on optimal gaussian signaling in mimo relay channels with partial decode and forward for gaussian multiple input multiple output mimo relay channels with partial decode and forward the optimal type of input distribution is still an open question in general recent research has revealed that in some other scenarios with unknown optimal input distributions e g interference channels improper i e noncircular gaussian distributions can outperform proper circular gaussian distributions in this paper we show that this is not the case for partial decode and forward in the gaussian mimo relay channel with gaussian transmit signals i e we show that a proper gaussian input distribution is the optimal one among all gaussian distributions in order to prove this property an innovation covariance matrix is introduced and a decomposition is performed by considering the optimization over this matrix as an outer problem a key point for showing optimality of proper signals then is a reformulation that reveals that one of the subproblems is equivalent to a sum rate maximization in a two user mimo broadcast channel under a sum covariance constraint for which the optimality of proper signals can be shown

a stabilized conforming nodal integration for galerkin mesh free methods domain integration by gauss quadrature in the galerkin mesh free methods adds considerable complexity to solution procedures direct nodal integration on the other hand leads to a numerical instability due to under integration and vanishing derivatives of shape functions at the nodes a strain smoothing stabilization for nodal integration is proposed to eliminate spatial instability in nodal integration for convergence an integration constraint ic is introduced as a necessary condition for a linear exactness in the mesh free galerkin approximation the gradient matrix of strain smoothing is shown to satisfy ic using a divergence theorem no numerical control parameter is involved in the proposed strain smoothing stabilization the numerical results show that the accuracy and convergent rates in the mesh free method with a direct nodal integration are improved considerably by the proposed stabilized conforming nodal integration method it is also demonstrated that the gauss integration method fails to meet ic in mesh free discretization for this reason the proposed method provides even better accuracy than gauss integration for galerkin mesh free method as presented in several numerical examples copyright 2001 john wiley sons ltd

uniquely decodable codes for deterministic relay channels the deterministic relay channel is analyzed and explicit code constructions for all binary and all ternary binary channels are given an explicit set of equivalence conditions is used to make a classification of all such relay channels for which also the capacity is evaluated the coding problem is then reduced to finding all possible output sequences of a certain finite state channel determined by the relay coding strategy the channel states correspond to the possible relay memory contents for some relay channels capacity is reached by using simple uniquely decodable codes thus establishing the zero error capacity of those channels with finite memory relay strategies for other relay channels the relay memory must be arbitrarily large to achieve zero error rates arbitrarily close to capacity one such code construction is given it is not known whether there exist relay channels for which the zero error capacity is strictly smaller than the average error capacity the code construction problem for the semideterministic relay channel and for the nonsynchronized relay channel is briefly considered

joint optimization of the transmit covariance and relay precoder in general gaussian amplify and forward relay channels the maximum data rate that can be achieved by the strictly causal full duplex amplify and forward af scheme in general gaussian relay channels is achieved by gaussian codebooks and can be cast as the solution of an optimization problem of the input transmit covariance and relay precoder this problem possesses an intricate nonconvex structure and is hence difficult to solve to circumvent this difficulty the relay precoder is assumed to be given and then the karush kuhn tucker conditions are used to obtain closed form expressions for the optimal input covariance corresponding to that precoder these expressions are used to show that subdiagonal precoders suffice to attain the maximum achievable rate of the af scheme at any source transmit power in addition to significantly reducing the effort expended in searching for the optimal relay precoder this observation enables us to find the optimal precoders at low and high source transmit powers for asymptotically low transmit powers the optimal relaying mechanism is shown to possess an interlacing structure thereby resembling half duplex operation in contrast for asymptotically high transmit powers it is optimal for the relay to be silent the asymptotic analysis enables us to develop an explicit formulation for a suboptimal precoder that at intermediate source transmit powers are shown numerically to outperform asymptotically optimal precoders

the capacity of the semideterministic relay channel corresp the capacity of the class of relay channels with sender x 1 a relay sender x 2 a relay receiver y 1 f x 1 x 2 and ultimate receiver y is proved to be c max min p x 1 x 2 i x 1 x 2 y h y 1 x 2 i x 1 y x 2 y 1

