finite element preconditioning for spectral multigrid methods abstract the good performance of finite element preconditioning for the algebraic spectral systems is demonstrated different types of multigrid strategies are compared the most efficient strategy consists of a pure richardson relaxation preconditioned by one v cycle of a finite element multigrid method the good smoothing properties of line relaxation become obvious the computational work for the various methods is estimated

a stochastic roundoff error analysis for the fast fourier transform we study the accuracy of the output of the fast fourier transform by estimating the expected value and the variance of the accompanying linear forms in terms of the expected value and variance of the relative roundoff errors for the elementary operations of addition and multiplication we compare the results with the corresponding ones for the direct algorithm for the discrete fourier transform and we give indications of the relative performances when different rounding schemes are used we also present the results of numerical experiments run to test the theoretical bounds and discuss their significance

pseudospectral solution of the two dimensional navier stokes equations in a disk an efficient and accurate algorithm for solving the two dimensional 2d incompressible navier stokes equations on a disk with no slip boundary conditions is described the vorticity stream function formulation of these equations is used and spatially the vorticity and stream functions are expressed as fourier chebyshev expansions the poisson and helmholtz equations which arise from the implicit explicit time marching scheme are solved as banded systems using a postconditioned spectral tau method the polar coordinate singularity is handled by expanding fields radially over the entire diameter using a parity modified chebyshev series and building partial regularity into the vorticity the no slip boundary condition is enforced by transferring one of the two boundary conditions imposed on the stream function onto the vorticity via a solvability constraint significant gains in run times were realized by parallelizing the code in message passage interface mpi

dynamic inflation of non linear elastic and viscoelastic rubber like membranes the present paper deals with the dynamic inflation of rubber like membranes the material is assumed to obey the hyperelastic mooney s model or the non linear viscoelastic christensen s model the governing equations of free inflation are solved by a total lagrangian finite element method for the spatial discretization and an explicit finite difference algorithm for the time integration scheme the numerical implementation of constitutive equations is highlighted and the special case of integral viscoelastic models is examined in detail the external force consists in a gas flow rate which is more realistic than a pressure time history then an original method is used to calculate the pressure evolution inside the bubble depending on the deformation state our numerical procedure is illustrated through different examples and compared with both analytical and experimental results these comparisons yield good agreement and show the ability of our approach to simulate both stable and unstable large strain inflations of rubber like membranes

the post critical analysis of axisymmetric hyper elastic membranes by the finite element method abstract an axisymmetric finite element that can model rubber like hyper elastic material has been employed to study post critical response in the inflation of axisymmetric membranes an extensive parametric study has been performed to investigate the non linear response of a tube under internal pressure the issue of combined proportional and non proportional loading in the context of incremental iterative solution is discussed further a robust bracketing procedure useful to compute clustered bifurcation points is proposed finally the eigen mode injection method is used to branch into the post critical paths contrary to previous findings the newton raphson method worked satisfactorily in all the cases tested

transient response analysis of systems with different damping models a response of systems with different damping models to transient excitations is studied using the finite element method for this purpose an efficient method using fast fourier transform has been developed this method is based on the trigonometrical representation of the input signals and matrix of the transfer functions as an example systems with viscous and viscoelastic structural and external damping are examined two forms of viscous damping are available in the present implementation raleigh damping and element damping the viscoelastic material behaviour is represented by the complex modulus model the present implementation gives the possibility to preserve exactly the frequency dependence of the storage and loss moduli of viscoelastic materials logarithmic decrements are determined using the steady state vibrations of systems to characterize their damping properties test problems and numerical examples are given to demonstrate the validity and application of the approach suggested in this paper

finite elasticity in spatial description linearization aspects with 3 d membrane applications the treatment of finite hyperelasticity set on the spatial configuration is described the fully consistent linearization of the corresponding field equations is carried out in detail it provides the basis of the exact newton raphson procedure for solution of the associated boundary value problem a membrane formulation is presented in which the incompressibility constraint usually employed in the description of rubber like materials is satisfied trivially the excellent performance of the proposed framework is demonstrated by means of 3 d membrane finite element simulations

