a mesh based partition of unity method for discontinuity modeling this study explores a numerical analysis scheme the manifold method within the framework of the partition of unity method the manifold method is rooted in the discrete element method and has been used in solving discrete continuum interaction problems at its core two meshes are employed in an analysis the mathematical mesh provides the nodes for building a finite covering of the solution domain and the partition of unity functions while the physical mesh provides the domain of integration after providing a geometric interpretation and giving a construct overview the working of the method is illustrated with a number of examples

analysis and design of tuned turbo codes it has been widely observed that there exists a fundamental tradeoff between the minimum hamming distance properties and the iterative decoding convergence behavior of turbo like codes while capacity achieving code ensembles typically are asymptotically bad in the sense that their minimum distance does not grow linearly with block length and they therefore exhibit an error floor at moderate to high signal to noise ratios asymptotically good codes usually converge further away from channel capacity in this paper we introduce the concept of tuned turbo codes a family of asymptotically good hybrid concatenated code ensembles where asymptotic minimum distance growth rates convergence thresholds and code rates can be tradedoff using two tuning parameters and by decreasing the asymptotic minimum distance growth rate is reduced in exchange for improved iterative decoding convergence behavior while increasing raises the asymptotic minimum distance growth rate at the expense of worse convergence behavior and thus the code performance can be tuned to fit the desired application by decreasing a similar tuning behavior can be achieved for higher rate code ensembles

transition to detonation in dynamic phase changes subsonically propagating phase boundaries kinks can be modelled by material discontinuities which satisfy integral conservation laws plus an additional jump condition governing the phase change kinetics the necessity of an additional jump condition distinguishes kinks from the conventional shocks which satisfy the lax criterion we study stability of kinks with respect to the breakup splitting into a sequence of waves we assume that all conventional shocks are admissible and that admissible kinks are selected by a prescribed kinetic relation as we show regardless of a particular choice of the kinetic relation sufficiently fast phase boundaries are unstable the mode of instability includes an emission of a centered riemann wave followed by a sonic shock chapman jouguet type phase boundary

finite cover method for linear and non linear analyses of heterogeneous solids we introduce the finite cover method fcm as a generalization of the finite element method fem and extend it to analyse the linear and non linear mechanical behaviour of heterogeneous solids and structures the name fcm is actually an alias for the manifold method mm and the basic idea of the method has already been established for linear analyses of structures with homogeneous materials after reviewing the concept of physical and mathematical covers for approximating functions in the fcm we present the formulation for the static equilibrium state of a structure with arbitrary physical boundaries including material interfaces the problem essentially involves the discontinuities in strains and possibly has the discontinuities in displacement caused by interfacial debonding or rupture of material interfaces we simulate such non linear mechanical behaviour after presenting simple numerical examples that demonstrate the equivalence between the approximation capabilities of the fcm and those of the fem copyright 2003 john wiley sons ltd

signal space characterization of iterative decoding by tracing the flow of computations in the iterative decoders for low density parity check codes we formulate a signal space view for a finite number of iterations in a finite length code on a gaussian channel maximum a posteriori map codeword decoding or maximum likelihood decoding decodes to the codeword signal that is closest to the channel output in euclidean distance in contrast we show that iterative decoding decodes to the pseudosignal that has highest correlation with the channel output the set of pseudosignals corresponds to pseudocodewords only a vanishingly small number of which correspond to codewords we show that some pseudocodewords cause decoding errors but that there are also pseudocodewords that frequently correct the deleterious effects of other pseudocodewords