orbital hp clouds for solving schrodinger equation in quantum mechanics solving schrodinger equation in quantum mechanics presents a challenging task in numerical methods due to the high order behavior and high dimension characteristics in the wave functions in addition to the highly coupled nature between wave functions this work introduces orbital and polynomial enrichment functions to the partition of unity for solution of schrodinger equation under the framework of hp clouds an intrinsic enrichment of orbital function and extrinsic enrichment of monomial functions are proposed due to the employment of higher order basis functions a higher order stabilized conforming nodal integration is developed the proposed methods are implemented using the density functional theory for solution of schrodinger equation analysis of several single and multi electron nucleus structures demonstrates the effectiveness of the proposed method

gaussian orthogonal relay channels optimal resource allocation and capacity a gaussian orthogonal relay model is investigated where the source transmits to the relay and destination in channel 1 and the relay transmits to the destination in channel 2 with channels 1 and 2 being orthogonalized in the time frequency plane in order to satisfy practical constraints the total available channel resource time and bandwidth is split into the two orthogonal channels and the resource allocation to the two channels is considered to be a design parameter that needs to be optimized the main focus of the analysis is on the case where the source to relay link is better than the source to destination link which is the usual scenario encountered in practice a lower bound on the capacity achievable rate is derived and optimized over the parameter spl theta which represents the fraction of the resource assigned to channel 1 it is shown that the lower bound achieves the max flow min cut upper bound at the optimizing spl theta the common value thus being the capacity of the channel at the optimizing spl theta furthermore it is shown that when the relay to destination signal to noise ratio snr is less than a certain threshold the capacity at the optimizing spl theta is also the maximum capacity of the channel over all possible resource allocation parameters spl theta finally the achievable rates for optimal and equal resource allocations are compared and it is shown that optimizing the resource allocation yields significant performance gains

on the relay channel with receiver transmitter feedback an achievable rate for the discrete memoryless relay channel with receiver transmitter feedback is proposed based on block markov superposition encoding the achievable rate can also be extended to gaussian channels a second achievable rate for the gaussian relay channel based on a schalkwijk kailath type scheme is presented for some channels both achievable rates strictly improve upon all previously known achievable rates for the discrete memoryless relay channel also a converse result is provided

practical quantizer design for half duplex estimate and forward relaying we propose a quantizer design method for practical half duplex estimate and forward ef relaying first we identify the regime in which ef relaying yields substantial gains where the snr is low and the relay destination link is strong then we discover design simplifications that reduce complexity with little loss in the above regime for relay quantizer design we first consider mean squared distortion minimization to illustrate the unsuitability of the approach we present an example with awgn links and a bpsk source where the quantizer with worst mean squared distortion in a given set maximizes achievable rate a distortion minimizing quantizer attempts to preserve the received signal at the relay the quantizer should instead preserve source information in information theoretical terms the quantizer should maximize the mutual information between the source transmission and the quantizer output conditioned on the side information at the destination subject to a rate constraint the above conclusion derived from information theoretical principles is then translated to a quantizer design method for the low snr regime using ldpc codes of blocklength 100000 bpsk modulation and quantizers designed using the proposed criterion we observe performance less than a decibel away from the achievable rate at a ber of 10 4

enforcement of essential boundary conditions in meshless approximations using finite elements abstract a technique for easily treating essential boundary conditions for approximations which are not interpolants such as moving least square approximations in the element free galerkin method is presented the technique employs a string of elements along the essential boundaries and combines the finite element shape functions with the approximation in the resulting approximation essential boundary conditions can be treated exactly as in finite elements it is shown that the resulting approximation can exactly reproduce linear polynomials so that it satisfies the patch test numerical studies show that the method retains the high rate of convergence associated with moving least square approximations

modified taylor reproducing formulas and h p clouds we study two different approximations of a multivariate function f by operators of the form n i 1 r f x i wi x wi x where w i is an m reproducing partition of unity and t f x i x are modified taylor polynomials of degree r expanded at x i the first approximation was introduced by xuli 2003 in the univariate case and generalized for convex domains by guessab et al 2005 the second one was introduced by duarte 1995 and proved in the univariate case in this paper we first relax the guessab s convexity assumption and we prove duarte s reproduction formula in the multivariate case then we introduce two related reproducing quasi interpolation operators in sobolev spaces a weighted error estimate and jackson s type inequalities for h p cloud function spaces are obtained last numerical examples are analyzed to show the approximative power of the method

a petrov galerkin modified operator formulation for convection diffusion problems a new petrov galerkin method to deal with convection diffusion problems is presented the formulation is derived from the concept of using a modifying function to make the differential operator self adjoint the so called optimal upwind parameter arises naturally from the process of approximating the modifying function transient and steady state examples on uniform and non uniform meshes are shown

