design of capacity approaching irregular low density parity check codes we design low density parity check ldpc codes that perform at rates extremely close to the shannon capacity the codes are built from highly irregular bipartite graphs with carefully chosen degree patterns on both sides our theoretical analysis of the codes is based on the work of richardson and urbanke see ibid vol 47 no 2 p 599 618 2000 assuming that the underlying communication channel is symmetric we prove that the probability densities at the message nodes of the graph possess a certain symmetry using this symmetry property we then show that under the assumption of no cycles the message densities always converge as the number of iterations tends to infinity furthermore we prove a stability condition which implies an upper bound on the fraction of errors that a belief propagation decoder can correct when applied to a code induced from a bipartite graph with a given degree distribution our codes are found by optimizing the degree structure of the underlying graphs we develop several strategies to perform this optimization we also present some simulation results for the codes found which show that the performance of the codes is very close to the asymptotic theoretical bounds

the discrete maximum principle for linear simplicial finite element approximations of a reaction diffusion problem abstract this paper provides a sufficient condition for the discrete maximum principle for a fully discrete linear simplicial finite element discretization of a reaction diffusion problem to hold it explicitly bounds the dihedral angles and heights of simplices in the finite element partition in terms of the magnitude of the reaction coefficient and the spatial dimension as a result it can be computed how small the acute simplices should be for the discrete maximum principle to be valid numerical experiments suggest that the bound which considerably improves a similar bound in p g ciarlet p a raviart maximum principle and uniform convergence for the finite element method comput methods appl mech eng 2 1973 17 31 is in fact sharp

performance of coding spreading tradeoff in ds cdma systems using rcpt and rcpc codes the use of rate compatible punctured turbo and rate compatible punctured convolutional rcpt rcpc codes as channel codes in a direct sequence code division multiple access system where the system bandwidth expansion is fixed is investigated the best rcpc and rcpt code rate in terms of maximizing the system spectral efficiency and minimizing the optimal power allocation where the receiver is either a matched filter mf or a minimum mean square error mmse device is assessed it is shown that for the mf receiver the coding spreading tradeoff favors a code rate reduction in the case of the mmse receiver when the e sub b n sub 0 value and the system load are increased the best code rate also increases by examining the slope of the performance curves it is deduced that under similar operating conditions the best code rate of the rcpt codes is lower than that of the rcpc codes also the best code rate for a rayleigh fading channel is lower than that for an additive white gaussian noise channel

nonlinear theory of defects in nematic liquid crystals phase transition and flow phenomena this is a summary of some recent mathematical advances in the theory of defects in nematic liquid crystals it also includes some new results concerning disclinations line defects which have not been published elsewhere

nonparabolic dissipative systems modeling the flow of liquid crystals we study a simplified system which retains most of the interesting mathematical properties of the original ericksen leslie equations for the flow of liquid crystals this is a coupled nonparabolic dissipative dynamic system we derive several energy laws which enable us to prove the global existence of the weak solutions and the classical solutions we also discuss uniqueness and some stability properties of the system 1995 john wiley sons inc

extrinsic information transfer functions model and erasure channel properties extrinsic information transfer exit charts are a tool for predicting the convergence behavior of iterative processors for a variety of communication problems a model is introduced that applies to decoding problems including the iterative decoding of parallel concatenated turbo codes serially concatenated codes low density parity check ldpc codes and repeat accumulate ra codes exit functions are defined using the model and several properties of such functions are proved for erasure channels one property expresses the area under an exit function in terms of a conditional entropy a useful consequence of this result is that the design of capacity approaching codes reduces to a curve fitting problem for all the aforementioned codes a second property relates the exit function of a code to its helleseth klove levenshtein information functions and thereby to the support weights of its subcodes the relation is via a refinement of information functions called split information functions and via a refinement of support weights called split support weights split information functions are used to prove a third property that relates the exit function of a linear code to the exit function of its dual

global strong solutions for the incompressible nematic liquid crystal flows with density dependent viscosity coefficient abstract this paper is concerned with an initial boundary value problem of the incompressible nematic liquid crystal flows with density dependent viscosity in a smooth bounded domain r 3 the global well posedness of strong solutions with large oscillations is established in vacuum provided u 0 l 2 d 0 l 2 is suitably small with arbitrary large initial density which extended the local strong solution by gao et al 12 to be a global one

existence and partial regularity of static liquid crystal configurations we establish the existence and partial regularity for solutions of some boundary value problems for the static theory of liquid crystals some related problems involving magnetic or electric fields are also discussed

maximum sum rate of repeat accumulate interleave division system by fixed point analysis a multi user repeat accumulate interleave division raid system is considered for a multiple access channel mac with binary inputs equal power and symbol synchronization in the system a regular repeat accumulate ra code serially concatenated with block spreading is employed for each user at the receiver multi user message passing decoding is performed on a single factor graph over the mac with additive white gaussian noise awgn a fixed point analysis is developed to obtain the optimal code rate and the spreading length that give the maximum sum rate for an arbitrary small decoding error rate

