adaptive finite element methods for hyperbolic systems with application to transient acoustics the solution of the hyperbolic systems of equations governing transient acoustics by adaptive finite elements and various finite difference time discretization schemes is addressed emphasis is placed on the use of a class of implicit runge kutta methods for temporal approximations

a new upper bound on the ml decoding error probability of linear binary block codes in awgn interference performance evaluation of maximum likelihood ml soft decision decoded binary block codes is usually carried out using bounding techniques many tight upper bounds on the error probability of binary codes are based on the so called gallager s first bounding technique gfbt the tangential sphere bound tsb of poltyrev which has been believed for many years to offer the tightest bound developed for binary block codes is an example within the framework of the tsb and gfbt we apply a new method referred to as the added hyper plane ahp technique to the decomposition of the error probability this results in a bound developed upon the application of two stages of the gfbt with two different gallager regions culminating in a tightened upper bound beyond the tsb the proposed bound is simple and only requires the spectrum of the binary code

on improved bounds on the decoding error probability of block codes over interleaved fading channels with applications to turbo like codes we derive here improved upper bounds on the decoding error probability of block codes which are transmitted over fully interleaved rician fading channels coherently detected and maximum likelihood ml decoded we assume that the fading coefficients during each symbol are statistically independent due to a perfect channel interleaver and that perfect estimates of these fading coefficients are provided to the receiver the improved upper bounds on the block and bit error probabilities are derived for fully interleaved fading channels with various orders of space diversity and are found by generalizing some previously introduced upper bounds for the binary input additive white gaussian nose awgn channel the advantage of these bounds over the ubiquitous union bound is demonstrated for some ensembles of turbo codes and low density parity check ldpc codes and it is especially pronounced in a portion of the rate region exceeding the cutoff rate our generalization of the duman and salehi bound duman and salehi 1998 duman 1998 which is based on certain variations of gallager s 1965 bounding technique is demonstrated to be the tightest reported upper bound we therefore apply it to calculate numerically upper bounds on the thresholds of some ensembles of turbo like codes referring to the optimal ml decoding for certain ensembles of uniformly interleaved turbo codes the upper bounds derived here also indicate good match with computer simulation results of efficient iterative decoding algorithms

on interleaved differentially encoded convolutional codes we study a serially interleaved concatenated code construction where the outer code is a standard convolutional code and the inner code is a recursive convolutional code of rate 1 we focus on the ubiquitous inner differential encoder used in particular to resolve phase ambiguities double differential encoder used to resolve both phase and frequency ambiguities and another rate 1 recursive convolutional code of memory 2 we substantiate analytically the rather surprising result that the error probabilities corresponding to a maximum likelihood ml coherently detected antipodal modulation over the additive white gaussian noise awgn channel for this construction are advantageous as compared to the stand alone outer convolutional code this is in spite of the fact that the inner code is of rate 1 the analysis is based on the tangential sphere upper bound of an ml decoder incorporating the ensemble weight distribution wd of the concatenated code where the ensemble is generated by all random and uniform interleavers this surprising result is attributed to the wd thinning observed for the concatenated scheme which shapes the wd of the outer convolutional code to resemble more closely the binomial distribution typical of a fully random code of the same length and rate this gain is maintained regardless of a rather dramatic decrease as demonstrated here in the minimum distance of the concatenated scheme as compared to the minimum distance of the outer stand alone convolutional code the advantage of the examined serially interleaved concatenated code given in terms of bit and or block error probability which is decoded by a practical suboptimal decoder over the optimally decoded standard convolutional code is demonstrated by simulations and some insights into the performance of the iterative decoding algorithm are also discussed though we have investigated only specific constructions of constituent inner rate 1 and outer codes we trust hinging on the rational of the arguments here that these results extend to many other constituent convolutional outer codes and rate 1 inner recursive convolutional codes

a new aitken type method for accelerating iterative sequences in this paper we present an improved acceleration method for solving nonlinear equations the new acceleration technique was inspired by one derivation of aitken s 2 process some numerical examples are given to illustrate the abilities of the new proposed acceleration technique

on the error exponents of improved tangential sphere bounds the performance of maximum likelihood ml decoded binary linear block codes over the additive white gaussian noise awgn channel is addressed via the tangential sphere bound tsb and two of its recent improved versions the correspondence is focused on the derivation of the error exponents of these bounds although it was shown that some recent improvements of the tsb tighten this bound for finite length codes it is demonstrated in this correspondence that their error exponents coincide for an arbitrary ensemble of binary linear block codes the common value of these error exponents is explicitly expressed in terms of the asymptotic growth rate of the average distance spectrum

gallager bounds for noncoherent decoders in fading channels recently gallager s bounding techniques have been used to derive tight performance bounds for coded systems in fading channels most works in this field have thus far dealt with coherent decoding this paper develops gallager bounds for noncoherent systems in fading channels unlike coherent decoding the exact error probability of a noncoherent decoder detector conditioned on the fading coefficients does not admit a closed form expression this difficulty is overcome in this paper by employing the chernoff technique although it weakens the bounds to some extent the chernoff technique enables the derivations of the limit before average lba bound and gallager bounds in closed form for noncoherent fading channels numerical examples show that the proposed bounds are convergent and are tighter than the conventional union bound

