelihood decoder gld this ensemble of fixed composition codes is shown to be no worse than any other ensemble of independent codewords that are drawn under a permutation invariant distribution e g independent identically distributed codewords we also present relationships between the error exponent of the trc and the ordinary random coding error exponent as well as the expurgated exponent for the gld finally we demonstrate that our analysis technique is applicable also to more general communication scenarios such as list decoding for fixed size lists as well as the decoding with an erasure list option in forney s sense

on the sharpness of certain local estimates for projections into finite element spaces influence of a re entrant corner in a plane polygonal domain with a reentrant corner consider a homogeneous dirichlet problem for poisson s equation au f with f smooth and the corresponding galerkin finite element solutions in a family of piecewise polynomial spaces based on quasi uniform uniformly regular triangulations with the diameter of each element compara