generalized mixed variational principles and solutions of ill conditioned problems in computational mechanics part ii shear locking abstract although the finite element method fem has been extensively applied to various areas of engineering the ill conditioned problems occurring in many situations are still thorny to deal with this study attempts to provide a high performing and simple approach to the solutions of ill conditioned problems the theoretical foundation of it is the parametrized variational principles called the generalized mixed variational principles gmvps initiated by rong in 1981 gmvps can solve many kinds of ill conditioned problems in computational mechanics among them four cases are investigated in detail the volumetric locking the shear locking the inhomogeneousness and the membrane locking problems composing four parts of the study part i part iv respectively this paper is part ii wherein a gmvp specially suited to the reissner plate theory and timoshenko beam theory is constructed providing a mathematical foundation for establishing fem formulations which can automatically unlock the shear locking and produce no spurious zero energy modes

design of rate compatible ra type low density parity check codes using splitting in this letter a new rate control scheme called splitting is proposed to construct low rate codes from high rate codes which splits rows of parity check matrices of repeat accumulate type ra type ldpc codes by adding new parity bits when a high degree check node is split into two low degree check nodes by making the check node degree distribution in a concentrated form the performance of low rate codes can be improved we also explicitly construct rate compatible repeat ra type ldpc rc ra type ldpc codes using splitting for code rates from 1 3 to 4 5 and compare this with other rc ra type ldpc codes

self compensation technique for simplified belief propagation algorithm the min sum algorithm is the most common method to simplify the belief propagation algorithm for decoding low density parity check ldpc codes however there exists a performance gap between the min sum and belief propagation algorithms due to nonlinear approximation in this paper a self compensation technique using dynamic normalization is thus proposed to improve the approximation accuracy the proposed scheme scales the min sum algorithm by a dynamic factor that can be derived theoretically from order statistics moreover applying the proposed technique to several ldpc codes for dvb s2 system the average signal to noise ratio degradation which results from approximation inaccuracy and quantization error is reduced to 0 2 db not only does it enhance the error correcting capability of the min sum algorithm but the proposed self compensation technique also preserves a modest hardware cost after realized with 0 13 mum standard cell library the dynamic normalization requires about 100 additional gates for each check node unit in the min sum algorithm

on the nonexistence of entire solutions of certain type of nonlinear differential equations abstract by utilizing nevanlinna s value distribution theory of meromorphic functions it is shown that the following type of nonlinear differential equations f n z p n 3 f p 1 e 1 z p 2 e 2 z has no nonconstant entire solutions where n is an integer 4 p 1 and p 2 are two polynomials 0 1 2 are two nonzero constants with 1 2 rational number and p n 3 f denotes a differential polynomial in f and its derivatives with polynomials in z as the coefficients of degree no greater than n 3 it is conjectured that the conclusion remains to be valid when p n 3 f is replaced by p n 1 f or p n 2 f

a recursive approach to low complexity codes a method is described for constructing long error correcting codes from one or more shorter error correcting codes referred to as subcodes and a bipartite graph a graph is shown which specifies carefully chosen subsets of the digits of the new codes that must be codewords in one of the shorter subcodes lower bounds to the rate and the minimum distance of the new code are derived in terms of the parameters of the graph and the subeodes both the encoders and decoders proposed are shown to take advantage of the code s explicit decomposition into subcodes to decompose and simplify the associated computational processes bounds on the performance of two specific decoding algorithms are established and the asymptotic growth of the complexity of decoding for two types of codes and decoders is analyzed the proposed decoders are able to make effective use of probabilistic information supplied by the channel receiver e g reliability information without greatly increasing the number of computations required it is shown that choosing a transmission order for the digits that is appropriate for the graph and the subcodes can give the code excellent burst error correction abilities the construction principles

finite alphabet iterative decoders part i decoding beyond belief propagation on the binary symmetric channel we introduce a new paradigm for finite precision iterative decoding on low density parity check codes over the binary symmetric channel the messages take values from a finite alphabet and unlike traditional quantized decoders which are quantized versions of the belief propagation bp decoder the proposed finite alphabet iterative decoders faids do not propagate quantized probabilities or log likelihoods and the variable node update functions do not mimic the bp decoder rather the update functions are maps designed using the knowledge of potentially harmful subgraphs that could be present in a given code thereby rendering these decoders capable of outperforming the bp in the error floor region on certain column weight three codes of practical interest we show that there exist faids that surpass the floating point bp decoder in the error floor region while requiring only three bits of precision for the representation of the messages hence faids are able to achieve a superior performance at much lower complexity we also provide a methodology for the selection of faids that is not code specific but gives a set of candidate faids containing potentially good decoders in the error floor region for any column weight three code we validate the code generality of our methodology by providing particularly good three bit precision faids for a variety of codes with different rates and lengths