bandwidth efficient modulation codes based on nonbinary irregular repeat accumulate codes using nonbinary low density parity check ldpc codes with random coset mapping bennatan and burshtein constructed bandwidth efficient modulation codes with remarkable performance under belief propagation bp decoding however due to the random nature of ldpc codes most of the good ldpc codes found in the literature do not have a simple encoding structure thus the encoding complexity of those ldpc codes can be as high as o n 2 where n is the codeword length to reduce the encoding complexity in this paper nonbinary irregular repeat accumulate ira codes with time varying characteristic and random coset mapping are proposed for bandwidth efficient modulation schemes the time varying characteristic and random coset mapping result in both permutation invariance and symmetry properties respectively in the densities of decoder messages the permutation invariance and symmetry properties of the proposed codes enable the approximations of densities of decoder messages using gaussian distributions under the gaussian approximation extrinsic information transfer exit charts for nonbinary ira codes are developed and several codes of different spectral efficiencies are designed based on exit charts in addition by proper selection of nonuniform signal constellations the constructed codes are inherently capable of obtaining shaping gains even without separate shaping codes simulation results indicate that the proposed codes not only have simple encoding schemes but also have remarkable performance that is even better than that constructed using nonbinary ldpc codes

low order polynomial approximation of propagators for the time dependent schro dinger equation abstract polynomial approximations for propagating the time dependent schrodinger equation are studied these methods are motivated by the numerical demands of systems with time dependent hamiltonian operators first order and second order magnus expansions are tested for approximating the time ordering operator the polynomials considered are based on a reduced basis space which is obtained by iterating the hamiltonian operator on an initial wavefunction the approximate polynomials are obtained by minimizing the error in the propagation one such approach which minimizes the residuum outside the reduced space is proved to be equivalent to the short time iterative lanczos procedure a second approach which uses a different optimization scheme the residuum method is found to be somewhat superior to the lanczos procedure numerical examples are used to illustrate the convergence of these methods the second order magnus approximation is found to be a significant improvement over the first order approximation regardless of method

on the asymptotic input output weight distributions and thresholds of convolutional and turbo like encoders we present a general method for computing the asymptotic input output weight distribution of convolutional encoders in some instances one can derive explicit analytic expressions in general though to determine the growth rate of the input output weight distribution for a particular normalized input weight spl kappa and output weight spl omega a system of polynomial equations has to be solved this method is then used to determine the asymptotic weight distribution of various concatenated code ensembles and to derive lower bounds on the thresholds of these ensembles under maximum likelihood ml decoding

serial concatenated tcm with an inner accumulate code part ii density evolution analysis in a companion paper we showed the existence of decoding thresholds for maximum likelihood ml decoding of a serial concatenated trellis coded modulation sctcm system with one or more inner accumulate codes in this paper we compute the decoding thresholds for an iterative non ml decoder by density evolution de assuming infinite blocklengths we also derive a stability condition for the particular case of an outer parity check code and a single inner accumulate code we show that for equiprobable signaling the bit wise log likelihood ratio densities for higher order constellations are symmetric furthermore when used in de these densities can be averaged without significantly affecting the resulting threshold values for an outer single parity check code the lowest decoding thresholds are achieved with two inner accumulate codes for an outer repeat code a single inner accumulate code gives the lowest thresholds at code rates r sub c 2 3 the decoding thresholds for the sctcm system are within 1 db of the constellation constrained channel capacity for additive white gaussian noise channels and within 1 5 db for independent identically distributed rayleigh channels simulation results verify the computed thresholds

instability investigation on fluid loaded pre stretched cylindrical membranes this paper discusses the evaluation of instabilities on the quasi static equilibrium path of fluid loaded pre stretched cylindrical membranes and the switching to a secondary branch at a bifurcation point the membrane is represented by only the in plane stress components for which an incompressible isotropic hyperelastic material model is assumed the free inflation problem yields governing equations and boundary conditions which are discretized by finite differences and solved by a newton raphson method an incremental arclength cubic extrapolation method is used to find generalized equilibrium paths with different parametrizations limit points and bifurcation points are observed on the equilibrium path when fluid level is seen as the controlling parameter an eigen mode injection method is employed to switch to a secondary equilibrium branch at the bifurcation point a limit point with respect to fluid level is observed for a partially filled membrane when the aspect ratio length radius is high whereas for smaller aspect ratios the limit point with respect to fluid level is observed at over filling pre stretch is observed to have a stiffening effect in the pre limit zone and a softening effect in the post limit zone

three dimensional elastic modeling by the fourier method earlier work on three dimensional forward modeling is extended to elastic waves using the equations of con servation of momentum and the stress strain relations for an isotropic elastic medium undergoing infinitesimal deformation in addition to arbitrary compressional or p wave velocity and density variation in lateral and vertical directions elastic modeling permits shear or s wave velocity variation as well the elastic wave equation is solved using a generalization of the method for the acoustic case computation of each time step begins by computing six strain components by per forming nine spatial partial differentiation operations on the three displacement components from the pre vious time step the six strains and two lame constants are linearly combined to yield six stress components