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

stabilized finite element method for the radial dirac equation a challenging difficulty in solving the radial dirac eigenvalue problem numerically is the presence of spurious unphysical eigenvalues among the genuine ones that are neither related to mathematical interpretations nor to physical explanations many attempts have been made and several numerical methods have been applied to solve the problem using the finite element method fem the finite difference method or other numerical schemes unfortunately most of these attempts failed to overcome the difficulty as a fem approach this work can be regarded as a first promising scheme to solve the spuriosity problem completely our approach is based on an appropriate choice of trial and test function spaces we develop a streamline upwind petrov galerkin method to the equation and derive an explicit stability parameter

poisson disorder problem with exponential penalty for delay we solve the poisson disorder problem when the delay is penalized exponentially our objective is to detect as quickly as possible the unobservable time of the change or disorder in the intensity of a poisson process the disorder time delimits two different regimes in which one employs distinct strategies e g investment advertising manufacturing we seek a stopping rule that minimizes the frequency of false alarms and an exponential unlike previous formulations which use a linear cost function of the detection delay in the financial applications the exponential penalty is a more apt measure for the delay cost because of the compounding of the investment growth the poisson disorder problem with a linear delay cost was studied by peskir and shiryaev 2002 solving the poisson disorder problem advances in finance and stochastics springer berlin germany 295 312 which is a limiting case of ours

a note on sequential detection with exponential penalty for the delay we study the continuous time analogue of the bayes problem of poor as usual the results on the optimal solution are more explicit than in the discrete time set up

enrichment and coupling of the finite element and meshless methods a mixed hierarchical approximation based on finite elements and meshless methods is presented two cases are considered the first one couples regions where finite elements or meshless methods are used to interpolate continuity and consistency is preserved the second one enriches a finite element mesh with particles thus there is no need to remesh in adaptive refinement processes in both cases the same formulation is used convergence is studied and examples are shown copyright 2000 john wiley sons ltd

diversity analysis of randomized linear dispersion codes in a half duplex amplify and forward multiple relay system a point to point multiple relay communication system with half duplex constraints is considered the relays operate under the amplify and forward paradigm and implement a linear dispersion distributed space time code with randomized dispersion matrices of independent and identically distributed entries the large signal to noise ratio behavior of the asymptotically large deterministic system is studied for both the optimum maximum likelihood receiver and the linear minimum mean squared error lmmse receiver the diversity order of the system is shown to have a strong dependence on the aspect ratio of the linear dispersion matrices more specifically when the linear dispersion matrices are sufficiently tall both receivers achieve the maximum diversity order i e the total number of relays plus one conversely when the linear dispersion matrices are fat in the sense that relays linearly compress the information received from the source the optimum receiver is shown to achieve an asymptotic diversity order of two whereas the lmmse receiver is totally unable to exploit the available spatial diversity

the diversity multiplexing tradeoff of the mimo half duplex relay channel the fundamental diversity multiplexing tradeoff of the three node multi input multi output mimo quasi static rayleigh faded half duplex relay channel is characterized for an arbitrary number of antennas at each node and in which opportunistic scheduling or dynamic operation of the relay is allowed i e the relay can switch between receive and transmit modes at a channel dependent time in this most general case the diversity multiplexing tradeoff is characterized as a solution to a simple two variable optimization problem this problem is then solved in closed form for special classes of channels defined by certain restrictions on the numbers of antennas at the three nodes the key mathematical tool developed here that enables the explicit characterization of the diversity multiplexing tradeoff is the joint eigenvalue distribution of three mutually correlated random wishart matrices besides being relevant here this distribution result is interesting in its own right previously without actually characterizing the diversity multiplexing tradeoff the optimality in this tradeoff metric of the dynamic compress and forward protocol based on the classical compress and forward scheme of cover and el gamal was shown by yuksel and erkip however this scheme requires global channel state information at the relay in this paper the so called quantize map and forward qmf coding scheme is adopted as the achievability scheme with the added benefit that it achieves optimal tradeoff with only the knowledge of the channel dependent switching time at the relay node moreover in special classes of the mimo half duplex relay channel the optimal tradeoff is shown to be attainable even without this knowledge such a result was previously known only for the half duplex relay channel with a single antenna at each node also via the qmf scheme more generally the explicit characterization of the tradeoff curve in this study enables the in depth comparisons herein of full duplex versus half duplex relaying as well as static versus dynamic relaying both as a function of the numbers of antennas at the three nodes