on locking free shear deformable beam finite elements abstract this is an elementary exposition of beam finite element models an overview of existing and new displacement finite element models of the euler bernoulli and shear deformation beam theories is presented a locking free finite element model using the form of the exact solution of the timoshenko beam theory is developed the element contains the euler bernoulli beam element as a special case and yields exact nodal values for the generalized displacements for constant material and geometric properties of beams the procedure is extended to develop a locking free finite element model of the simplified third order theory of beams the element contains the euler bernoulli and the locking free timoshenko beam finite elements as special cases the element stiffness matrix of the unified beam bending element is 4 4 and yet has the superconvergence character the advantage of this element is that it can be used to obtain exact nodal displacements and forces from the equilibrium equations of the element in a frame structural analysis using one finite element per a structural member this cannot be achieved with the traditional equal interpolation reduced integration element because the element exhibits shear locking for thin members unless two or more elements per a structural member are used

iterative decoding of one step majority logic deductible codes based on belief propagation previously the belief propagation bp algorithm has received a lot of attention in the coding community mostly due to its near optimum decoding for low density parity check ldpc codes and its connection to turbo decoding in this paper we investigate the performance achieved by the bp algorithm for decoding one step majority logic decodable osmld codes the bp algorithm is expressed in terms of likelihood ratios rather than probabilities as conventionally presented the proposed algorithm fits better the decoding of osmld codes with respect to its numerical stability due to the fact that the weights of their check sums are often much higher than that of the corresponding ldpc codes although it has been believed that osmld codes are far inferior to ldpc codes we show that for medium code lengths say between 200 1000 bits the bp decoding of osmld codes can significantly outperform bp decoding of their equivalent ldpc codes the reasons for this behavior are elaborated

a deviation based conditional upper bound on the error floor performance for min sum decoding of short ldpc codes conditional upper bounds are given for min sum decoding of low density parity check codes in the error floor region it is generally thought that absorbing sets i e small collections of variable nodes connected to a relatively small number of unsatisfied check nodes are the primary source of errors in the error floor region the conditional upper bounds presented here are based on the assumption that all error floor errors are caused by absorbing sets in order to bound the probability of error associated with each absorbing set a directed edge tanner graph is used to link absorbing sets to low weight deviations these low weight deviations result when a proportionally large number of nodes within a stopping set belong to an absorbing set contained inside the stopping set a complete collection of the most problematic absorbing sets and the minimum deviation weights that result from them are used to derive a conditional upper bound on the probability of error for min sum decoding of low density parity check codes simulation results are given to demonstrate the accuracy of the bound

a kinematically exact finite element formulation of planar elastic plastic frames a finite element formulation of finite deformation static analysis of plane elastic plastic frames subjected to static loads is presented in which the only function to be interpolated is the rotation of the centroid axis of the beam one of the advantages of such a formulation is that the problem of the field consistency does not arise exact non linear kinematic relationships of the finite strain beam theory are used which assume the bernoulli hypothesis of plane cross sections finite displacements and rotations as well as finite extensional and bending strains are accounted for the effects of shear strains and non conservative loads are at present neglected yet they can simply be incorporated in the formulation because the potential energy of internal forces does not exist with elastic plastic material the principle of virtual work is introduced as the basis of the finite element formulation a generalized principle of virtual work is proposed in which the displacements rotation extensional and bending strains and the lagrangian multipliers are independent variables by exploiting the special structure of the equations of the problem the displacements the strains and the multipliers are eliminated from the generalized principle of virtual work a novel principle is obtained in which the rotation becomes the only function to be approximated in its finite element implementation it is shown that n 1 point numerical integration must be employed in conjunction with n node interpolation polynomials for the rotation and the lobatto rule is recommended regarding the integration over the cross section it is demonstrated by numerical examples that due to discontinuous integrands no integration order defined as computationally efficient yet accurate enough could be suggested the theoretical findings and a nice performance of the derived finite elements are illustrated by numerical examples

block processing soft input soft output demodulator for coded psk using dct based phase noise estimation this paper considers the detection of coded phaseshift keying signals subjected to additive white gaussian noise and oscillator phase noise we propose a detector that partitions the received frame into smaller blocks and models the unknown phasor variations over each block as a truncated discrete cosine transform dct expansion detection and decoding are iteratively performed between a soft input soft output siso demodulator a siso demapper and a siso decoder based on the sum product algorithm and the factor graph framework whereas the expectation maximization algorithm is used in the demodulator for the dct coefficients estimation the resulting demodulator is shown to have an excellent performance complexity tradeoff and to be well suited for parallel processing on multiple cores

low complexity x ems algorithms for nonbinary ldpc codes the extended min sum ems algorithm is redescribed as a reduced search trellis algorithm called m ems algorithm two variants of the m ems algorithm called t ems algorithm and d ems algorithm are presented simulation results show that these three algorithms referred to as x ems algorithms for convenience combined with factor correction techniques perform almost as well as the q ary sum product algorithm qspa but with a much lower complexity