an integrated procedure for three dimensional structural analysis with the finite cover method in this paper an integrated procedure for three dimensional 3d structural analyses with the finite cover method fcm is introduced in the pre process of this procedure the geometry of a structure is modelled by 3d cad followed by digitization to have the corresponding voxel model and then the structure is covered by a union of mathematical covers namely a mathematical mesh independently generated for approximation purposes since the mesh topology in the fcm does not need to conform to the physical boundaries of the structure the mesh can be regular and structured thus the numerical analysis procedure is free from the difficulties mesh generation typically poses and in this sense enables us to realize the mesh free analysis after formulating the fcm with interface elements for the static equilibrium state of a structure we detail the procedure of the finite cover modelling including the geometry modelling with 3d cad and the identification of the geometry covered by a regular mesh for numerical integration prior to full 3d modelling and analysis we present a simple numerical example to confirm the equivalence of the performance of the fcm and that of the standard finite element method fem finally representative numerical examples are presented to demonstrate the capabilities of the proposed analysis procedure

kinetic relations and the propagation of phase boundaries in solids this paper treats the dynamics of phase transformations in elastic bars the specific issue studied is the compatibility of the field equations and jump conditions of the one dimensional theory of such bars with two additional constitutive requirements a kinetic relation controlling the rate at which the phase transition takes place and a nucleation criterion for the initiation of the phase transition a special elastic material with a piecewise linear non monotonic stress strain relation is considered and the riemann problem for this material is analyzed for a large class of initial data it is found that the kinetic relation and the nucleation criterion together single out a unique solution to this problem from among the infinitely many solutions that satisfy the entropy jump condition at all strain discontinuities

turbo decoding on the binary erasure channel finite length analysis and turbo stopping sets this paper is devoted to the finite length analysis of turbo decoding over the binary erasure channel bec the performance of iterative belief propagation decoding of low density parity check ldpc codes over the bec can be characterized in terms of stopping sets we describe turbo decoding on the bec which is simpler than turbo decoding on other channels we then adapt the concept of stopping sets to turbo decoding and state an exact condition for decoding failure apply turbo decoding until the transmitted codeword has been recovered or the decoder fails to progress further then the set of erased positions that will remain when the decoder stops is equal to the unique maximum size turbo stopping set which is also a subset of the set of erased positions furthermore we present some improvements of the basic turbo decoding algorithm on the bec the proposed improved turbo decoding algorithm has substantially better error performance as illustrated by the given simulation results finally we give an expression for the turbo stopping set size enumerating function under the uniform interleaver assumption and an efficient enumeration algorithm of small size turbo stopping sets for a particular interleaver the solution is based on the algorithm proposed by garello et al in 2001 to compute an exhaustive list of all low weight codewords in a turbo code

on ensembles of low density parity check codes asymptotic distance distributions we derive expressions for the average distance distributions in several ensembles of regular low density parity check codes ldpc among these ensembles are the standard one defined by matrices having given column and row sums ensembles defined by matrices with given column sums or given row sums and an ensemble defined by bipartite graphs

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

distance distributions in ensembles of irregular low density parity check codes we derive asymptotic expressions for the average distance distributions in ensembles of irregular low density parity check ldpc codes the ensembles are defined by matrices with given profiles of column and row sums

evolution of phase boundaries by configurational forces an initial boundary value problem modeling the evolution of phase interfaces in materials showing martensitic transformations is studied the model which is derived rigorously from a sharp interface model with phase interfaces driven by configurational forces and which generalizes that model consists of the equations of linear elasticity coupled with a nonlinear partial differential equation of hyperbolic character governing the evolution of the order parameter it is proved that in one space dimension global solutions exist for which the order parameter belongs to the space of functions of bounded variation other models for interface motion by martensitic transformations and by interface diffusion are suggested

asymptotic enumeration methods for analyzing ldpc codes we show how asymptotic estimates of powers of polynomials with nonnegative coefficients can be used in the analysis of low density parity check ldpc codes in particular we show how these estimates can be used to derive the asymptotic distance spectrum of both regular and irregular ldpc code ensembles we then consider the binary erasure channel bec using these estimates we derive lower bounds on the error exponent under iterative decoding of ldpc codes used over the bec both regular and irregular code structures are considered these bounds are compared to the corresponding bounds when optimal maximum likelihood ml decoding is applied