solution of the time dependent liouville von neumann equation dissipative evolution a mathematical and numerical framework has been worked out to represent the density operator in phase space and to propagate it in time under dissipative conditions the representation of the density operator is based on the fourier pseudospectral method which allows a description both in configuration as well as in momentum space a new propagation scheme which treats the complex eigenvalue structure of the dissipative liouville superoperator has been developed the framework has been designed to incorporate modern computer architecture such as parallelism and vectorization comparing the results to closed form solutions exponentially fast convergence characteristics in phase space as well as in the time propagation is demonstrated as an example of its usefulness the new method has been successfully applied to dissipation under the constraint of selection rules more specifically a harmonic oscillator which relaxes to equilibrium under the constraint of second order coupling to the bath was studied

on the renyi divergence joint range of relative entropies and a channel coding theorem this paper starts by considering the minimization of the renyi divergence subject to a constraint on the total variation distance based on the solution of this optimization problem the exact locus of the points bigl d q p 1 d q p 2 bigr is determined when p 1 p 2 and q are arbitrary probability measures which are mutually absolutely continuous and the total variation distance between p 1 and p 2 is not below a given value it is further shown that all the points of this convex region are attained by probability measures which are defined on a binary alphabet this characterization yields a geometric interpretation of the minimal chernoff information subject to a constraint on the variational distance this paper also derives an exponential upper bound on the performance of binary linear block codes or code ensembles under maximum likelihood decoding its derivation relies on the gallager bounding technique and it reproduces the shulman feder bound as a special case the bound is expressed in terms of the renyi divergence from the normalized distance spectrum of the code or the average distance spectrum of the ensemble to the binomially distributed distance spectrum of the capacity achieving ensemble of random block codes this exponential bound provides a quantitative measure of the degradation in performance of binary linear block codes or code ensembles as a function of the deviation of their distance spectra from the binomial distribution an efficient use of this bound is considered

analyzing the positivity preservation of numerical methods for the liouville von neumann equation abstract the density matrix is a widely used tool in quantum mechanics in order to determine its evolution with respect to time the liouville von neumann equation must be solved however analytic solutions of this differential equation exist only for simple cases additionally if the equation is coupled to maxwell s equations to model light matter interaction the resulting equation set the maxwell bloch or maxwell liouville von neumann mln equations becomes nonlinear in these advanced cases numerical methods are required since the density matrix has certain mathematical properties the numerical methods applied should be designed to preserve those properties we establish the criterion that only methods that have a completely positive trace preserving cptp update map can be used in long term simulations subsequently we assess the three most widely used methods the matrix exponential me method the runge kutta rk method and the predictor corrector pc approach whether they provide this feature and demonstrate that only the update step of the matrix exponential method is a cptp map

fast mixed radix real fourier transforms abstract it is shown that the self sorting variants of the mixed radix fft algorithm may be specialized to the case of real or conjugate symmetric input data in comparison with conventional procedures savings of around 20 are achieved in terms of operation counts a multiple real half complex transform package on the cray 1 based on the algorithms described here achieves a 30 saving in cpu time compared with a package using conventional algorithms a similar package has also been implemented on the cyber 205

exponential integrators for large systems of differential equations we study the numerical integration of large stiff systems of differential equations by methods that use matrix vector products with the exponential or a related function of the jacobian for large problems these can be approximated by krylov subspace methods which typically converge faster than those for the solution of the linear systems arising in standard stiff integrators the exponential methods also offer favorable properties in the integration of differential equations whose jacobian has large imaginary eigenvalues we derive methods up to order 4 which are exact for linear constant coefficient equations the implementation of the methods is discussed numerical experiments with reaction diffusion problems and a time dependent schrodinger equation are included

on restart and error estimation for krylov approximation of w f a v krylov algorithms are widely used for the solution of large scale linear systems a krylov approach is implemented also for the approximation of the vector w which results from operating with a function of a matrix on a vector v for example when solving a set of linear odes we have w f a v where f z rm exp tz the main drawback of the krylov algorithm lies in the need to store all the vectors spanning the approximation space when solving linear systems it is possible to overcome this drawback by restarting in this paper we show how to apply restarts in the general case of approximating w f a v this new algorithm allows a much more efficient approximation of the exponential operator than the standard krylov algorithm and it is especially useful in the case of functions which cannot be factored into a product of functions yet another interesting subject is the error estimate the scheme given here provides error estimates for free a trait which enables us to stop the algorithm whenever the desired accuracy is achieved