mean field and mixed mean field iterative decoding of low density parity check codes in this paper the mean field mf and mixed mean field mmf algorithms for decoding low density parity check ldpc codes are considered the mf principle is well established in statistical physics and artificial intelligence instead of using a single completely factorized approximated distribution as in the mf approach the mixed mf algorithm forms a weighted average of several mf distributions as an approximation of the true posterior probability distribution the mf decoding algorithm for linear block codes is derived and shown to be an approximation of the a posteriori probability app decoding algorithm the mf approach is then developed in the context of iterative decoding and presented as an approximation of the popular belief propagation decoding method these results are extended to iterative decoding with the mmf algorithm simulation results show that the mf and mmf decoding algorithms yield a good performance complexity tradeoff especially when employed for decoding ldpc codes based on finite geometries

message passing algorithms and improved lp decoding linear programming lp decoding for low density parity check codes and related domains such as compressed sensing has received increased attention over recent years because of its practical performance coming close to that of iterative decoding algorithms and its amenability to finite blocklength analysis several works starting with the work of feldman showed how to analyze lp decoding using properties of expander graphs this line of analysis works for only low error rates about a couple of orders of magnitude lower than the empirically observed performance it is possible to do better for the case of random noise as shown by daskalakis and koetter and vontobel building on work of koetter and vontobel we obtain a novel understanding of lp decoding which allows us to establish a 0 05 fraction of correctable errors for rate codes this comes very close to the performance of iterative decoders and is significantly higher than the best previously noted correctable bit error rate for lp decoding our analysis exploits an explicit connection between lp decoding and message passing algorithms and unlike other techniques directly works with the primal linear program an interesting byproduct of our method is a notion of a locally optimal solution that we show to always be globally optimal i e it is the nearest codeword such a solution can in fact be found in near linear time by a reweighted version of the min sum algorithm obviating the need for lp our analysis implies in particular that this reweighted version of the min sum decoder corrects up to a 0 05 fraction of errors

error floor approximation for ldpc codes in the awgn channel this paper addresses the prediction of error floors of low density parity check codes transmitted over the additive white gaussian noise channel using a linear state space model to estimate the behavior of the sum product algorithm spa decoder in the vicinity of trapping sets tss we study the performance of the spa decoder in the log likelihood ratio llr domain as a function of the llr saturation level when applied to several widely studied codes the model accurately predicts a significant decrease in the error floor as the saturation level is allowed to increase for nonsaturating decoders however we find that the state space model breaks down after a small number of iterations due to the strong correlation of llr messages we then revisit richardson s importance sampling methodology for estimating error floors due to tss when those floors are too low for monte carlo simulation we propose modifications that account for the behavior of a nonsaturating decoder and present the resulting error floor estimates for the margulis code these estimates are much lower significantly steeper and more sensitive to iteration count than those previously reported

quantized iterative message passing decoders with low error floor for ldpc codes the error floor phenomenon observed with ldpc codes and their graph based iterative message passing mp decoders is commonly attributed to the existence of error prone substructures variously referred to as near codewords trapping sets absorbing sets or pseudocodewords in a tanner graph representation of the code many approaches have been proposed to lower the error floor by designing new ldpc codes with fewer such substructures or by modifying the decoding algorithm using a theoretical analysis of iterative mp decoding in an idealized trapping set scenario we show that a contributor to the error floors observed in the literature may be the imprecise implementation of decoding algorithms and in particular the message quantization rules used we then propose a new quantization method q 1 bit quasi uniform quantization that efficiently increases the dynamic range of messages thereby overcoming a limitation of conventional quantization schemes finally we use the quasi uniform quantizer to decode several ldpc codes that suffer from high error floors with traditional fixed point decoder implementations the performance simulation results provide evidence that the proposed quantization scheme can for a wide variety of codes significantly lower error floors with minimal increase in decoder complexity

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

long term stable time integration scheme for dynamic analysis of planar geometrically exact timoshenko beams abstract in this paper an energy momentum method for geometrically exact timoshenko type beam is proposed the classical time integration schemes in dynamics are known to exhibit instability in the non linear regime the so called timoshenko type beam with the use of rotational degree of freedom leads to simpler strain relations and simpler expressions of the inertial terms as compared to the well known bernoulli type model the treatment of the bernoulli model has been recently addressed by the authors in this present work we extend our approach of using the strain rates to define the strain fields to in plane geometrically exact timoshenko type beams the large rotational degrees of freedom are exactly computed the well known enhanced strain method is used to avoid locking phenomena conservation of energy momentum and angular momentum is proved formally and numerically the excellent performance of the formulation will be demonstrated through a range of examples

reduced complexity iterative decoding of low density parity check codes based on belief propagation two simplified versions of the belief propagation algorithm for fast iterative decoding of low density parity check codes on the additive white gaussian noise channel are proposed both versions are implemented with real additions only which greatly simplifies the decoding complexity of belief propagation in which products of probabilities have to be computed also these two algorithms do not require any knowledge about the channel characteristics both algorithms yield a good performance complexity trade off and can be efficiently implemented in software as well as in hardware with possibly quantized received values