constructing free energy approximations and generalized belief propagation algorithms important inference problems in statistical physics computer vision error correcting coding theory and artificial intelligence can all be reformulated as the computation of marginal probabilities on factor graphs the belief propagation bp algorithm is an efficient way to solve these problems that is exact when the factor graph is a tree but only approximate when the factor graph has cycles we show that bp fixed points correspond to the stationary points of the bethe approximation of the free energy for a factor graph we explain how to obtain region based free energy approximations that improve the bethe approximation and corresponding generalized belief propagation gbp algorithms we emphasize the conditions a free energy approximation must satisfy in order to be a valid or maxent normal approximation we describe the relationship between four different methods that can be used to generate valid approximations the bethe method the junction graph method the cluster variation method and the region graph method finally we explain how to tell whether a region based approximation and its corresponding gbp algorithm is likely to be accurate and describe empirical results showing that gbp can significantly outperform bp

enumerators for protograph based ensembles of ldpc and generalized ldpc codes protograph based ldpc and generalized ldpc g ldpc codes have the advantages of a simple design procedure and highly structured encoders and decoders the design of such protograph based codes relies on what is effectively a computer based search as such following gallager it is prudent to restrict the search to a good ensemble for example an ensemble whose minimum distance grows linearly with codeword length a good ensemble can also mean one with good stopping set trapping set or pseudocodeword properties in this paper ensemble codeword weight enumerators for finite length ldpc and g ldpc codes based on protographs were derived and then the asymptotic case was considered the asymptotic results allow us to determine whether or not the typical relative minimum distance in the ensemble grows linearly with codeword length then the codeword weight enumerator technique is adapted to yield ensemble stopping set trapping set and pseudocodeword enumerators for protograph ldpc and g ldpc codes in this case the asymptotic results allow us to determine whether or not the typical relative smallest stopping set size trapping set size and pseudoweight grows linearly with codeword length trapping set enumerators for g ldpc code ensembles represent a more complex problem which we do not consider here

kinetic stabilization of a nonlinear sonic phase boundary we consider a system arising in the study of phase transitions in elastodynamics a system of two conservation laws in a single space dimension the system has two hyperbolic regions with an elliptic zone in between a phase boundary is a strong discontinuity in a solution with left and right states belonging to different hyperbolic regions we call such a solution a phase wave

using linear programming to decode binary linear codes a new method is given for performing approximate maximum likelihood ml decoding of an arbitrary binary linear code based on observations received from any discrete memoryless symmetric channel the decoding algorithm is based on a linear programming lp relaxation that is defined by a factor graph or parity check representation of the code the resulting lp decoder generalizes our previous work on turbo like codes a precise combinatorial characterization of when the lp decoder succeeds is provided based on pseudocodewords associated with the factor graph our definition of a pseudocodeword unifies other such notions known for iterative algorithms including stopping sets irreducible closed walks trellis cycles deviation sets and graph covers the fractional distance d sub frac of a code is introduced which is a lower bound on the classical distance it is shown that the efficient lp decoder will correct up to spl lceil d sub frac 2 spl rceil 1 errors and that there are codes with d sub frac spl omega n sup 1 spl epsi an efficient algorithm to compute the fractional distance is presented experimental evidence shows a similar performance on low density parity check ldpc codes between lp decoding and the min sum and sum product algorithms methods for tightening the lp relaxation to improve performance are also provided

admissible riemann solvers for genuinely nonlinear p systems of mixed type abstract we consider in this paper the riemann problem for p systems of mixed type that define two hyperbolic phases with a stress function satisfying general genuinely nonlinear hypotheses we describe here all the global riemann solvers that are continuous for the l 1 distance with respect to initial data while conserving the natural symmetry properties of the p system and coinciding with the lax solution when defined these riemann solvers can be described entirely by a kinetic function used to select a manifold of subsonic phase transitions and a corresponding set of supersonic phase transitions