some multi step iterative methods for solving nonlinear equations in this paper we develop some new iterative methods for solving nonlinear equations by using the techniques introduced in golbabai and javidi 2007 1 and rafiq and rafiullah 2008 20 we establish the convergence analysis of the proposed methods and then demonstrate their efficiency by taking some test problems

a new ber upper bound for multiuser downlink systems we consider improvement of bit error rate ber upper bounds based on the notion of decomposable error vectors devs introduced by s verdu for downlink multiuser space time systems over rayleigh fading channels although omission of devs and limiting before averaging lba technique are known to improve the standard union bound ub considerably it is mathematically intractable to obtain a bound in a closed form in this paper assuming maximum likelihood ml detection for downlink multiuser space time spreading sts systems we introduce a new modification of the decomposability of error vectors and propose a new ber upper bound we prove that the proposed bound is tighter than the standard union bound and the bound based on the overall decomposability the numerical results show that the proposed bound is also tighter than the bound based on positive sum decomposability psd in the scenario of downlink multiuser transmission

performance bounds for erasure list and decision feedback schemes with linear block codes a message independence property and some new performance upper bounds are derived in this work for erasure list and decision feedback schemes with linear block codes transmitted over memoryless symmetric channels similar to the classical work of forney this work is focused on the derivation of some gallager type bounds on the achievable tradeoffs for these coding schemes where the main novelty is the suitability of the bounds for both random and structured linear block codes or code ensembles the bounds are applicable to finite length codes and to the asymptotic case of infinite block length and they are applied to low density parity check code ensembles

on the order of convergence of adomian method in this paper we contemplate the order of convergence of the decomposition method and we apply the results to some problems

convergent series solution of nonlinear equations abstract the author s decomposition method 1 provides a new efficient computational procedure for solving large classes of nonlinear and or stochastic equations these include differential equations containing polynomial exponential and trigonometric terms negative or irrational powers and product nonlinearities 2 also included are partial differential equations 3 delay differential equations 4 algebraic equations 5 and matrix equations 6 which describe physical systems essentially the method provides a systematic computational procedure for equations containing any nonlinear terms of physical significance the procedure depends on calculation of the author s a n a finite set of polynomials 1 13 in terms of which the nonlinearities can be expressed this paper shows important properties of the a n which ensure an accurate and computable convergent solution by the author s decomposition method 1 since the nonlinearities and or stochasticity which can be handled are quite general the results are potentially extremely useful for applications and make a number of common approximations such as linearization unnecessary

bounds on maximum likelihood decoding performance for linear codes at low rates for a given linear code ensemble upper bounds on the error probability under maximum likelihood decoding are investigated at low rates a class of symmetric memoryless channels suitable for bhattacharyya type bounds which are particularly of importance at low rates is introduced over a symmetric channel a lower bound on the error exponent is derived for a given linear code a sufficient condition for achieving the expurgated exponent which is the best among known error exponents at low rates within a fixed discrepancy is given over a general discrete memoryless channel the same analysis provides a lower bound on the average error exponent for an ensemble of coset codes generated by a given linear code the bounding technique is extended to the case of generalized maximum likelihood decoding with erasure and list decoding options

new performance bounds for turbo codes we derive a new upper bound on the word and bit error probabilities of turbo codes with maximum likelihood decoding by using the gallager bound since the derivation of the bound for a given interleaver is intractable we assume uniform interleaving as in the derivation of the standard union bound for turbo codes the result is a generalization of the transfer function bound and remains useful for a wider range of signal to noise ratios particularly for some range below the channel cutoff rate the new bound is also applicable to other linear codes

tightened upper bounds on the ml decoding error probability of binary linear block codes the performance of maximum likelihood ml decoded binary linear block codes is addressed via the derivation of tightened upper bounds on their decoding error probability the upper bounds on the block and bit error probabilities are valid for any memoryless binary input and output symmetric communication channel and their effectiveness is exemplified for various ensembles of turbo like codes over the additive white gaussian noise awgn channel an expurgation of the distance spectrum of binary linear block codes further tightens the resulting upper bounds

unilateral contact of two solids subject to large deformations formulation and existence results the approach that is currently the most widely used for formulating the unilateral frictionless contact between two deformable solids involves two key elements the orthogonal projection of one potential contact material surface on another and the action reaction principle of contact forces in the present paper we investigate this approach in the general case of large deformations and study unilateral frictionless boundary value problems of elasticity formulated by means of it the conditions for the orthogonal projection to be unique or further a c 1 diffeomorphism are established an extended action reaction principle is explicitly given for the forces acting on a pair of potential contact surfaces assuming the solids under consideration can be described by polyconvex hyperelastic laws we formulate the associated unilateral frictionless boundary value problem as a minimum principle and show the existence of a solution to it