nonbinary hybrid ldpc codes in this paper a new class of low density parity check ldpc codes named hybrid ldpc codes is introduced hybrid ldpc codes are characterized by an irregular connectivity profile and heterogeneous orders of the symbols in the codeword it is shown in particular that the class of hybrid ldpc codes can be asymptotically characterized and optimized using density evolution de framework and a technique to maximize the minimum distance of the code is presented numerical assessment of hybrid ldpc code performances is provided by comparing them to protograph based and multiedge type met ldpc codes hybrid ldpc codes are shown to allow to achieve an interesting tradeoff between good error floor performance and good waterfall region with nonbinary coding techniques

energy decaying scheme for non linear beam models abstract this paper is concerned with the time integration of the equations of motion describing the non linear dynamic response of beams desirable characteristics of integration schemes for structural dynamics problems include unconditional stability accuracy and high frequency numerical dissipation several schemes exist that present all these features when applied to linear problems though the application of those schemes to non linear problems is often successful proofs of unconditional stability are rarely derived a finite difference integration scheme is derived in this paper for the non linear dynamic response of beams though of a finite difference nature the proposed scheme mimics the integration scheme obtained by applying the time discontinuous galerkin methodology to a single degree of freedom linear oscillator a formal proof of unconditional stability for the non linear problem is derived based on an energy decay argument numerical examples using the proposed scheme are given and the results are compared with the predictions of other available schemes the accuracy of the proposed scheme and its high frequency numerical dissipation characteristics are demonstrated in these examples

bit interleaved coded modulation with mismatched decoding metrics bit interleaved coded modulation bicm has become the de facto coding standard for communication systems recently bicm has been cast as a mismatched decoding scheme due to the assumption of independent bit metrics in addition to this inherent mismatch practical demodulators may produce mismatched decoding metrics because of implementation constraints such as clipping and metric approximation to reduce computational complexity in this paper we investigate bicm with such metrics in line with recent works on this topic we adopt the generalized mutual information gmi as the pertinent performance measure first we show that level dependent scaling of logarithmic bit metrics can improve the bicm gmi second we propose a uniform metric scaling which can lead to an improved performance of mismatched sum product symbol by symbol decoding even if the gmi is not changed third we investigate general metric mismatch correction methods and analyze their effects in terms of the gmi by means of three application examples we illustrate that metric mismatch correction including metric scaling can significantly increase bicm rates

design of ldpc decoders for improved low error rate performance quantization and algorithm choices many classes of high performance low density parity check ldpc codes are based on parity check matrices composed of permutation submatrices we describe the design of a parallel serial decoder architecture that can be used to map any ldpc code with such a structure to a hardware emulation platform high throughput emulation allows for the exploration of the low bit error rate ber region and provides statistics of the error traces which illuminate the causes of the error floors of the 2048 1723 reed solomon based ldpc rs ldpc code and the 2209 1978 array based ldpc code two classes of error events are observed oscillatory behavior and convergence to a class of non codewords termed absorbing sets the influence of absorbing sets can be exacerbated by message quantization and decoder implementation in particular quantization and the log tanh function approximation in sum product decoders strongly affect which absorbing sets dominate in the errorfloor region we show that conventional sum product decoder implementations of the 2209 1978 array based ldpc code allow low weight absorbing sets to have a strong effect and as a result elevate the error floor dually quantized sum product decoders and approximate sum product decoders alleviate the effects of low weight absorbing sets thereby lowering the error floor

entire solutions of certain type of differential equations ii abstract we analyze the transcendental entire solutions of the following type of nonlinear differential equations f n z p f p 1 e 1 z p 2 e 2 z in the complex plane where p 1 p 2 and 1 2 are nonzero constants and p f denotes a differential polynomial in f of degree at most n 1 with small functions of f as the coefficients

decoding algorithms for nonbinary ldpc codes over gf q in this letter we address the problem of decoding nonbinary low density parity check ldpc codes over finite fields gf q with reasonable complexity and good performance in the first part of the letter we recall the original belief propagation bp decoding algorithm and its fourier domain implementation we show that the use of tensor notations for the messages is very convenient for the algorithm description and understanding in the second part of the letter we introduce a simplified decoder which is inspired by the min sum decoder for binary ldpc codes we called this decoder extended min sum ems we show that it is possible to greatly reduce the computational complexity of the check node processing by computing approximate reliability measures with a limited number of values in a message by choosing appropriate correction factors or offsets we show that the ems decoder performance is quite good and in some cases better than the regular bp decoder the optimal values of the factor and offset correction are obtained asymptotically with simulated density evolution our simulations on ultra sparse codes over very high order fields show that nonbinary ldpc codes are promising for applications which require low frame error rates for small or moderate codeword lengths the ems decoder is a good candidate for practical hardware implementations of such codes