a model for the simulation of turbulent boundary layers in an incompressible stratified flow a model with several original physical and numerical features has been developed for direct numerical and large eddy simulations of a turbulent boundary layer in a stratified fluid the large scale flow for which the model was developed involves internal waves reflecting from a sloping boundary in the model the internal waves are generated by a new technique that forces monochromatic waves at specified wavelengths and frequencies a new analytic solution has been obtained representative of the forcing conditions in the model time discretization is based upon the projection method incorporating a third order adams bashforth scheme with variable time steps and spatial discretization employs fourth order compact differencing techniques on a variable grid that increases resolution close to the boundary the model is periodic in two dimensions and in the third dimension employs an open boundary and a solid sloping surface the pressure field is determined using a fast direct solution method of fourth order accuracy the model includes flow analysis aids such as tracking lagrangian particles and advected scalar quantities flow measurements are made of the integrated kinetic and potential energy balances local dissipation rates and the energy spectra the utility of the model is examined in a number of test problems it appears that the model is well suited for simulations of transitioning and turbulent boundary layers

on krylov subspace approximations to the matrix exponential operator krylov subspace methods for approximating the action of matrix exponentials are analyzed in this paper we derive error bounds via a functional calculus of arnoldi and lanczos methods that reduces the study of krylov subspace approximations of functions of matrices to that of linear systems of equations as a side result we obtain error bounds for galerkin type krylov methods for linear equations namely the biconjugate gradient method and the full orthogonalization method for krylov approximations to matrix exponentials we show superlinear error decay from relatively small iteration numbers onwards depending on the geometry of the numerical range the spectrum or the pseudospectrum the convergence to exp tau a v is faster than that of corresponding krylov methods for the solution of linear equations i tau a x v which usually arise in the numerical solution of stiff ordinary differential equations odes we therefore propose a new class of time integration methods for large systems of nonlinear differential equations which use krylov approximations to the exponential function of the jacobian instead of solving linear or nonlinear systems of equations in every time step

a comparison of different propagation schemes for the time dependent schro dinger equation abstract a comparison of three widely used time propagation algorithms for the time dependent schrodinger equation is described a typical evolution problem is chosen to demonstrate the efficiency and accuracy of the various methods on a numerical grid using a pseudo spectral fft spatial representation for scattering and bound state evolution the methods used second order differencing split operator propagation chebyshev polynomial expansion are discussed in terms of their applicability to various classes of dynamic problems a new method is introduced which is based upon a low order lanczos technique this method appears to offer an accurate and flexible alternative to the existing techniques overall the chebyshev method is recommended for time independent potentials and the lanczos method for time dependent potentials

the serial concatenation of rate 1 codes through uniform random interleavers until the analysis of repeat accumulate codes by divsalar et al 1998 few people would have guessed that simple rate 1 codes could play a crucial role in the construction of good binary codes we construct good binary linear block codes at any rate r 1 by serially concatenating an arbitrary outer code of rate r with a large number of rate 1 inner codes through uniform random interleavers we derive the average output weight enumerator we for this ensemble in the limit as the number of inner codes goes to infinity using a probabilistic upper bound on the minimum distance we prove that long codes from this ensemble will achieve the gilbert varshamov 1952 bound with high probability numerical evaluation of the minimum distance shows that the asymptotic bound can be achieved with a small number of inner codes in essence this construction produces codes with good distance properties which are also compatible with iterative turbo style decoding for selected codes we also present bounds on the probability of maximum likelihood decoding mld error and simulation results for the probability of iterative decoding error

a fourier method solution for the time dependent schrodinger equation as a tool in molecular dynamics a new method is presented for the solution of the time dependent schrbdinger equation in its application to physical and chemical molecular phenomena the method is based on discretizing space and time on a grid and using the fourier method to produce both spatial derivatives and second order differencing for time derivatives the method conserves norm and energy and preserves quantum mechanical commutation relations one and twodimensional examples where a comparison to analytic results is possible are investigated many phenomena of physics and chemistry have a common dynamical evolution pattern this pattern begins with an initial state which under the influence of the potentials evolves through time to produce a final asymptotic state among such phenomena are chemical reactions photodissociation unimolecular breakdown surface scattering and desorption the present study presents a numerical solution based on quantum mechanics for the common pattern or for the time dependent evolution of the state of the system the importance of exact numerical solutions is twofold first these solutions give a quantitative description of physical problems and also are of use as a bench mark to check approximation methods and to define their range of validity

methods for the numerical solution of the nonlinear schroedinger equation optimal l2 rates of convergence are established for several fully discrete schemes for the numerical solution of the nonlinear schroedinger equation both finite differences and finite elements are considered for the discretization in space while the integration in time is treated either by the leap frog technique or by a modified crank nicolson procedure which generalizes the one suggested by delfour fortin and payne and possesses two useful conserved quantities