generalized union bound for space time codes gallager s second bounding technique also known as the generalized union bound is employed to derive a new upper bound on the error probability of space time codes stcs with maximum likelihood ml decoding on quasi static rayleigh fading channels the new bound is distinguished by two characteristics unlike the classical union bound the new bound is rapidly convergent and is only a few decibels away from simulation results and compared with gallager s first bound it has better computational efficiency and numerical stability hence the new bound is a useful tool for performance analysis and computer search of good stcs moreover the correlation between fading coefficients is easily accommodated by the new bound the application of the new bound to convolutional coding on block fading channels is also demonstrated and an improved version is derived for the bit error probability of maximum a posteriori probability decoding

formulation and analysis of conserving algorithms for frictionless dynamic contact impact problems this paper presents the formulation of conserving time stepping algorithms for frictionless dynamic contact of solids a new class of finite element methods is proposed for the solution of these problems that exhibit the same conservation laws as the underlying continuum dynamical system the proposed methods are based on a penalty regularization of the constrained contact problem and lead to full conservation of the total energy of the system including the regularization penalty potential during persistent contact and restoration of the original energy upon release both linear and angular momenta are conserved by the scheme furthermore the newly developed methods have the ability to enforce the associated constraints in the velocity besides the impenetrability constraint in the displacements while preserving the conservation restoration properties of the final numerical scheme a modification of these schemes is described that assures positive energy dissipation if desired even in the highly nonlinear setting of contact impact problems leading to contact schemes with high frequency energy dissipation representative numerical simulations are presented illustrating the performance of the proposed numerical schemes

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

a new iterative method to compute nonlinear equations the aim of this paper is to construct a new efficient iterative method to solve nonlinear equations the new method is based on the proposals of abbasbandy on improving the order of accuracy of newton raphson method s abbasbandy improving newton raphson method for nonlinear equations by modified adomian decomposition method applied mathematics and computation 145 2003 887 893 and on the proposals of babolian and biazar on improving the order of accuracy of adomian s decomposition method e babolian j biazar on the order of convergence of adomian method applied mathematics and computation 130 2002 383 387 the convergence of the new scheme is proved and at least the cubic order of convergence is established several examples are presented and compared to other methods showing the accuracy and fast convergence of this new method also it is shown in this paper that the modified adomian s method developed by babolian and biazar to solve nonlinear equations e babolian j biazar solution of nonlinear equations by modified adomian decomposition method applied mathematics and computation 132 2002 167 172 should be slightly modified due to the fact that convergence of adomian s method does not ensure convergence of the modified method an example illustrates this fact which unlike what is claimed by the authors does not converge with their method but with a simple different choice of the zero component becomes convergent

new techniques for upper bounding the ml decoding performance of binary linear codes in this paper new techniques are presented to either simplify or improve most existing upper bounds on the maximum likelihood ml decoding performance of the binary linear codes over additive white gaussian noise awgn channels firstly the recently proposed union bound using truncated weight spectrum by ma et al is re derived in a detailed way based on gallager s first bounding technique gfbt where the good region is specified by a sub optimal list decoding algorithm the error probability caused by the bad region can be upper bounded by the tail probability of a binomial distribution while the error probability caused by the good region can be upper bounded by most existing techniques secondly we propose two techniques to tighten the union bound on the error probability caused by the good region the first technique is based on pair wise error probabilities the second technique is based on triplet wise error probabilities which can be upper bounded by the fact that any three bipolar vectors form a non obtuse triangle the proposed bounds improve the conventional union bounds but have a similar complexity since they involve only the q function the proposed bounds can also be adapted to bit error probabilities

numerical approximation of a wave equation with unilateral constraints the system u tt u xx ni f x in 0 l times 0 t with initial data u x 0 u 0 x u t x 0 u 1 x almost everywhere on 0 l and boundary conditions u 0 t 0 for all t geq 0 and the unilateral condition u x l t geq 0 u l t geq k 0 u l t k 0 u x l t 0 models the longitudinal vibrations of a rod whose motion is limited by a rigid obstacle at one end a new variational formulation is given existence and uniqueness are proved finite elements and finite difference schemes are given and their convergence is proved numerical experiments are reported the characteristic schemes perform better in terms of accuracy and the subcharacteristic schemes look better

design of energy conserving algorithms for frictionless dynamic contact problems this paper proposes a formulation of dynamic contact problems which enables exact algorithmic conservation of linear momentum angular momentum and energy in finite element simulations it is seen that a lagrange multiplier enforcement of an appropriate contact rate constraint produces these conservation properties a related method is presented in which a penalty regularization of the aforementioned rate constraint is utilized this penalty method sacrifices the energy conservation property but is dissipative under all conditions of changing contact so that the global algorithm remains stable notably it is also shown that augmented lagrangian iteration utilizing this penalty kernel reproduces the energy conserving i e lagrange multiplier solution to any desired degree of accuracy the result is a robust stable method even in the context of large deformations as is shown by some representative numerical examples in particular the ability of the formulation to produce accurate results where more traditional integration schemes fail is emphasized by the numerical simulations 1997 by john wiley sons ltd