pseudo codeword analysis of tanner graphs from projective and euclidean planes we consider coded data transmission over a binary input output symmetric memoryless channel using a binary linear code in order to understand the performance of maximum likelihood ml decoding one studies the codewords in particular the minimal codewords and their hamming weights in the context of linear programming lp decoding one s attention needs to be shifted to the pseudo codewords in particular to the minimal pseudo codewords and their pseudo weights in this paper we investigate some families of codes that have good properties under lp decoding namely certain families of low density parity check ldpc codes that are derived from projective and euclidean planes we study the structure of their minimal pseudo codewords and give lower bounds on their pseudo weight besides this main focus we also present some results that hold for pseudo codewords and minimal pseudo codewords of any tanner graph and we highlight how the importance of minimal pseudo codewords under lp decoding varies depending on which binary input output symmetric memoryless channel is used

quasi cyclic generalized ldpc codes with low error floors in this paper a novel methodology for designing structured generalized low density parity check g ldpc codes is presented the proposed design results in quasi cyclic g ldpc codes for which efficient encoding is feasible through shift register based circuits the structure imposed on the bipartite graphs together with the choice of simple component codes leads to a class of codes suitable for fast iterative decoding a pragmatic approach to the construction of g ldpc codes is proposed the approach is based on the substitution of check nodes in the protograph of a low density parity check code with stronger nodes based for instance on hamming codes such a design approach which we call low density parity check ldpc code doping leads to low rate quasi cyclic g ldpc codes with excellent performance in both the error floor and waterfall regions on the additive white gaussian noise channel

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

the generalized finite element method this paper describes a pilot design and implementation of the generalized finite element method gfem as a direct extension of the standard finite element method sfem or fem which makes possible the accurate solution of engineering problems in complex domains which may be practically impossible to solve using the fem the development of the gfem is illustrated for the laplacian in two space dimensions in domains which may include several hundreds of voids and or cracks for which the construction of meshes used by the fem is practically impossible the two main capabilities are 1 it can construct the approximation using meshes which may overlap part or all of the domain boundary 2 it can incorporate into the approximation handbook functions which are known analytically or are generated numerically and approximate well the solution of the boundary value problem in the neighborhood of corner points voids cracks etc the main tool is a special integration algorithm which we call the fast remeshing approach which is robust and works for any domain with arbitrary complexity the incorporation of the handbook functions into the gfem is done by employing the partition of unity method pum the presented formulations and implementations can be easily extended to the multi material medium where the voids are replaced by inclusions of various shapes and sizes and to the case of the elasticity problem this work can also be understood as a pilot study for the feasibility and demonstration of the capabilities of the gfem which is needed before analogous implementations are attempted in the three dmensional and nonlinear cases which are the cases of main interest for future work

finite length analysis of low density parity check codes on the binary erasure channel in this paper we are concerned with the finite length analysis of low density parity check ldpc codes when used over the binary erasure channel bec the main result is an expression for the exact average bit and block erasure probability for a given regular ensemble of ldpc codes when decoded iteratively we also give expressions for upper bounds on the average bit and block erasure probability for regular ldpc ensembles and the standard random ensemble under maximum likelihood ml decoding finally we present what we consider to be the most important open problems in this area

non classical riemann solvers with nucleation we introduce a new nonclassical riemann solver for scalar conservation laws with concave convex flux function this solver is based on both a kinetic relation which determines the propagation speed of undercompressive nonclassical shock waves and a nucleation crite rion which makes a choice between a classical riemann solution and a nonclassical one we establish the existence of nonclassical entropy solutions of the cauchy problem and discuss several examples of wave interactions we also show the existence of a class of solutions called splitting merging solutions which are made of two large shocks and small bv bounded variation perturbations the nucleation solvers as we call them are applied to and actually motivated by the theory of thin film flows they help explain numerical results observed for such flows