explicit exponential runge kutta methods for semilinear parabolic problems the aim of this paper is to analyze explicit exponential runge kutta methods for the time integration of semilinear parabolic problems the analysis is performed in an abstract banach space framework of sectorial operators and locally lipschitz continuous nonlinearities we commence by giving a new and short derivation of the classical nonstiff order conditions for exponential runge kutta methods but the main interest of our paper lies in the stiff case by expanding the errors of the numerical method in terms of the solution we derive new order conditions that form the basis of our error bounds for parabolic problems we show convergence for methods up to order four and we analyze methods that were recently presented in the literature these methods have classical order four but they do not satisfy some of the new conditions therefore an order reduction is expected we present numerical experiments which show that this order reduction in fact arises in practical examples based on our new conditions we finally construct methods that do not suffer from order reduction

the minimum distance of turbo like codes worst case upper bounds are derived on the minimum distance of parallel concatenated turbo codes serially concatenated convolutional codes repeat accumulate codes repeat convolute codes and generalizations of these codes obtained by allowing nonlinear and large memory constituent codes it is shown that parallel concatenated turbo codes and repeat convolute codes with sub linear memory are asymptotically bad it is also shown that depth two serially concatenated codes with constant memory outer codes and sublinear memory inner codes are asymptotically bad most of these upper bounds hold even when the convolutional encoders are replaced by general finite state automata encoders in contrast it is proven that depth three serially concatenated codes obtained by concatenating a repetition code with two accumulator codes through random permutations can be asymptotically good

accuracy of the discrete fourier transform and the fast fourier transform fast fourier transform fft based computations can be far more accurate than the slow transforms suggest discrete fourier transforms computed through the fft are far more accurate than slow transforms and convolutions computed via fft are far more accurate than the direct results however these results depend critically on the accuracy of the fft software employed which should generally be considered suspect popular recursions for fast computation of the sine cosine table or twiddle factors are inaccurate due to inherent instability some analyses of these recursions that have appeared heretofore in print suggesting stability are incorrect even in higher dimensions the fft is remarkably stable

semi global approach for propagation of the time dependent schrdinger equation for time dependent and nonlinear problems a detailed exposition of highly efficient and accurate method for the propagation of the time dependent schrdinger equation 50 is presented the method is readily generalized to solve an arbitrary set of ode s the propagation is based on a global approach in which large time intervals are treated as a whole replacing the local considerations of the common propagators the new method is suitable for various classes of problems including problems with a time dependent hamiltonian nonlinear problems non hermitian problems and problems with an inhomogeneous source term in this paper a thorough presentation of the basic principles of the propagator is given we give also a special emphasis on the details of the numerical implementation of the method for the first time we present the application for a non hermitian problem by a numerical example of a one dimensional atom under the influence of an intense laser field the efficiency of the method is demonstrated by a comparison with the common rungekutta approach

a spectral scheme for wave propagation simulation in 3 d elastic anisotropic media this work presents a new scheme for wave propagation simulation in three dimensional 3 d elastic anisotropic media the algorithm is based on the rapid expansion method rem as a time integration algorithm and the fourier pseudospectral method for computation of the spatial derivatives the rem expands the evolution operator of the second order wave equation in terms of chebychev polynomials constituting an optimal series expansion with exponential convergence the modeling allows arbitrary elastic coefficients and density in lateral and vertical directions numerical methods which are based on finite difference techniques in time and space are not efficient when applied to realistic 3 d models since they require considerable computer memory and time to obtain accurate results on the other hand the fourier method permits a significant reduction of the working space and the rem algorithm gives machine accuracy with half the computational effort as the usual second order temporal differencing sch

nesting strategies for prime factor fft algorithms abstract several nesting techniques for the prime factor fft algorithm are examined these include the full nesting strategy of winograd s algorithm which gives a very low multiplication count a split nesting technique which requires the same number of multiplications as winograd s fft but fewer additions and a partial nesting technique which further reduces the addition count at the cost of some extra multiplications and requires the lowest total number of floating point operations applications to large multidimensional transforms as well as to 1 dimensional transforms are discussed on large scientific computers where the multiplications can be overlapped with the additions the prime factor algorithm without nesting remains the fastest and is the easiest to implement

solution of the schrodinger equation by a spectral method abstract a new computational method for determining the eigenvalues and eigenfunctions of the schrodinger equation is described conventional methods for solving this problem rely on diagonalization of a hamiltonian matrix or iterative numerical solutions of a time independent wave equation the new method in contrast is based on the spectral properties of solutions to the time dependent schrodinger equation the method requires the computation of a correlation function r 0 r t from a numerical solution r t fourier analysis of this correlation function reveals a set of resonant peaks that correspond to the stationary states of the system analysis of the location of these peaks reveals the eigenvalues with high accuracy additional fourier transforms of r t with respect to time generate the eigenfunctions the effectiveness of the method is demonstrated for a one dimensional asymmetric double well potential and for the two dimensional henon heiles potential