improvement of gallager upper bound and its variations for discrete channels a new tight upper bound on the maximum likelihood ml word and bit error decoding probabilities for specific codes over discrete channels is presented it constitutes an enhanced version of the gallager upper bound and its variations resulting from the duman salehi second bounding technique an efficient technique is developed that in the case of symmetric channels overcomes the difficulties associated with the direct computation of the proposed bound surprisingly apart from the distance and input output weight enumerating functions iowefs the bound depends also on the coset weight distribution of the code

exact solutions of some coupled nonlinear partial differential equations using the homotopy perturbation method the purpose of this study is to introduce a modification of the homotopy perturbation method using laplace transform and pade approximation to obtain closed form solutions of nonlinear coupled systems of partial differential equations two test examples are given the coupled nonlinear system of burger equations and the coupled nonlinear system in one dimensional thermoelasticity the results obtained ensure that this modification is capable of solving a large number of nonlinear differential equations that have wide application in physics and engineering

improved upper bounds on the ml decoding error probability of parallel and serial concatenated turbo codes via their ensemble distance spectrum the ensemble performance of parallel and serial concatenated turbo codes is considered where the ensemble is generated by a uniform choice of the interleaver and of the component codes taken from the set of time varying recursive systematic convolutional codes following the derivation of the input output weight enumeration functions of the ensembles of random parallel and serial concatenated turbo codes the tangential sphere upper bound is employed to provide improved upper bounds on the block and bit error probabilities of these ensembles of codes for the binary input additive white gaussian noise awgn channel based on coherent detection of equi energy antipodal signals and maximum likelihood decoding the influence of the interleaver length and the memory length of the component codes is investigated the improved bounding technique proposed here is compared to the conventional union bound and to a alternative bounding technique by duman and salehi 1998 which incorporates modified gallager bounds the advantage of the derived bounds is demonstrated for a variety of parallel and serial concatenated coding schemes with either fixed or random recursive systematic convolutional component codes and it is especially pronounced in the region exceeding the cutoff rate where the performance of turbo codes is most appealing these upper bounds are also compared to simulation results of the iterative decoding algorithm

an augmented lagrangian method for discrete large slip contact problems reference lmaf article 1993 001view record in web of science record created on 2005 09 14 modified on 2017 05 10

non linear dynamics of three dimensional rods exact energy and momentum conserving algorithms the long term dynamic response of non linear geometrically exact rods under going finite extension shear and bending accompanied by large overall motions is addressed in detail the central objective is the design of unconditionally stable time stepping algorithms which exactly preserve fundamental constants of the motion such as the total linear momentum the total angular momentum and for the hamiltonian case the total energy this objective is accomplished in two steps first a class of algorithms is introduced which conserves linear and angular momentum this result holds independently of the definition of the algorithmic stress resultants second an algorithmic counterpart of the elastic constitutive equations is developed such that the law of conservation of total energy is exactly preserved conventional schemes exhibiting no numerical dissipation symplectic algorithms in particular are shown to lead to unstable solutions when the high frequencies are not resolved compared to conventional schemes there is little if any additional computational cost involved in the proposed class of energy momentum methods the excellent performance of the new algorithm in comparison to other standard schemes is demonstrated in several numerical simulations

an analytical method for approximate performance evaluation of binary linear block codes an analytical method for approximate performance evaluation of binary linear block codes using an additive white gaussian noise channel model with binary phase shift keying modulation is presented we focus on the probability density function of the bit log likelihood ratio llr which is expressed in terms of the gram charlier series expansion this expansion requires knowledge of the statistical moments of the bit llr we introduce an analytical method for calculating these moments this is based on some recursive calculations involving certain weight enumerating functions of the code it is proved that the approximation can be as accurate as desired if we use enough terms in the gram charlier series expansion numerical results are provided for some examples which demonstrate close agreement with simulation results

dynamic contact impact problems energy conservation and planetary gear trains abstract the paper is a continuation of the work presented in comp meth appl mech eng 190 2001 1903 aimed at modeling of a general class of dynamic contact impact problems for systems of rigid bodies the contact is assumed to be frictionless and the main challenge is to model the exchange between the kinetic and elastic energies in the system this calls for a discretization scheme that conserves linear and angular momentum and first of all the total energy at the discrete level such a scheme has been presented in comp meth appl mech eng 190 2001 1903 and in this work we complement it with a very general treatment of the no penetration condition for two elastic bodies the approach is based on the concept of the sign rvachev function and it provides a natural generalization of the classical point to line condition arch computat meth eng 2 1995 1 the work has been motivated with the modeling of planetary gear trains and has resulted in the first to our best knowledge two dimensional parallel finite element simulator for gear sets parallel finite element simulator of planetary gear trains ph d dissertation the university of texas 2001