global continuous riemann solver for nonlinear elasticity we consider in this paper an isothermal model of nonlinear elasticity this model is described by two conservation laws that define a problem of mixed type both elliptic and hyperbolic we restrict ourselves to the linearly degenerate case and consider riemann data that lies in the hyperbolic regions the lack of uniqueness of the riemann problem is solved by the introduction of a so called kinetic relation used to narrow the set of admissible subsonic phase transitions in this situation we consider the riemann problem for any data lying in the hyperbolic region using either explicit computations or geometric arguments this construction allows us to give sufficient conditions on the kinetic relation in order that the generated riemann solver possesses properties of uniqueness globality and continuous dependence on the initial data in the l 1 distance

the design and analysis of the generalized finite element method abstract in this paper we introduce the generalized finite element method gfem as a combination of the classical finite element method fem and the partition of unity method pum the standard finite element spaces are augmented by adding special functions which reflect the known information about the boundary value problem and the input data e g the singular functions obtained from the local asymptotic expansion of the exact solution in the neighborhood of a corner point etc the special functions are multiplied with the partition of unity corresponding to the standard linear vertex shape functions and pasted together with the existing finite element basis to construct an augmented conforming finite element space in this way the local approximability afforded by the special functions is included in the approximation while maintaining the existing infrastructure of finite element codes the major features of the gfem are 1 the essential boundary conditions can be imposed exactly as in the standard fem unlike other partition of unity based methods where this is a major issue 2 the accuracy of the numerical integration of the entries of the stiffness matrix and load vector is controlled adaptively so that the errors in integration of the special functions do not affect the accuracy of the constructed approximation this issue also has not been sufficiently addressed in other implementations of partition of unity or meshless methods and 3 linear dependencies in the system of equations are resolved by employing an easy modification of the direct linear solver the power of the gfem for solving problems in domains with complex geometry with less error and less computer resources than the standard fem is illustrated by numerical examples

finite element analysis on implicitly defined domains an accurate representation based on arbitrary parametric surfaces in this paper we present some novel results and ideas for robust and accurate implicit representation of geometric surfaces in finite element analysis the novel contributions of this paper are threefold 1 describe and validate a method to represent arbitrary parametric surfaces implicitly 2 represent arbitrary solids implicitly including sharp features using level sets and boolean operations 3 impose arbitrary dirichlet and neumann boundary conditions on the resulting implicitly defined boundaries the methods proposed do not require local refinement of the finite element mesh in regions of high curvature ensure the independence of the domain s volume on the mesh do not rely on boundary regularization and are well suited to methods based on fixed grids such as the extended finite element method xfem numerical examples are presented to demonstrate the robustness and effectiveness of the proposed approach and show that it is possible to achieve optimal convergence rates using a fully implicit representation of object boundaries this approach is one step in the desired direction of tying numerical simulations to computer aided design cad similarly to the isogeometric analysis paradigm

counting in graph covers a combinatorial characterization of the bethe entropy function we present a combinatorial characterization of the bethe entropy function of a factor graph such a characterization being in contrast to the original analytical definition of this function we achieve this combinatorial characterization by counting valid configurations in finite graph covers of the factor graph analogously we give a combinatorial characterization of the bethe partition function whose original definition was also of an analytical nature as we point out our approach has similarities to the replica method but also stark differences the above findings are a natural backdrop for introducing a decoder for graph based codes that we will call symbolwise graph cover decoding a decoder that extends our earlier work on blockwise graph cover decoding both graph cover decoders are theoretical tools that help toward a better understanding of message passing iterative decoding namely blockwise graph cover decoding links max product min sum algorithm decoding with linear programming decoding and symbolwise graph cover decoding links sum product algorithm decoding with bethe free energy function minimization at temperature one in contrast to the gibbs entropy function which is a concave function the bethe entropy function is in general not concave everywhere in particular we show that every code picked from an ensemble of regular low density parity check codes with minimum hamming distance growing with high probability linearly with the block length has a bethe entropy function that is convex in certain regions of its domain