spectra and minimum distances of repeat multiple accumulate codes in this paper the ensembles of repeat multiple accumulate codes ram which are obtained by interconnecting a repeater with a cascade of m accumulate codes through uniform random interleavers are analyzed it is proved that the average spectral shapes of these code ensembles are equal to 0 below a threshold distance epsivm and moreover they form a nonincreasing sequence in m converging uniformly to the maximum between the average spectral shape of the linear random ensemble and 0 consequently the sequence epsivm converges to the gilbert varshamov gv distance a further analysis allows to conclude that if m ges 2 the ram are asymptotically good and that epsivm is the typical normalized minimum distance when the interleaver length goes to infinity combining the two results it is possible to conclude that the typical distance of the ensembles ram converges to the gilbert varshamov bound

robust procedures for converting among lindblad kraus and matrix representations of quantum dynamical semigroups given a quantum dynamical semigroup expressed as an exponential superoperator acting on a space of n dimensional density operators eigenvalue methods are presented by which canonical kraus and lindblad operator sum representations can be computed these methods provide a mathematical basis on which to develop novel algorithms for quantum process tomography the statistical estimation of superoperators and their generators from a wide variety of experimental data theoretical arguments and numerical simulations are presented which imply that these algorithms will be quite robust in the presence of random errors in the data

fast radix 2 3 4 and 5 kernels for fast fourier transformations on computers with overlapping multiply add instructions we present a new formulation of fast fourier transformation fft kernels for radix 2 3 4 and 5 which have a perfect balance of multiplies and adds these kernels give higher performance on machines that have a single multiply add mult add instruction we demonstrate the superiority of this new kernel on ibm and sgi workstations

nineteen dubious ways to compute the exponential of a matrix twenty five years later in principle the exponential of a matrix could be computed in many ways methods involving approximation theory differential equations the matrix eigenvalues and the matrix characteristic polyn

serial concatenated tcm with an inner accumulate code part i maximum likelihood analysis we propose a serial concatenated trellis coded modulation system using one or more inner rate 1 accumulate codes and a mapping to a higher order gray labeled signal constellation as outer codes we consider repeat codes single parity check codes and convolutional codes we show that under maximum likelihood decoding there exists a signal to noise ratio threshold beyond which the bit error probability goes to zero as the blocklength goes to infinity we then evaluate the performance for finite blocklengths using a modified union bound computer simulations demonstrate that the proposed system despite its use of a simple rate 1 inner code achieves performance in additive white gaussian noise and rayleigh fading that is comparable to or better than that of more complex systems suggested in the literature

performance analysis of 3 d turbo codes in this work we consider the minimum distance properties and convergence thresholds of 3 d turbo codes 3d tcs recently introduced by berrou here we consider binary 3d tcs while the original work of berrou considered double binary codes in the first part of the paper the minimum distance properties are analyzed from an ensemble perspective both in the finite length regime and in the asymptotic case of large block lengths in particular we analyze the asymptotic weight distribution of 3d tcs and show numerically that their typical minimum distance dmin may depending on the specific parameters asymptotically grow linearly with the block length i e the 3d tc ensemble is asymptotically good for some parameters in the second part of the paper we derive some useful upper bounds on the dmin when using quadratic permutation polynomial qpp interleavers with a quadratic inverse furthermore we give examples of interleaver lengths where an upper bound appears to be tight the best codes in terms of estimated dmin obtained by randomly searching for good pairs of qpps for use in the 3d tc are compared to a probabilistic lower bound on the dmin when selecting codes from the 3d tc ensemble uniformly at random this comparison shows that the use of designed qpp interleavers can improve the dmin significantly for instance we have found a 6144 2040 3d tc with an estimated dmin of 147 while the probabilistic lower bound is 69 higher rates are obtained by puncturing nonsystematic bits and optimized periodic puncturing patterns for rates 1 2 2 3 and 4 5 are found by computer search finally we give iterative decoding thresholds computed from an extrinsic information transfer chart analysis and present simulation results on the additive white gaussian noise channel to compare the error rate performance to that of conventional turbo codes

minimum distance and convergence analysis of hamming accumulate accumulate codes in this letter we consider the ensemble of codes formed by the serial concatenation of a hamming code and two accumulate codes we show that this ensemble is asymptotically good in the sense that most codes in the ensemble have minimum distance growing linearly with the block length thus the resulting codes achieve high minimum distances with high probability about half or more of the minimum distance of a typical random linear code of the same rate and length in our examples the proposed codes also show reasonably good iterative convergence thresholds which makes them attractive for applications requiring high code rates and low error rates such as optical communications and magnetic recording