performance analysis on ldpc coded systems over quasi static mimo fading channels in this paper we derive closed form upper bounds on the error probability of low density parity check ldpc coded modulation schemes operating on quasi static fading channels the bounds are obtained from the so called fano gallager s tight bounding techniques and can be readily calculated when the distance spectrum of the code is available in deriving the bounds for multiple input multiple output mimo systems we assume the ldpc code is concatenated with the orthogonal space time block code as an inner code we obtain an equivalent single input single output siso channel model for this concatenated coded modulation system the upper bounds derived here indicate good matches with simulation results of a complete transceiver system over rayleigh and rician mimo fading channels in which the iterative detection and decoding algorithm is employed at the receiver

high order taylor galerkin and adaptive h p methods for second order hyperbolic systems application to elastodynamics a new family of high order taylor galerkin schemes is presented for the analysis of second order hyperbolic systems the use of such schemes within an adaptive h p finite element strategy for spatial approximation in two dimensional problems is described numerical results are presented to demonstrate performance of these methods

upper bounds to error probabilities of coded systems beyond the cutoff rate a family of upper bounds to error probabilities of coded systems was recently proposed by d divsalar see ieee communication theory workshop 1999 jpl tmo prog rep 42 139 1999 these bounds are valid for transmission over the additive white gaussian noise channel and require only the knowledge of the weight spectrum of the code words after illustrating these bounds we extend them to fading channels contrary to the union bound our bounds maintain their effectiveness below the signal to noise ratio snr at which the cutoff rate of the channel equals the rate of the code some applications are shown first we derive upper bounds to the minimum snr necessary to achieve zero error probability as the code block length increases to infinity next we use our bounds to predict the performance of turbo codes and low density parity check codes

coding for parallel channels gallager bounds and applications to turbo like codes the transmission of coded communication systems is widely modeled to take place over a set of parallel channels this model is used for transmission over block fading channels rate compatible puncturing of turbo like codes multicarrier signaling multilevel coding etc new upper bounds on the maximum likelihood ml decoding error probability are derived in the parallel channel setting we focus on the generalization of the gallager type bounds and discuss the connections between some versions of these bounds the tightness of these bounds for parallel channels is exemplified for structured ensembles of turbo codes repeat accumulate ra codes and some of their recent variations e g punctured accumulate repeat accumulate codes the bounds on the decoding error probability of an ml decoder are compared to computer simulations of iterative decoding the new bounds show a remarkable improvement over the union bound and some other previously reported bounds for independent parallel channels this improvement is exemplified for relatively short block lengths and it is pronounced when the block length is increased in the asymptotic case where we let the block length tend to infinity inner bounds on the attainable channel regions of modern coding techniques under ml decoding are obtained based solely on the asymptotic growth rates of the average distance spectra of these code ensembles

numerical solution of differential equations in the deterministic limit of stochastic theory although the methodology of stochastic differential equations was developed to achieve statistical separability in the stochastic case the deterministic limit is investigated both as a verification of the theory and also for possible value as a deterministic technique

a formulation of conserving impact system based on localized lagrange multipliers this paper proposes a new finite element method of frictional impact of elastic bodies the formulation introduces a contact frame that is placed in between contacting bodies and represents the contact surface the nonpenetration condition and the slip stick condition are defined between the contacting body and the contact frame with the aid of the independent localized lagrange multipliers representing the contact forces the position of the contact frame and the local coordinate of the contacting node along the contact frame are also treated as the independent variable which enables the exact satisfaction of the constraint conditions without the deficiency or redundant constraint the energy and momentum conservation algorithm is applied to the proposed impact system for the case of frictional impact the linear momentum is exactly conserved and the angular momentum is approximately conserved with negligible error copyright 2006 john wiley sons ltd

a continuum based finite element formulation for the implicit solution of multibody large deformation frictional contact problems in this paper a formulation is presented for the finite element treatment of multibody large deformation frictional contact problems the term multibody is used to mean that when two bodies mechanically contact both may be deformable a novel aspect of the approach advocated is that the equations governing contact are developed in the continuum setting first before deriving the corresponding finite element equations this feature distinguishes the current work from many earlier treatments of contact problems and renders it considerably more general in particular the approach yields a characterization of the frictional constraint assuming a coulomb law suitable for arbitrary discretizations in either two or three dimensions a geometric framework is constructed within which both frictionless and frictional response are naturally described making subsequent finite element discretization a straightforward substitution of finite dimensional solution spaces for their continuum counterparts to our knowledge this general formulation and implementation of the frictional contact problem in a finite element setting has not been reported previously in the literature the development includes exact linearization of the statement of virtual work which enables optimal convergence properties for newton raphson solution strategies and which appears to be highly desirable if not essential for the general robustness of implicit finite element techniques since the theory and subsequent linearization require no limitations on the amount of deformation or relative sliding that can occur the resulting treatment of frictional contact is suitable for a wide range of examples displaying significant non linear behaviour this assertion is substantiated through presentation of a variety of examples in both two and three dimensions