iterative decoding of binary block and convolutional codes iterative decoding of two dimensional systematic convolutional codes has been termed turbo de coding using log likelihood algebra we show that any decoder can be used which accepts soft inputs including a priori values and delivers soft outputs that can be split into three terms the soft channel and a priori inputs and the extrinsic value the extrinsic value is used as an a priori value for the next iteration decoding algorithms in the log likelihood domain are given not only for convolutional codes but also for any linear binary systematic block code the iteration is controlled by a stop criterion derived from cross entropy which results in a minimal number of iterations optimal and suboptimal decoders with reduced complexity are presented simulation results show that very simple component codes are sufficient block codes are appropriate for high rates and convolutional codes for lower rates less than 2 3 any combination of block and convolutional component codes is possible several interleaving techniques are described at a bit error rate ber of 10 sup 4 the performance is slightly above or around the bounds given by the cutoff rate for reasonably simple block convolutional component codes interleaver sizes less than 1000 and for three to six iterations

augmented belief propagation decoding of low density parity check codes we propose an augmented belief propagation bp decoder for low density parity check ldpc codes which can be utilized on memoryless or intersymbol interference channels the proposed method is a heuristic algorithm that eliminates a large number of pseudocodewords that can cause nonconvergence in the bp decoder the augmented decoder is a multistage iterative decoder where at each stage the original channel messages on select symbol nodes are replaced by saturated messages the key element of the proposed method is the symbol selection process which is based on the appropriately defined subgraphs of the code graph and or the reliability of the information received from the channel we demonstrate by examples that this decoder can be implemented to achieve substantial gains compared to the standard locally operating bp decoder for short ldpc codes decoded on both memoryless and intersymbol interference gaussian channels using the margulis code example we also show that the augmented decoder reduces the error floors finally we discuss types of bp decoding errors and relate them to the augmented bp decoder

on implementation of min sum algorithm and its modifications for decoding low density parity check ldpc codes the effects of clipping and quantization on the performance of the min sum algorithm for the decoding of low density parity check ldpc codes at short and intermediate block lengths are studied it is shown that in many cases only four quantization bits suffice to obtain close to ideal performance over a wide range of signal to noise ratios moreover we propose modifications to the min sum algorithm that improve the performance by a few tenths of a decibel with just a small increase in decoding complexity a quantized version of these modified algorithms is also studied it is shown that when optimized modified quantized min sum algorithms perform very close to and in some cases even slightly outperform the ideal belief propagation algorithm at observed error rates

near optimum universal belief propagation based decoding of low density parity check codes in this paper we propose a belief propagation bp based decoding algorithm which utilizes normalization to improve the accuracy of the soft values delivered by a previously proposed simplified bp based algorithm the normalization factors can be obtained not only by simulation but also importantly theoretically this new bp based algorithm is much simpler to implement than bp decoding as it requires only additions of the normalized received values and is universal i e the decoding is independent of the channel characteristics some simulation results are given which show this new decoding approach can achieve an error performance very close to that of bp on the additive white gaussian noise channel especially for low density parity check ldpc codes whose check sums have large weights the principle of normalization can also be used to improve the performance of the max log map algorithm in turbo decoding and some coding gain can be achieved if the code length is long enough

development of simple models for the elastic forces in the absolute nodal co ordinate formulation abstract the objective of this study is to develop simple and accurate elastic force models that can be used in the absolute nodal co ordinate formulation for the analysis of two dimensional beams these force models which account for the coupling between bending and axial deformations are derived using a continuum mechanics approach without the need for introducing a local element co ordinate system four new different force models that include different degrees of complexity are presented it is shown that the vector of the elastic forces can be significantly simplified as compared to the elastic force model developed for the absolute nodal co ordinate formulation using a local element frame 1 despite the simplicity of the new models they account for elastic non linearity in the strain displacement relationship therefore they lead to more accurate results as compared to the more complex models developed using the local frame method which does not account for the non linearities in the strain displacement relationships numerical results are presented in order to demonstrate the use of the new models and test their performances in the analysis of large deformations of flexible multibody systems

a differential binary message passing ldpc decoder in this paper we propose a binary message passing algorithm for decoding low density parity check ldpc codes the algorithm substantially improves the performance of purely hard decision iterative algorithms with a small increase in the memory requirements and the computational complexity we associate a reliability value to each nonzero element of the code s parity check matrix and differentially modify this value in each iteration based on the sum of the extrinsic binary messages from the check nodes for the tested random and finite geometry ldpc codes the proposed algorithm can perform as close as about 1 db and 0 5 db to belief propagation bp at the error rates of interest respectively this is while unlike bp the algorithm does not require the estimation of channel signal to noise ratio low memory and computational requirements and binary message passing make the proposed algorithm attractive for high speed low power applications