bayesian switching multiple disorder problems the switching multiple disorder problem seeks to determine an ordered infinite sequence of times of alarms which are as close as possible to the unknown times of disorders or change points at which the observable process changes its probability characteristics we study a bayesian formulation of this problem for an observable brownian motion with switching constant drift rates the method of proof is based on the reduction of the initial problem to an associated optimal switching problem for a three dimensional diffusion posterior probability process and the analysis of the equivalent coupled parabolic type free boundary problem we derive analytic form estimates for the bayesian risk function and the optimal switching boundaries for the components of the posterior probability process

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

a joint time invariant filtering approach to the linear gaussian relay problem in this paper the linear gaussian relay problem is considered under the linear time invariant lti model the rate maximization problem in the linear gaussian relay channel is formulated in the frequency domain based on the toeplitz distribution theorem under the further assumption of realizable input spectra the rate maximization problem is converted to the problem of joint source and relay filter design with two power constraints one at the source and the other at the relay and a practical solution to this problem is proposed based on the adaptive projected sub gradient method numerical results show that the proposed method yields a considerable gain over the instantaneous amplify and forward af scheme in inter symbol interference isi channels also the optimality of the af scheme within the class of one tap relay filters is established in flat fading channels

optimal switching in an economic activity under uncertainty this paper considers the problem of finding the optimal sequence of opening starting and closing stopping times of a multi activity production process given the costs of opening running and closing the activities and assuming that the state of the economic system is a stochastic process the problem is formulated as an extended impulse control problem and solved using stochastic calculus as an application the optimal starting and stopping strategy are explicitly found for a resource extraction when the price of the resource is following a geometric brownian motion

accumulation of discrete eigenvalues of the radial dirac operator abstract for bounded potentials which behave like cx at infinity we investigate whether discrete eigenvalues of the radial dirac operatorh accumulate at 1 or not it is well known that 2 is the critical exponent we show thatc 1 8 1 2 is the critical coupling constant in the case 2 our approach is to transform the radial dirac equation into a sturm liouville equation nonlinear in the spectral parameter and to apply a new general result on accumulation of eigenvalues of such equations

a stable petrov galerkin method for convection dominated problems in this paper a new petrov galerkin formulation for solving convection dominated problems is presented the method developed achieves the quasi optimal convergence rates when the solution is regular and provides the necessary stability to avoid spurious oscillations when strong gradients are present such important properties allow the use of p refinement to improve the solution in regions with discontinuities because of the stability engendered by the new petrov galerkin method in this matter a proper evaluation of the intrinsic time scale function appearing in the design of this method is crucial to guarantee the required accuracy

the capacity of a relay channel both with and without delay in this correspondence we point out the incorrectness of an upper bound in van der meulen advances in applied probability vol 3 no 1 pp 120 154 1971 and report the correct relay capacity for one of the examples given there we also show that when viewed as a relay without delay channel the capacity of this channel is strictly larger than its classical relay capacity

state dependent relay channel achievable rate and capacity of a semideterministic class this paper considers the problem of communicating over a relay channel with state when noncausal state information is partially available at the nodes we first establish a lower bound on the achievable rates based on noisy network coding and gelfand pinsker coding and show that it provides an alternative characterization of a previously known bound we then introduce the class of state decoupled relay channels and show that our lower bound is tight for a subclass of semideterministic channels we also compute the capacity for two specific examples of this subclass a channel with multiplicative binary fading and a channel with additive gaussian interference these examples are not special cases of previous classes of semideterministic relay channels with known capacity

study of gaussian relay channels with correlated noises in this paper we consider the full duplex and half duplex gaussian relay channels where the noises at the relay and destination are arbitrarily correlated we first derive the capacity upper bound and the achievable rates with three existing schemes decode and forward df compress and forward cf and amplify and forward af we present two capacity results under specific noise correlation coefficients one being achieved by df and the other being achieved by direct link transmission or a special case of cf the channel for the former capacity result is equivalent to the traditional gaussian degraded relay channel and the latter corresponds to the gaussian reversely degraded relay channel for cf and af schemes we show that their achievable rates are strictly decreasing functions of the correlation coefficient when the correlation coefficient is negative moreover when the noise correlation coefficient is positive the cf achievable rate may also outperform the independent noise case if the noise correlation coefficient is within a certain range through numerical comparisons under different channel settings we observe that although df completely disregards the noise correlation while the other two can potentially exploit such extra information none of the three relay schemes always outperforms the others over different correlation coefficients moreover the exploitation of noise correlation by cf and af accrues more benefit when the source relay link is weak this paper also considers the optimal power allocation problem under the correlated noise channel setting with individual power constraints at the relay and the source it is shown that the relay should use all its available power to maximize the achievable rates under any correlation coefficient with a total power constraint across the source and the relay the achievable rates are proved to be concave functions over the power allocation factor for af and cf under full duplex mode where the closed form power allocation strategy is derived