linear precoders for bit interleaved coded modulation on awgn channels analysis and design criteria this paper investigates linear precoding for bit interleaved coded modulation bicm on additive white gaussian noise awgn channels concatenating a linear precoder as an inner encoder with an outer convolutional encoder produces a powerful code with a limited decoding complexity linear precoders are examined and optimized for two scenarios using i a noniterative decoding strategy and ii an iterative decoding strategy under a perfect feedback assumption the precoder design is based on an information theoretical approach on the one hand and a pair wise error probability pep analysis on the other hand both approaches render convenient precoder design rules for a binary phase shift keying bpsk signal set the optimal precoders that result from these rules are also derived numerical results confirm the analytical findings and simulations illustrate the effectiveness of the approach

explicit magnus expansions for solving the time dependent schrodinger equation the symmetric implicit operator difference multi layer schemes for solving the time dependent schr dinger equation based on decomposition of the evolution operator via the explicit magnus expansion up to the sixth order of accuracy with respect to the time step are presented reduced schemes for solving the set of coupled time dependent schr dinger equations with respect to the hyper radial variable are devised by using the kantorovich expansion of the wave packet over a set of appropriate parametric basis angular functions further discretization of the resulting problem with symmetric operators is implemented by means of the finite element method the convergence and efficiency of the numerical schemes are demonstrated in benchmark calculations of the exactly solvable models of a one dimensional time dependent oscillator a two dimensional oscillator in time dependent electric field by using the conventual angular basis and the inexactly solvable model of a three dimensional kicked hydrogen atom in a magnetic field by using a parametric basis of the angular oblate spheroidal functions developed in our previous paper chuluunbaatar o et al 2007 j phys a math theor 40 11485 524

minimum pseudoweight analysis of 3 dimensional turbo codes in this paper we consider pseudocodewords of relaxed linear programming lp decoding of 3 dimensional turbo codes 3d tcs we present a relaxed lp decoder for 3d tcs adapting the relaxed lp decoder for conventional turbo codes proposed by feldman in his thesis we show that the 3d tc polytope is proper and c symmetric and make a connection to finite graph covers of the 3d tc factor graph this connection is used to show that the support set of any pseudocodeword is a stopping set of iterative decoding of 3d tcs using maximum a posteriori constituent decoders on the binary erasure channel furthermore we compute ensemble average pseudoweight enumerators of 3d tcs and perform a finite length minimum pseudoweight analysis for small cover degrees moreover an explicit description of the fundamental cone of the 3d tc polytope is given finally we present an extensive numerical study of small to medium block length 3d tcs which shows that 1 typically i e in most cases when the minimum distance d min and or the stopping distance h min is high the minimum pseudoweight on the additive white gaussian noise channel is strictly smaller than both d min and h min and that 2 the minimum pseudoweight grows with the block length at least for small to medium block lengths

self sorting mixed radix fast fourier transforms abstract some examples are given of the uses of the fft algorithm in numerical weather prediction the algorithm is derived by means of matrix factorization in such a way that the many possible variants can be obtained in a unified manner particular attention is paid to self sorting variants of the algorithm but skeleton fortran routines are included for all the canonical forms the fft works by decomposing the discrete fourier transform into a sequence of short transforms algorithms for these short transforms are presented and used to derive operation counts for the whole algorithm the implementation of the fft on vector computers is described and in the final section it is demonstrated how savings can be achieved in the case of two dimensional transforms

a semi implicit spectral method for the anelastic equations this paper describes the efficient and accurate solution of the two dimensional anelastic equations by a fourier chebyshev spectral method a fourth order runge kutta method is used for the time integration with the diffusion terms treated implicitly and all other terms including the pressure gradient treated explicitly the model is free from aliasing and converges quickly once the solution is resolved numerical results are given for nonlinear flow generated by an atmospheric density current

self sorting in place fft algorithm with minimum working space presents a modification of temperton s 1991 self sorting in place radix p fft algorithm this modification reduces the required temporary working space from order of p sup 2 to p 1 providing a better match to the limited number of registers in a cpu

a new set of minimum add small n rotated dft modules abstract a self sorting in place prime factor fft algorithm introduced in an earlier paper was based on a set of modules for performing small discrete fourier transforms dfts with an optional rotation of the results the modules were designed to reduce the total number of additions in the fft algorithm in specializing this algorithm to the case of real or conjugate symmetric input data it was found necessary to redesign these modules to impose a particular structure in some cases the new modules proved to require fewer operations than the old we describe the design procedure and compare the new operation counts with those for winograd s dft modules the algorithms for the new modules are given in detail these will be useful in coding fft algorithms of either the prime factor or conventional variety