on decoding irregular tanner codes with local optimality guarantees we consider decoding of binary linear tanner codes using message passing iterative decoding and linear programming lp decoding in memoryless binary input output symmetric mbios channels we present new certificates that are based on a combinatorial characterization for the local optimality of a codeword in irregular tanner codes with respect to any mbios channel this characterization is a generalization of arora proc acm symp theory of computing 2009 and vontobel proc inf theory and appl workshop 2010 and is based on a conical combination of normalized weighted subtrees in the computation trees of the tanner graph these subtrees may have any finite height h even equal or greater than half of the girth of the tanner graph in addition the degrees of local code nodes in these subtrees are not restricted to two i e these subtrees are not restricted to skinny trees we prove that local optimality in this new characterization implies maximum likelihood ml optimality and lp optimality and show that a certificate can be computed efficiently we also present a new message passing iterative decoding algorithm called normalized weighted min sum nwms nwms decoding is a belief propagation bp type algorithm that applies to any irregular binary tanner code with single parity check local codes e g low density and high density parity check codes we prove that if a locally optimal codeword with respect to height parameter h exists whereby notably h is not limited by the girth of the tanner graph then nwms decoding finds this codeword in h iterations the decoding guarantee of the nwms decoding algorithm applies whenever there exists a locally optimal codeword because local optimality of a codeword implies that it is the unique ml codeword the decoding guarantee also provides an ml certificate for this codeword finally we apply the new local optimality characterization to regular tanner codes and prove lower bounds on the noise thresholds of lp decoding in mbios channels when the noise is below these lower bounds the probability that lp decoding fails to decode the transmitted codeword decays doubly exponentially in the girth of the tanner graph

geometric non linear substructuring for dynamics of flexible mechanical systems a substructure synthesis formulation is presented that permits use of established flexible multibody dynamic analysis computer codes to account for structural geometric non linear effects large relative displacement is permitted between points within bodies that undergo small strain elastic deformation components are divided into substructures on each of which the theory of linear elasticity relative to a body reference frame is adequate to describe deformation and its coupling with system motion normal vibration and static correction deformation modes are used to account for elastic deformation within each substructure compatibility conditions are derived and imposed as constraint equations at boundary points between substructures system equations of motion that include geometric non linear effects of large rotation in terms of generalized co ordinates of a reference frame for each substructure and a set of deformation modes that are defined within the substructure are assembled the method is implemented in an industry standard flexible multibody dynamics code with minimal modification use of the formulation is illustrated on the classical problem of a spinning beam with geometric stiffening and on a space structure that experiences large deformation

performance of ldpc codes under faulty iterative decoding departing from traditional communication theory where decoding algorithms are assumed to perform without error a system where noise perturbs both computational devices and communication channels is considered here this paper studies limits in processing noisy signals with noisy circuits by investigating the effect of noise on standard iterative decoders for low density parity check ldpc codes concentration of decoding performance around its average is shown to hold when noise is introduced into message passing and local computation density evolution equations for simple faulty iterative decoders are derived in one model computing nonlinear estimation thresholds shows that performance degrades smoothly as decoder noise increases but arbitrarily small probability of error is not achievable probability of error may be driven to zero in another system model the decoding threshold again decreases smoothly with decoder noise as an application of the methods developed an achievability result for reliable memory systems constructed from unreliable components is provided

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

finite element formulation of geometrically exact three dimensional beam theories based on interpolation of strain measures this paper presents a new finite element formulation of the geometrically exact finite strain beam theory the governing equations of the beam element are derived in which the strain vectors are the only unknown functions the consistency condition that the equilibrium and the constitutive internal force and moment vectors are equal is enforced to be satisfied at chosen points the solution is found by a collocation algorithm the linearity of the strain space not only simplifies the application of newton s method on the non linear configuration space but also leads to the strain objectivity of the proposed method the accuracy and the efficiency of the derived numerical algorithm are demonstrated by several examples c 2003 elsevier b v all rights reserved

on the growth of logarithmic differences difference quotients and logarithmic derivatives of meromorphic functions a crucial ingredient in the recent discovery by ablowitz halburd herbst and korhonen 2000 2007 that a connection exists between discrete painleve equations and finite order nevanlinna theory is an estimate of the integrated average of log f z 1 f z on z r we obtained essentially the same estimate in our previous paper 2008 independent of halburd et al 2006 we continue our study in this paper by establishing complete asymptotic relations amongst the logarithmic differences difference quotients and logarithmic derivatives for finite order meromorphic functions in addition to the potential applications of our new estimates in integrable systems they are also of independent interest in particular our findings show that there are marked differences between the growth of meromorphic functions with nevanlinna order less than and greater than one we have established a difference analogue of the classical wiman valiron type estimates for meromorphic functions with order less than one which allow us to prove that all entire solutions of linear difference equations with polynomial coefficients of order less than one must have positive rational order of growth we have also established that any entire solution to a first order algebraic difference equation with polynomial coefficients must have a positive order of growth which is a difference analogue of a classical result of polya