numerical solution of the dirac equation by a mapped fourier grid method an efficient numerical method is developed to solve the relativistic hydrogenic coulomb problem combining a pseudospectral method and a change of coordinates a matrix representation of the relativistic hamiltonian is constructed in position space the radial coordinate is mapped from the semi infinite r axis to a finite range the accuracy of the calculation is tested by comparing eigenvalues sum rules and eigenfunctions with known analytic results the method can be applied to central field problems for which analytic solutions are unknown

analysis of the generalized df cf for gaussian relay channels decode or compress we consider a three node quasi static communication system with a full duplex relay the goal is to determine the relaying mode that enables rate efficient communication under given channel conditions to achieve this goal we consider a generalized scheme that subsumes the decode and forward df and compress and forward cf schemes as special cases the generalized scheme is considered when the source and relay signals are synthesized from commonly used gaussian codebooks which are shown to be capacity achieving in two asymptotic cases perfect relay destination link and broken source destination link studying the generalized df cf scheme it is shown that for two non asymptotic cases in which the signal to noise ratios snrs of the links satisfy certain conditions this scheme reduces to either df or cf for another set of non asymptotic snrs the generalized scheme is shown to yield strictly higher rates than both df and cf despite the complexity of the generalized scheme its rate advantage over df and cf is shown to be upper bounded by 0 5 bits per channel use this indicates that the practical benefit of the analysis of this scheme is to enable selecting the relaying mode that suits a given channel realization numerical results show that under rayleigh fading conditions this selection yields significant gains over fixed df and cf

on instantaneous relaying the gaussian three node relay channel with orthogonal receive components i e the transmitted signals from the source and the relay do not interfere with each other is investigated for such channels linear relaying is a suboptimal strategy in general this is because a linear scheme merely repeats the received noisy signal and does not utilize the available degrees of freedom efficiently at this background nonlinear symbol wise as opposed to block wise relaying strategies are developed to compensate for the shortcomings of the linear strategy optimal strategies are presented for two special cases of the general scenario and it is shown that memoryless relaying can achieve the capacity furthermore for the general gaussian relay channel a parametric piecewise linear pl mapping is proposed and analyzed the achievable rates obtained by the pl mapping are computed numerically and optimized for a certain number of design parameters it is concluded that optimized pl relaying always outperforms conventional instantaneous linear relaying amplify and forward it is also illustrated that the proposed pl relaying scheme can improve on sophisticated block markov encoding i e decode and forward when the source relay link is ill conditioned relative to other links furthermore pl relaying can work at rates close to those achieved by side information encoding i e compress and forward but at a much lower complexity

on the starting and stopping problem application in reversible investments in this work we solve completely the starting and stopping problem when the dynamics of the system are a general adapted stochastic process we use backward stochastic differential equations bsdes and snell envelopes finally we give some numerical results

a petrov galerkin formulation for advection reaction diffusion problems abstract in this work we present a new method called su c pg to solve advection reaction diffusion scalar equations by the finite element method fem the supg for streamline upwind petrov galerkin method is currently one of the most popular methods for advection diffusion problems due to its inherent consistency and efficiency in avoiding the spurious oscillations obtained from the plain galerkin method when there are discontinuities in the solution following this ideas tezduyar and park treated the more general advection reaction diffusion problem and they developed a stabilizing term for advection reaction problems without significant diffusive boundary layers in this work an supg extension for all situations is performed covering the whole plane represented by the peclet number and the dimensionless reaction number the scheme is based on the extension of the super convergence feature through the inclusion of an additional perturbation function and a corresponding proportionality constant both proportionality constants that one corresponding to the standard perturbation function from supg and the new one introduced here are selected in order to verify the super convergence feature i e exact nodal values are obtained for a restricted class of problems uniform mesh no source term constant physical properties it is also shown that the su c pg scheme verifies the discrete maximum principle dmp that guarantees uniform convergence of the finite element solution moreover it is shown that super convergence is closely related to the dmp motivating the interest in developing numerical schemes that extend the super convergence feature to a broader class of problems