time domain simulations of the nonlinear maxwell equations using operator exponential methods in this paper we propose a krylov subspace based operator exponential method for time domain simulations of the maxwell equations with general nonlinear polarizations this includes classical chi 2 or chi 3 nonlinearities and or nonlinear coupled system dynamics as an illustration we compare the performance of our approach to certain well known methods for the case of pulse self steepening in a material with negative kerr nonlinearity for this system we also develop an appropriate analytical reference solution in addition we demonstrate that our approach allows to treat the complex nonlinear dynamics of various physical systems classical and or quantum coupled to electromagnetic fields

random coding techniques for nonrandom codes this work provides techniques to apply the channel coding theorem and the resulting error exponent which was originally derived for totally random block code ensembles to ensembles of codes with less restrictive randomness demands as an example the random coding technique can even be applied for an ensemble that contains a single code for a specific linear code we get an upper bound for the error probability which equals gallager s 1968 random coding bound up to a factor determined by the maximum ratio between the weight distribution of the code and the expected random weight distribution

computing the action of the matrix exponential with an application to exponential integrators a new algorithm is developed for computing e ta b where a is an n times n matrix and b is n times n 0 with n 0 ll n the algorithm works for any a its computational cost is dominated by the formation of products of a with n times n 0 matrices and the only input parameter is a backward error tolerance the algorithm can return a single matrix e ta b or a sequence e t ka b on an equally spaced grid of points t k it uses the scaling part of the scaling and squaring method together with a truncated taylor series approximation to the exponential it determines the amount of scaling and the taylor degree using the recent analysis of al mohy and higham siam j matrix anal appl 31 2009 pp 970 989 which provides sharp truncation error bounds expressed in terms of the quantities a k 1 k for a few values of k where the norms are estimated using a matrix norm estimator shifting and balancing are used as preprocessing steps to reduce the cost of the algorithm numerical experiments show that the algorithm performs in a numerically stable fashion across a wide range of problems and analysis of rounding errors and of the conditioning of the problem provides theoretical support experimental comparisons with matlab codes based on krylov subspace chebyshev polynomial and laguerre polynomial methods show the new algorithm to be sometimes much superior in terms of computational cost and accuracy an important application of the algorithm is to exponential integrators for ordinary differential equations it is shown that the sums of the form sum k 0 p varphi k a u k that arise in exponential integrators where the varphi k are related to the exponential function can be expressed in terms of a single exponential of a matrix of dimension n p built by augmenting a with additional rows and columns and the algorithm of this paper can therefore be employed

an axisymmetric b spline model for the non linear inflation of rubberlike membranes a new b spline interpolation model for the free inflation of axisymmetric rubberlike membranes is presented in this paper the membrane coordinates are interpolated by cubic b splines and the treatment of the spline boundary conditions is highlighted both circular and cylindrical cases are considered the formulation of the element is detailed and formulas for the tangent operator are presented in order to solve the non linear system of equations the newton raphson algorithm is sucessfully associated with the arc length method some numerical examples are presented to validate our approach and to exhibit convergence properties of the method

unveiling turbo codes some results on parallel concatenated coding schemes a parallel concatenated coding scheme consists of two simple constituent systematic encoders linked by an interleaver the input bits to the first encoder are scrambled by the interleaver before entering the second encoder the codeword of the parallel concatenated code consists of the input bits to the first encoder followed by the parity check bits of both encoders this construction can be generalized to any number of constituent codes parallel concatenated schemes employing two convolutional codes as constituent codes in connection with an iterative decoding algorithm of complexity comparable to that of the constituent codes have been previously shown to yield remarkable coding gains close to theoretical limits they have been named and are known as turbo codes we propose a method to evaluate an upper bound to the bit error probability of a parallel concatenated coding scheme averaged over all interleavers of a given length the analytical bounding technique is then used to shed some light on some crucial questions which have been floating around in the communications community since the proposal of turbo codes

efficient methods for linear schrodinger equation in the semiclassical regime with time dependent potential we build efficient and unitary hence stable methods for the solution of the linear time dependent schrodinger equation with explicitly time dependent potentials in a semiclassical regime the magnus zassenhaus schemes presented here are based on a combination of the zassenhaus decomposition bader et al 2014 found comput math 14 689 720 doi 10 1007 s10208 013 9182 8 1 with the magnus expansion of the time dependent hamiltonian we conclude with numerical experiments 1 http dx doi org 10 1007 s10208 013 9182 8