divide and concur and difference map bp decoders for ldpc codes the divide and concur dc algorithm introduced by gravel and elser can be considered a competitor to the belief propagation bp algorithm in that both algorithms can be applied to a wide variety of constraint satisfaction optimization and inference problems we show that dc can be interpreted as a message passing algorithm on a normal factor graph the difference map dynamics of the dc algorithm enables it to avoid traps which may be related to the trapping sets or pseudo codewords that plague bp decoders of low density parity check ldpc codes in the error floor regime we investigate two decoders for ldpc codes based on these ideas the first decoder is based directly on dc while the second decoder borrows the important difference map concept from the dc algorithm and translates it into a bp like decoder we show that this difference map belief propagation dmbp decoder has dramatically improved error floor performance compared to standard bp decoders while maintaining a similar computational complexity we present simulation results for ldpc codes comparing dc and dmbp decoders with other decoders based on sum product bp linear programming and mixed integer linear programming we also describe the close relation of the dmbp decoder to reweighted min sum algorithms including those recently proposed by ruozzi and tatikonda

uniqueness and value distribution of differences of entire functions abstract we consider the existence of transcendental entire solutions of certain type of non linear difference equations as an application we investigate the value distribution of difference polynomials of entire functions in particular we are interested in the existence of zeros of f n z f m z c f m z a where f is an entire function n m are two integers such that n m 0 and are non zero complex numbers we also obtain a uniqueness result in the case where shifts of two entire functions share a small function

comparisons between reliability based iterative min sum and majority logic decoding algorithms for ldpc codes a modified reliability based iterative majority logic decoding mrbi mlgd algorithm for two classes of structured ldpc codes is presented based on a recent work by huang et al compared with the original one the modified algorithm has better performance with slightly increased complexity then a reliability based iterative min sum decoding rbi msd algorithm is presented for the presented rbi msd algorithm reliability based integer messages are processed and exchanged between variable nodes and check nodes the main computations include only binary logical operations and integer additions different from the conventional min sum algorithm the variable nodes pass full messages rather than extrinsic messages to check nodes this can reduce the memory loads and the computational complexity but with a little or negligible performance degradation simulation results show that compared with the m rbi mlgd algorithms the presented rbi msd algorithm achieves better error performance faster decoding convergence rate and fewer quantization bits with moderate increased computational complexity furthermore the rbi msd algorithm is also applicable to decoding random ldpc codes a distinct difference from the m rbi mlgd algorithms finally we point out that the scaling factors employed in the mrbi mlgd algorithm and the rbi msd algorithm can be optimized using discretized density evolution

low complexity decoding for non binary ldpc codes in high order fields in this paper we propose a new implementation of the extended min sum ems decoder for non binary ldpc codes a particularity of the new algorithm is that it takes into accounts the memory problem of the non binary ldpc decoders together with a significant complexity reduction per decoding iteration the key feature of our decoder is to truncate the vector messages of the decoder to a limited number nm of values in order to reduce the memory requirements using the truncated messages we propose an efficient implementation of the ems decoder which reduces the order of complexity to nm log2 nm this complexity starts to be reasonable enough to compete with binary decoders the performance of the low complexity algorithm with proper compensation is quite good with respect to the important complexity reduction which is shown both with a simulated density evolution approach and actual simulations

a consistent equilibrium in a cross section of an elastic plastic beam abstract a phenomenon of inequality of equilibrium and constitutive internal forces in a cross section of elastic plastic beams is common to many finite element formulations it is here discussed in a rate independent elastic plastic beam context and a possible treatment is presented the starting point of our discussion is reissners finite strain beam theory and its finite element implementation the questions of the consistency of interpolations for displacements and rotations and the related locking phenomena are fully avoided by considering the rotation function of the centroid axis of a beam as the only unknown function of the problem approximate equilibrium equations are derived by the use of the distribution theory in conjunction with the collocation method the novelty of our formulation is an inclusion of a balance function that measures the error between the equilibrium and constitutive bending moments in a cross section an advantage of the present approach is that the locations where the balance of equilibrium and constitutive moments should be satisfied can be prescribed in advance in order to minimize the error explicit analytical expressions are used for the constitutive forces for a rectangular cross section and bilinear constitutive law they are given in appendix a the comparison between the results of the two finite element formulations the one using consistent and the other inconsistent equilibrium in a cross section is shown for a cantilever beam subjected to a point load the problem of high curvature gradients in a plastified region is also discussed and solved by using an adapted collocation method in which the coordinate system is transformed such to follow high gradients of curvature