asymptotic spectra of trapping sets in regular and irregular ldpc code ensembles we evaluate the asymptotic normalized average distributions of a class of combinatorial configurations in random regular and irregular binary low density parity check ldpc code ensembles among the configurations considered are trapping and stopping sets these sets represent subsets of variable nodes in the tanner graph of a code that play an important role in determining the height and point of onset of the error floor in its performance curve the techniques used for deriving the spectra include large deviations theory and statistical methods for enumerating binary matrices with prescribed row and column sums these techniques can also be applied in a setting that involves more general structural entities such as subcodes and or minimal codewords that are known to characterize other important properties of soft decision decoders of linear block codes

prediction of rank deficiency in partition of unity based methods with plane triangular or quadrilateral meshes in the partition of unity pu based methods the global approximation is built by multiplying a partition of unity by local approximations within this framework high order approximations are achieved by directly adopting high order polynomials as local approximations and therefore nodes along sides or inside elements which are usually adopted in the conventional finite element methods are no more required however the pu based approximation constructed in this way may suffer from rank deficiency due to the linear dependence of the global degrees of freedom in this paper the origin of the rank deficiency in the pu based approximation space is first dissected at an element level and then an approach to predict the rank deficiency for a mesh is proposed together with the principle of the increase of rank deficiency finally examples are investigated to validate the present approach the current work indicates such a fact that the rank deficiency is an unrelated issue to the nullity of the global matrix it can be resolved in its own manner

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

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

an efficient pseudocodeword search algorithm for linear programming decoding of ldpc codes in linear programming lp decoding of a low density parity check ldpc code one minimizes a linear functional with coefficients related to log likelihood ratios over a relaxation of the polytope spanned by the codewords in order to quantify lp decoding it is important to study vertexes of the relaxed polytope so called pseudocodewords we propose a technique to heuristcally create a list of pseudocodewords close to the zero codeword and their distances our pseudocodeword search algorithm starts by randomly choosing configuration of the noise the configuration is modified through a discrete number of steps each step consists of two substeps one applies an lp decoder to the noise configuration deriving a pseudocodeword and then finds configuration of the noise equidistant from the pseudocodeword and the zero codeword the resulting noise configuration is used as an entry for the next step the iterations converge rapidly to a pseudocodeword neighboring the zero codeword repeated many times this procedure is characterized by the distribution function of the pseudocodeword effective distance the efficiency of the procedure is demonstrated on examples of the tanner code and margulis codes operating over an additive white gaussian noise awgn channel

quasi cyclic ldpc codes influence of proto and tanner graph structure on minimum hamming distance upper bounds quasi cyclic qc low density parity check ldpc codes are an important instance of proto graph based ldpc codes in this paper we present upper bounds on the minimum hamming distance of qc ldpc codes and study how these upper bounds depend on graph structure parameters like variable degrees check node degrees girth of the tanner graph and of the underlying proto graph moreover for several classes of proto graphs we present explicit qc ldpc code constructions that achieve or come close to the respective minimum hamming distance upper bounds because of the tight algebraic connection between qc codes and convolutional codes we can state similar results for the free hamming distance of convolutional codes in fact some qc code statements are established by first proving the corresponding convolutional code statements and then using a result by tanner that says that the minimum hamming distance of a qc code is upper bounded by the free hamming distance of the convolutional code that is obtained by unwrapping the qc code

two scale diffusion deformation coupling model for material deterioration involving micro crack propagation in this paper we introduce a two scale diffusion deformation coupled model that represents the aging material deterioration of two phase materials involving micro crack propagations the mathematical homogenization method is applied to relate the micro and macroscopic field variables and a weak coupling solution method is employed to solve the two way coupling phenomena between the diffusion of scalar fields and the deformation of quasi brittle solids the macroscopic mechanical behavior represented by the derived two scale two way coupled model reveals material nonlinearity due to micro scale cracking induced by the scalar field induced deformation which can be simulated by the finite cover method after verifying the fundamental validity of the proposed model and the analysis method we perform a simple numerical example to demonstrate their ability to predict aging material deterioration copyright 2010 john wiley sons ltd