finite element method for solving the dirac eigenvalue problem with linear basis functions abstract in this work we will treat the spurious eigenvalues obstacle that appears in the computation of the radial dirac eigenvalue problem using numerical methods the treatment of the spurious solution is based on applying petrov galerkin finite element method the significance of this work is the employment of just continuous basis functions thus the need of a continuous function which has a continuous first derivative as a basis as in 2 3 is no longer required the petrov galerkin finite element method for the dirac eigenvalue problem strongly depends on a stability parameter that controls the size of the diffusion terms added to the finite element formulation for the problem the mesh dependent parameter is derived based on the given problem with the particular basis functions

a new implementation of the element free galerkin method abstract element free galerkin methods efg are methods for solving partial differential equations with moving least squares interpolants efg methods require only nodal data no element connectivity is needed in a previous implementation of the efg method lagrange multipliers were used to enforce the essential boundary condition however the use of lagrange multipliers increases the cost of solving the linear algebraic equations a new implementation is developed based on a modified variational principle in which the lagrange multipliers are replaced at the outset by their physical meaning so that the discrete equations are banded in addition weighted orthogonal basis functions are constructed so the need for solving equations at each quadrature point is eliminated numerical examples show that the present implementation effectively computes stress concentrations and stress intensity factors at cracks with very irregular arrangements of nodes the latter makes it very advantageous for modelling progressive cracking

on channel capacity per unit cost memoryless communication channels with arbitrary alphabets where each input symbol is assigned a cost are considered the maximum number of bits that can be transmitted reliably through the channel per unit cost is studied it is shown that if the input alphabet contains a zero cost symbol then the capacity per unit cost admits a simple expression as the maximum normalized divergence between two conditional output distributions the direct part of this coding theorem admits a constructive proof via stein s lemma on the asymptotic error probability of binary hypothesis tests single user multiple access and interference channels are studied

capacity of a class of multicast tree networks in this paper we characterize the capacity of a new class of discrete memoryless multicast networks having a tree topology for achievability a novel coding scheme is constructed where some relays employ a combination of decode and forward and compress and forward and the other relays perform a random binning such that codebook constructions and relay operations are independent for each node and do not depend on the network topology for converse a new technique of iteratively manipulating inequalities exploiting the tree topology is used this class of multicast tree networks includes the class of diamond networks studied by kang and ulukus as a special case

hp cloud approximation of the dirac eigenvalue problem the way of stability we apply hp cloud method to the radial dirac eigenvalue problem the difficulty of occurrence of spurious eigenvalues among the genuine ones in the computation is resolved the method of treatment is based on assuming hp cloud petrov galerkin scheme to construct the weak formulation of the problem which adds a consistent diffusivity to the variational formulation the size of the artificially added diffusion term is controlled by a stability parameter tau the derivation of tau assumes the limit behavior of the eigenvalues at infinity the parameter tau is applicable for generic basis functions this is combined with the choice of appropriate intrinsic enrichments in the construction of the cloud shape functions c 2014 elsevier inc all rights reserved

filter and forward relay design for mimo ofdm systems in this paper the filter and forward ff relay design for multiple input multiple output mimo orthogonal frequency division multiplexing ofdm systems is investigated due to the considered mimo structure the ff relay design is investigated in the framework of joint design together with the linear mimo transceiver as the design criterion first the minimization of weighted sum mean square error mse is considered the joint design in this case is approached based on alternating optimization that iterates between the optimal design of the ff relay for given mimo precoding and decoding matrices and the optimal design of mimo precoding and decoding matrices for a given ff relay filter second a more advanced problem of joint design for rate maximization is considered the second problem is approached based on the obtained result regarding the first problem of weighted sum mse minimization and the existing result regarding the relationship between weighted mse minimization and rate maximization numerical results show the effectiveness of the proposed ff relay design method and significant performance improvement by the proposed ff relay over widely considered simple af relays for mimo ofdm systems