low density parity check codes based on finite geometries a rediscovery and new results this paper presents a geometric approach to the construction of low density parity check ldpc codes four classes of ldpc codes are constructed based on the lines and points of euclidean and projective geometries over finite fields codes of these four classes have good minimum distances and their tanner 1981 graphs have girth 6 finite geometry ldpc codes can be decoded in various ways ranging from low to high decoding complexity and from reasonably good to very good performance they perform very well with iterative decoding furthermore they can be put in either cyclic or quasi cyclic form consequently their encoding can be achieved in linear time and implemented with simple feedback shift registers this advantage is not shared by other ldpc codes in general and is important in practice finite geometry ldpc codes can be extended and shortened in various ways to obtain other good ldpc codes several techniques of extension and shortening are presented long extended finite geometry ldpc codes have been constructed and they achieve a performance only a few tenths of a decibel away from the shannon theoretical limit with iterative decoding

the strain based beam finite elements in multibody dynamics we present a strain based finite element formulation for the dynamic analysis of flexible elastic planar multibody systems composed of planar beams we consider finite displacements rotations and strains the discrete dynamic equations of motion are obtained by the collocation method the strains are the basic interpolated variables which makes the formulation different from other formulations the further speciality of the formulation is the strong satisfaction of the cross sectional constitutive conditions at collocation points in order to avoid the nested integrations a special algorithm for the numerical integration over the length of the finite element is proposed the midpoint scheme is used for the time integration the performance of the formulation is illustrated via numerical examples including a stiff multibody system

reduced complexity decoding of ldpc codes various log likelihood ratio based belief propagation llr bp decoding algorithms and their reduced complexity derivatives for low density parity check ldpc codes are presented numerically accurate representations of the check node update computation used in llr bp decoding are described furthermore approximate representations of the decoding computations are shown to achieve a reduction in complexity by simplifying the check node update or symbol node update or both in particular two main approaches for simplified check node updates are presented that are based on the so called min sum approximation coupled with either a normalization term or an additive offset term density evolution is used to analyze the performance of these decoding algorithms to determine the optimum values of the key parameters and to evaluate finite quantization effects simulation results show that these reduced complexity decoding algorithms for ldpc codes achieve a performance very close to that of the bp algorithm the unified treatment of decoding techniques for ldpc codes presented here provides flexibility in selecting the appropriate scheme from performance latency computational complexity and memory requirement perspectives

a two dimensional shear deformable beam element based on the absolute nodal coordinate formulation in this study a new two dimensional shear deformable beam element is proposed for large deformation problems the kinematics of the beam are defined using an exact displacement field where the rotation angles of the cross section caused by bending and shear deformations are described separately cubic interpolation is used for determining the curvature of the beam due to bending while linear interpolation polynomials are used for the shear strain the absolute nodal coordinate formulation in which global displacements and slopes are used as the nodal coordinates is employed for the finite element discretization of the beam the capability of the element to predict static deformation is studied using numerical examples the results imply that the element is free of a phenomenon called shear locking the capability of the element to model highly nonlinear behaviour is established using a bending test where the cantilever is bent into a full circle using only four elements a flexible pendulum and a spin up manoeuvre are modelled in order to study the behaviour of the element in dynamical problems the proposed element is also compared with an existing shear deformable beam element based on the absolute nodal coordinate formulation finally the simple linearization of the beam curvature based on the assumption of small strain will be discussed

decoding of high rate convolutional codes using the dual trellis this paper deals with a posteriori probability app decoding of high rate convolutional codes using the dual code s trellis after deriving the dual app dapp algorithm from the app relation its trellis based implementation is addressed the challenge involved in practical implementation of a dapp decoder is then highlighted metric representation schemes similar to the log domain used for log app decoding are shown to be unattractive for dapp decoding due to quantization requirements after explaining the nature of the dapp metrics an arc hyperbolic tangent aht scheme is proposed and its equivalent arithmetic operations derived by using an efficient approximation an addition is translated to an addition in the aht domain efficient techniques for normalization and extrinsic log likelihood ratio llr calculation are presented which reduce implementation complexity significantly simulation results with different high rate codes are given to show that the aht dapp decoder performs similarly to a log app decoder and at the same time performs better than a decoder for a punctured code a fully fixed point model of an aht dapp decoder is shown to perform close to an optimum decoder the decoding complexity of the log app and aht dapp decoders are listed and compared for several rate k k 1 codes it is shown that an aht dapp decoder starts to be less complex from a code rate of 7 8 when compared against a max log app decoder the aht dapp decoder is less complex at a code rate of 9 10 and above

iterative decoding using eigenmessages the eigenmessage approach to iterative decoding introduces a degree of nonlocality into a belief propagation decoder by representing an entire set of messages around a cycle of the tanner graph as a linear operator the eigenvector for the operator represents a fixed point of the belief propagation algorithm around a cycle with incident messages fixed a multiple eigenmessage approach is also presented in which messages around several cycles are simultaneously expressed the eigenmessage approach may be applied to any graph with cycles but we demonstrate its use on ldpc decoding in this setting computational results compare eigenmessage methods with conventional belief propagation decoding showing using simulation and exit charts that the eigenmessage approaches slightly reduce the number of decoder iterations compared to belief propagation decoding while preserving the probability of error of conventional decoding