development of contact algorithm for three dimensional numerical manifold method summary this paper customizes a contact detection and enforcing scheme to fit the three dimensional 3 d numerical manifold method nmm a hierarchical contact system is established for efficient contact detection the mathematical mesh a unique component in the nmm is utilized for global searching of possible contact blocks and elements followed by the local searching to identify primitive hierarchies all the potential contact pairs are then transformed into one of the two essential entrance modes point to plane and crossing lines modes among which real contact pairs are detected through a unified formula the penalty method is selected to enforce the contact constraints and a general contact solution procedure in the 3 d nmm is established because of the implicit framework an open close iteration is performed within each time step to determine the correct number of contact pairs among multi bodies and to achieve complete convergence of imposed contact force at corresponding position the proposed contact algorithm extensively utilizes most of the original components of the nmm namely the mathematical mesh cells and the manifold elements as well as the external components associated with contacts such as the contact body the contact facet and the contact vertex in particular the utilization of two mutually approaching mathematical cells is efficient in detecting contacting territory which makes this method particularly effective for both convex and non convex bodies the validity and accuracy of the proposed contact algorithm are verified and demonstrated through three benchmark problems copyright 2013 john wiley sons ltd

interleavers for turbo codes using permutation polynomials over integer rings a class of deterministic interleavers for turbo codes tcs based on permutation polynomials over spl zopf sub n is introduced the main characteristic of this class of interleavers is that they can be algebraically designed to fit a given component code moreover since the interleaver can be generated by a few simple computations storage of the interleaver tables can be avoided by using the permutation polynomial based interleavers the design of the interleavers reduces to the selection of the coefficients of the polynomials it is observed that the performance of the tcs using these permutation polynomial based interleavers is usually dominated by a subset of input weight 2m error events the minimum distance and its multiplicity or the first few spectrum lines of this subset are used as design criterion to select good permutation polynomials a simple method to enumerate these error events for small m is presented searches for good interleavers are performed the decoding performance of these interleavers is close to s random interleavers for long frame sizes for short frame sizes the new interleavers outperform s random interleavers

pseudocodewords of tanner graphs this paper presents a detailed analysis of pseudocodewords of tanner graphs pseudocodewords arising on the iterative decoder s computation tree are distinguished from pseudocodewords arising on finite degree lifts lower bounds on the minimum pseudocodeword weight are presented for the bec bsc and awgn channel some structural properties of pseudocodewords are examined and pseudocodewords and graph properties that are potentially problematic with min sum iterative decoding are identified an upper bound on the minimum degree lift needed to realize a particular irreducible lift realizable pseudocodeword is given in terms of its maximal component and it is shown that all irreducible lift realizable pseudocodewords have components upper bounded by a finite value t that is dependent on the graph structure examples and different tanner graph representations of individual codes are examined and the resulting pseudocodeword distributions and iterative decoding performances are analyzed the results obtained provide some insights in relating the structure of the tanner graph to the pseudocodeword distribution and suggest ways of designing tanner graphs with good minimum pseudocodeword weight

diffusive dispersive travelling waves and kinetic relations v singular diffusion and nonlinear dispersion we consider scalar hyperbolic conservation laws with non convex flux and vanishing nonlinear and possibly singular diffusion and dispersion terms the diffusion has the form r u u x x and we cover for instance the singular diffusion u x p u x x where p 0 is arbitrary we investigate the existence uniqueness and various properties of classical and non classical travelling waves and of the kinetic function the latter serves to characterize non classical shock waves via an additional algebraic constrain called a kinetic relation we discover that p is a somewhat unexpected critical value for p we obtain properties that are qualitatively similar to those we established earlier for regular and linear diffusion however for p the behaviour of the kinetic function is very different as for instance non classical shocks can have arbitrary small strength the behaviour of the kinetic function near the origin is carefully investigated and depends on whether p p or p in particular in the special case of the cubic flux function and for the regularization u x p u x x with p 0 or 1 the kinetic function can be computed explicitly when p the kinetic function is simply a linear function of its argument