quickest detection with exponential penalty for delay the problem of detecting a change in the probability distribution of a random sequence is considered stopping times are derived that optimize the tradeoff between detection delay and false alarms within two criteria in both cases the detection delay is penalized exponentially rather than linearly as has been the case in previous formulations of this problem the first of these two criteria is to minimize a worst case measure of the exponential detection delay within a lower bound constraint on the mean time between false alarms expressions for the performance of the optimal detection rule are also developed for this case it is seen for example that the classical page cusum test can be arbitrarily unfavorable relative to the optimal test under exponential delay penalty the second criterion considered is a bayesian one in which the unknown change point is assumed to obey a geometric prior distribution in this case the optimal stopping time effects an optimal trade off between the expected exponential detection delay and the probability of false alarm finally generalizations of these results to problems in which the penalties for delay may be path dependent are also considered

asymptotic analysis of amplify and forward relaying in a parallel mimo relay network this paper studies the setup of a parallel mimo relay network in which k relays each equipped with n antennas assist in transmitting data between a source and a destination each equipped with m antennas m n in the half duplex mode it is assumed that there is no direct source destination link and the communication is performed in two hops an amplify and forward relaying scheme called incremental cooperative beamforming scheme icbs is introduced and shown to achieve the capacity of the network in the asymptotic case of k with a gap scaling of at most log k 4 k this result is shown to hold as long as the power of each relay is significantly larger than log3 k log log k k in addition in the case that the source power is equal to the relays power and both tend to infinity the proposed scheme is shown to achieve the full multiplexing gain regardless of the number of relays simulation results confirm the validity of analytical arguments

gaussian half duplex relay networks improved constant gap and connections with the assignment problem this paper considers a gaussian relay network where a source transmits a message to a destination with the help of n half duplex relays the information theoretic cut set upper bound to the capacity is shown to be achieved to within 1 96 n 2 bits by noisy network coding thereby reducing the previously known gap this gap is obtained as a special case of a more general constant gap result for gaussian half duplex multicast networks it is then shown that the generalized degrees of freedom of this network is the solution of a linear program where the coefficients of the linear inequality constraints are proved to be the solution of several linear programs referred as the assignment problem in graph theory for which efficient numerical algorithms exist the optimal schedule that is the optimal value of the 2 n possible transmit receive configuration states for the relays is investigated and known results for diamond networks are extended to general relay networks it is shown for the case of n 2 relays that only n 1 3 out of the 2 n 4 possible states have a strictly positive probability and suffice to characterize the capacity to within a constant gap extensive experimental results show that for a general n relay network with n leq 8 the optimal schedule has at most n 1 states with a strictly positive probability as an extension of a conjecture presented for diamond networks it is conjectured that this result holds for any half duplex relay network and any number of relays finally a network with n 2 relays is studied in detail to illustrate the channel conditions under which selecting the best relay is not optimal and to highlight the nature of the rate gain due to multiple relays

on the spurious solutions in the high order finite difference methods for eigenvalue problems in this paper the origins of spurious solutions occurring in the high order finite difference methods are studied based on a uniform mesh spurious modes are found in the high order one sided finite difference discretizations of many eigenvalue problems spurious modes are classified as spectral pollution and non spectral pollution the latter can be partially avoided by mesh refinement while the former persists when the mesh is refined through numerical studies of some prototype eigenvalue problems such as those of the helmholtz and beam equations we show that perfect central differentiation schemes do not produce any spurious modes nevertheless high order central difference schemes encounter difficulties in implementing complex boundary conditions we further show that the central difference schemes will produce spurious modes as well if asymmetric approximation is involved in boundary treatments in general central difference schemes are less likely to produce spurious modes than one sided difference schemes 2007 elsevier b v all rights reserved

streamline upwind petrov galerkin formulations for convection dominated flows with particular emphasis on the incompressible navier stokes equations abstract a new finite element formulation for convection dominated flows is developed the basis of the formulation is the streamline upwind concept which provides an accurate multidimensional generalization of optimal one dimensional upwind schemes when implemented as a consistent petrov galerkin weighted residual method it is shown that the new formulation is not subject to the artificial diffusion criticisms associated with many classical upwind methods the accuracy of the streamline upwind petrov galerkin formulation for the linear advection diffusion equation is demonstrated on several numerical examples the formulation is extended to the incompressible navier stokes equations an efficient implicit pressure explicit velocity transient algorithm is developed which accomodates several treatments of the incompressibility constraint and allows for multiple iterations within a time step the effectiveness of the algorithm is demonstrated on the problem of vortex shedding from a circular cylinder at a reynolds number of 100