variations on the gallager bounds with some applications by generalizing the framework of the second version of the duman salehi bound encompassing also deterministic and random codes we demonstrate its rather broad features and show that this variation provides the natural bridge between the 1961 and 1965 gallager bounds this approach entails a natural geometric interpretation encompassing also a large class of e0cient recent bounds or their cherno2 versions which are demonstrated to be special cases of the generalized second version of the duman salehi bound implications and applications of these observations are pointed out referring to known bounds as well as a novel extended version of the shulman feder bound c 2001 elsevier science b v all rights reserved

coding theorems for turbo code ensembles this paper is devoted to a shannon theoretic study of turbo codes we prove that ensembles of parallel and serial turbo codes are good in the following sense for a turbo code ensemble defined by a fixed set of component codes subject only to mild necessary restrictions there exists a positive number spl gamma sub 0 such that for any binary input memoryless channel whose bhattacharyya noise parameter is less than spl gamma sub 0 the average maximum likelihood ml decoder block error probability approaches zero at least as fast as n sup spl beta where spl beta is the interleaver gain exponent defined by benedetto et al in 1996

new gallager bounds in block fading channels in this paper we propose a new upper bound on the error performance of binary linear codes over block fading channels by employing gallager s first and second bounding techniques as the proposed bound is numerically intensive in its general form we consider two special cases namely the spherical bound and the ds2 exponential bound which are found to be tight in nonergodic and near ergodic block fading channels respectively the tightness of the proposed bounds is demonstrated for turbo codes many existing bounds for quasistatic or fully interleaved fading channels can be viewed as special cases of the proposed gallager bound

on the solution of algebraic equations by the decomposition method abstract the decomposition method g adomian stochastic systems academic press new york 1983 developed to solve nonlinear stochastic differential equations has recently been generalized to nonlinear and or stochastic partial differential equations systems of equations and delay equations and applied to diverse applications as pointed out previously see reference above the methodology is an operator method which can be used for nondifferential operators as well extension has also been made to algebraic equations involving real or complex coefficients this paper deals specifically with quadratic cubic and general higher order polynomial equations and negative or nonintegral powers and random algebraic equations further work on this general subject appears elsewhere g adomian stochastic systems ii academic press new york in press

performance bounds for nonbinary linear block codes over memoryless symmetric channels the performance of nonbinary linear block codes is studied in this paper via the derivation of new upper bounds on the block error probability under maximum likelihood ml decoding the transmission of these codes is assumed to take place over a memoryless and symmetric channel the new bounds which are based on the gallager bounds and their variations are applied to the gallager ensembles of nonbinary and regular low density parity check ldpc codes these upper bounds are also compared with sphere packing lower bounds this study indicates that the new upper bounds are useful for the performance evaluation of coded communication systems which incorporate nonbinary coding techniques

distance spectrum and performance of channel coded physical layer network coding for binary input gaussian two way relay channels we investigate a channel coded physical layer network coding cpnc scheme for binary input gaussian two way relay channels in this scheme the codewords of the two users are transmitted simultaneously the relay computes and forwards a network coded nc codeword without complete decoding of the two users individual messages we propose a new punctured codebook method to explicitly find the distance spectrum of the cpnc scheme based on that we derive an asymptotically tight performance bound for the error probability our analysis shows that compared to the single user scenario the cpnc scheme exhibits the same minimum euclidean distance but an increased multiplicity of error events with minimum distance at a high snr this leads to an snr penalty of at most ln2 in linear scale for long channel codes of various rates our analytical results match well with the simulated performance

variations on the gallager bounds connections and applications there has been renewed interest in deriving tight bounds on the error performance of specific codes and ensembles based on their distance spectrum we discuss many reported upper bounds on the maximum likelihood ml decoding error probability and demonstrate the underlying connections that exist between them in addressing the gallager bounds and their variations we focus on the duman and salehi see ieee trans commun vol 46 p 717 723 1998 variation which originates from the standard gallager bound a large class of efficient bounds or their chernoff versions is demonstrated to be a special case of the generalized second version of the duman and salehi bounds implications and applications of these observations are pointed out including the fully interleaved fading channel resorting to either matched or mismatched decoding the proposed approach can be generalized to geometrically uniform nonbinary codes finite state channels bit interleaved coded modulation systems and it can be also used for the derivation of upper bounds on the conditional decoding error probability

a numerically stable dual method for solving strictly convex quadratic programs an efficient and numerically stable dual algorithm for positive definite quadratic programming is described which takes advantage of the fact that the unconstrained minimum of the objective function can be used as a starting point its implementation utilizes the cholesky and qr factorizations and procedures for updating them the performance of the dual algorithm is compared against that of primal algorithms when used to solve randomly generated test problems and quadratic programs generated in the course of solving nonlinear programming problems by a successive quadratic programming code the principal motivation for the development of the algorithm these computational results indicate that the dual algorithm is superior to primal algorithms when a primal feasible point is not readily available the algorithm is also compared theoretically to the modified simplex type dual methods of lemke and van de panne and whinston and it is illustrated by a numerical example

solution of the fully fuzzy linear systems using the decomposition procedure abstract this paper tries to extend the adomian decomposition method for solving fully fuzzy linear systems shown as ffls for finding a positive fuzzy vector x that satisfies a x b where a and b are respectively a fuzzy matrix and a fuzzy vector we employ dubois and prade s approximate arithmetic operators on lr fuzzy numbers we also transform the ffls and use the adomian decomposition method for solving an ffls then we compare this method with the jacobi iterative technique additionally we give some numerical examples

steady state forced response of a mechanical oscillator with combined parametric excitation and clearance type non linearity a mechanical system exhibiting combined parametric excitation and clearance type non linearity is examined analytically and experimentally in an effort to explain complex behavior that is commonly observed in the steady state forced response of rotating machines the specific case of a preloaded mechanical oscillator having a periodically time varying stiffness function and subject to a symmetric backlash condition is considered a generalized solution methodology is proposed based on the harmonic balance method the resulting non linear algebraic equations are solved by using a direct newton raphson technique in which a closed form jacobian matrix is computed using frequency domain methods analytical solutions are validated by comparison with numerical integration results and experimental measurements obtained from a gear dynamics test rig

transmission of nonuniform memoryless sources via nonsystematic turbo codes we investigate the joint source channel coding problem of transmitting nonuniform memoryless sources over binary phase shift keying modulated additive white gaussian noise and rayleigh fading channels via turbo codes in contrast to previous work recursive nonsystematic convolutional encoders are proposed as the constituent encoders for heavily biased sources we prove that under certain conditions and when the length of the input source sequence tends to infinity the encoder state distribution and the marginal output distribution of each constituent recursive convolutional encoder become asymptotically uniform regardless of the degree of source nonuniformity we also give a conjecture which is empirically validated on the condition for the higher order distribution of the encoder output to be asymptotically uniform irrespective of the source distribution consequently these conditions serve as design criteria for the choice of good encoder structures as a result the outputs of our selected nonsystematic turbo codes are suitably matched to the channel input since a uniformly distributed input maximizes the channel mutual information and hence achieves capacity simulation results show substantial gains by the nonsystematic codes over previously designed systematic turbo codes furthermore their performance is within 0 74 1 17 db from the shannon limit finally we compare our joint source channel coding system with two tandem schemes which employ a fourth order huffman code performing near optimal data compression and a turbo code that either gives excellent waterfall bit error rate ber performance or good error floor performance at the same overall transmission rate our system offers robust and superior performance at low bers 10 sup 4 while its complexity is lower

performance of parallel concatenated coding schemes in this paper ensembles of parallel concatenated codes are studied and rigorous results on their asymptotic performance under the assumption of maximum likelihood ml decoding are presented in particular it is proven that in any parallel concatenation scheme with k branches where all k encoders are recursive and the bhattacharyya parameter of the channel is sufficiently small the bit error rate ber and the word error rate go to 0 exactly like n 1 k and n 2 k respectively different types of ensembles by changing the subgroup of permutations used to interconnect the various encoders are considered

kocak s method shows that an unwittingly exaggerated convergence order is in fact 2 iterative solution of a nonlinear equation f x 0 usually means a repetitive scheme to locate a fixed point of a related equation x g x kocak s acceleration method smoothly gears up iterations with the aid of a superior secondary solver g k x g x g x x g x m x x 1 m x where g x 1 1 m x is a gain and m x 1 1 g x is a straight line slope the accelerator shows that a previously published article a biazar a amirtemoori an improvement to the fixed point iterative method amc 182 2006 567 571 unwittingly exaggerated the convergence order of the solver it presented this solver boils down to an indirect application of newton s method solving g x x 0 which means that it is of second order hence their claim that it increases the order of convergence as much as desired is false the scheme wastes higher derivatives

a perturbed lagrangian formulation for the finite element solution of contact problems making use of a perturbed lagrangian formulation a finite element procedure for contact problems is developed for the general case in which node to node contact no longer holds the proposed procedure leads naturally to a discretization of the contact interface into contact segments within the context of a bilinear interpolation for the displacement field a mixed finite element approximation is introduced by assuming discont naous contact pressure constant on the contact segment because of this piece wise constant approximation the gap function enters into the formulation in an average sense instead of through a point wise definition numerical examples are presented that illustrate the performance of the proposed procedure current finite element formulations for contact problems based on either the classical lagrange parameter procedure l 3 12 203 or the penalty function method 4 6 11 are characterized by a point wise enforcement of the contact constraint condition in the sense that penetration of the bodies is established on a nodal basis moreover in this methods the recovery of the contact pressure over the element from the contact nodal forces generally requires an additional procedure within the framework of classical lagrange multiplier methods the contact condition is exactly satisfied by transforming the constrained problem into an unconstrained one with the introduction of additional variables lagrange multipliers these extra variables add computational effort to the solution process which often requires special procedures to handle the presence of zero diagonal terms penalty methods on the other hand enable one to transform the constrained problem into an unconstrained one without introducing additional variables the constraint condition is now satisfied only approximately for finite values of the penalty parameter the main difhculty associated with these methods however lies in the poor conditioning of the problem as the penalty is increased to more accurately enforce the constraint condition this is a well understood phenomenon particularly in the context of the incompressible and nearly incompressible problem in solid and fluid mechanics e g see l 22 25 for a review recently augmented lagrangian procedures have been proposed as a promising way to partially overcome these difficulties and regularize the penalty formulation e g see the survey in 7 8 within the framework of zinearited e u c it is possible to restrict the finite element formulation of contact problems by assuming that node to node contact occurs this is in fact the case often considered in the literature l 2 4 6 12 20 211 in the general context of fully

a co rotational element time integration strategy for non linear dynamics new procedures are proposed for implicit dynamic analysis using the finite element method the main aim is to give stable solutions with significant rigid body motions in particular rotations in contrast to most conventional approaches the time integration strategy is closely linked to the element technologies with the latter involving a form of co rotational procedure for the undamped situation one of the solution procedures leads to an algorithm that exactly conserves energy when constant external forces are applied i e with gravity loading

outage exponent a unified performance metric for parallel fading channels the parallel fading channel which consists of finite number of subchannels is very important because it can be used to formulate many practical communication systems the outage probability on the other hand is widely used to analyze the relationship among the communication efficiency reliability signal to noise ratio snr and channel fading to the best of our knowledge the previous works only studied the asymptotic outage performance of the parallel fading channels which are only valid for a large number of subchannels or high snrs in this paper a unified performance metric which we shall refer to as the outage exponent will be proposed our approach is mainly based on the large deviations theory and meijer s g function it is shown that the proposed outage exponent is not only an accurate estimation of the outage probability for any number of subchannels any snr and any target transmission rate but also provides an easy way to compute the outage capacity finite snr diversity multiplexing tradeoff and snr gain the asymptotic performance metrics such as the delay limited capacity ergodic capacity and diversity multiplexing tradeoff can be directly obtained by letting the number of subchannels or snr tend to infinity similar to gallager s error exponent a reliable function for parallel fading channels which illustrates a fundamental relationship between the transmission reliability and efficiency can also be defined from the outage exponent therefore the proposed outage exponent provides a complete and comprehensive performance measure for parallel fading channels

nonlinear stochastic differential delay equations abstract the methods used by adomian and his co workers to solve linear and nonlinear stochastic differential equations will be demonstrated to be applicable to differential equations deterministic or stochastic involving delays constant time dependent or random

conservative discretization of contact impact problems for nearly rigid bodies abstract a discretization scheme for contact impact problems related to modeling of gears is proposed the problem is first discretized in time and then a variational formulation for the resulted one step problem is developed a finite element discretization completes the discretization process the scheme is a reinterpretation of the general simo laursen chavla algorithm in the context of the rigid body motion superimposed with small elastic deformation it conserves precisely the linear momentum and total energy and approximately the angular momentum the discretization method is illustrated with two numerical examples the standard 1d impact problem for an elastic rod and a 2d model problem of an elastic wheel bouncing within a constraining box

scalable tfeti with optional preconditioning by conjugate projector for transient frictionless contact problems of elasticity abstract the feti based domain decomposition method is adapted to implement the time step of the newmark scheme for the solution of dynamic contact problems without friction if the ratio of the decomposition and discretization parameters is kept uniformly bounded then the cost of the time step is proved to be proportional to the number of nodal variables the algorithm uses our in a sense optimal mprgp algorithm for the solution of strictly convex bound constrained quadratic programming problems with optional preconditioning by the conjugate projector to the subspace defined by the trace of the rigid body motions on the artificial subdomain interfaces the proof of optimality combines the convergence theory of our mprgp algorithm the classical bounds on the spectrum of the mass and stiffness matrices and our theory of the preconditioning by a conjugate projector for nonlinear problems the results are confirmed by numerical solution of 2d and 3d dynamic contact problems

an improvement to the fixed point iterative method the problem of convergence of the fixed point iterative method has been studied in this article the main object of this article is to improve the convergence so that the number of iterations is reduced to just few iterations a technique is presented to increase the order of convergence as much as desired to illustrate the ability of this technique some examples for which regular method needs many times of iterations are presented

solution of nonlinear equations by modified adomian decomposition method in this paper we modify the standard adomian method for solution of the nonlinear equation f x 0 four examples are presented and compared using standard and modified adomian methods

tight exponential upper bounds on the ml decoding error probability of block codes over fully interleaved fading channels we derive tight exponential upper bounds on the decoding error probability of block codes which are operating over fully interleaved rician fading channels coherently detected and maximum likelihood decoded it is assumed that the fading samples are statistically independent and that perfect estimates of these samples are provided to the decoder these upper bounds on the bit and block error probabilities are based on certain variations of the gallager bounds these bounds do not require integration in their final version and they are reasonably tight in a certain portion of the rate region exceeding the cutoff rate of the channel by inserting interconnections between these bounds we show that they are generalized versions of some reported bounds for the binary input additive white gaussian noise channel

nonlinear stochastic dynamical systems in physical problems abstract a number of important equations of physics are shown to fit into the structure of a nonlinear stochastic differential equation which can then be solved by the decomposition 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