global solution to the incompressible flow of liquid crystals abstract the initial boundary value problem for the three dimensional incompressible flow of liquid crystals is considered in a bounded smooth domain the existence and uniqueness is established for both the local strong solution with large initial data and the global strong solution with small data it is also proved that when the strong solution exists a weak solution must be equal to the unique strong solution with the same data

analysis of sum product decoding of low density parity check codes using a gaussian approximation density evolution is an algorithm for computing the capacity of low density parity check ldpc codes under message passing decoding for memoryless binary input continuous output additive white gaussian noise awgn channels and sum product decoders we use a gaussian approximation for message densities under density evolution to simplify the analysis of the decoding algorithm we convert the infinite dimensional problem of iteratively calculating message densities which is needed to find the exact threshold to a one dimensional problem of updating the means of the gaussian densities this simplification not only allows us to calculate the threshold quickly and to understand the behavior of the decoder better but also makes it easier to design good irregular ldpc codes for awgn channels for various regular ldpc codes we have examined thresholds can be estimated within 0 1 db of the exact value for rates between 0 5 and 0 9 codes designed using the gaussian approximation perform within 0 02 db of the best performing codes found so far by using density evolution when the maximum variable degree is 10 we show that by using the gaussian approximation we can visualize the sum product decoding algorithm we also show that the optimization of degree distributions can be understood and done graphically using the visualization

global weak solutions to the equations of compressible flow of nematic liquid crystals in two dimensions we consider weak solutions to a simplified ericksen leslie system of two dimensional compressible flow of nematic liquid crystals an initial boundary value problem is first studied in a bounded domain by developing new techniques and estimates to overcome the difficulties induced by the supercritical nonlinearity nabla mathbf d 2 mathbf d in the equations of angular momentum on the direction field and adapting the standard three level approximation scheme and the weak convergence arguments for the compressible navier stokes equations we establish the global existence of weak solutions under a restriction imposed on the initial energy including the case of small initial energy then the cauchy problem with large initial data is investigated and we prove the global existence of large weak solutions by using the domain expansion technique and the rigidity theorem provided that the second component of initial data of the direction field satisfies some geometric angle condition

unique solvability for the density dependent navier stokes equations abstract in this paper we consider the incompressible navier stokes equations with a density dependent viscosity in a bounded domain of r n n 2 3 we prove the local existence of unique strong solutions for all initial data satisfying a natural compatibility condition this condition is also necessary for a very general initial data moreover we provide a blow up criterion for the regularity of the strong solution for these results the initial density need not be strictly positive it may vanish in an open subset of

global regularity to the 3d incompressible nematic liquid crystal flows with vacuum abstract this paper is concerned with the 3d incompressible nematic liquid crystal equations in smooth bounded domains where the velocity u and macroscopic molecular orientation d admit the dirichlet and neumann boundary condition respectively global in time strong solution is proved to exist when the basic energy is suitably small the initial vacuum is allowed

error analysis for a mimetic discretization of the steady stokes problem on polyhedral meshes we present the development convergence analysis and numerical tests of the mimetic finite difference method for the stokes problem on two dimensional polygonal and three dimensional polyhedral meshes

a weak discrete maximum principle for hp fem in this paper we prove a new discrete maximum principle dmp for the one dimensional poisson equation discretized by the hp fem while the dmp for piecewise linear elements is a classical result from the 1970s no extensions to hp fem are available to the present day due to a negative result by hohn and mittelmann from 1981 related to quadratic lagrange elements it was long assumed that higher order finite elements do not satisfy discrete maximum principles in this paper we explain why it is not possible to make a straightforward extension of the classical dmp to the higher order case and we propose stronger assumptions on the right hand side under which an extension is possible

strong and weak discrete maximum principles for matrices associated with elliptic problems abstract we consider the strong and weak discrete maximum principles for matrix equations associated with the elliptic problems we also give some examples and an application to illustrate the usefulness of the discrete maximum principles

convergence of the mimetic finite difference method for eigenvalue problems in mixed form optimal convergence rates for the mimetic finite difference method applied to eigenvalue problems in mixed form are proved the analysis is based on a new a priori error bound for the source problem and relies on the existence of an appropriate elemental lifting of the mimetic discrete solution compared to the original convergence analysis of the method the new a priori estimate does not require any extra regularity assumption on the right hand side of the source problem numerical results confirming the optimal behavior of the method are presented

a higher order formulation of the mimetic finite difference method a new mimetic finite difference method for the diffusion problem is developed by using a linear interpolation for the numerical fluxes this approach provides a higher order accurate approximation to the flux of the exact solution in analogy with the original formulation a family of local scalar products is constructed to satisfy the fundamental properties of local consistency and spectral stability the scalar solution field is approximated by a piecewise constant function a computationally efficient postprocessing technique is also proposed to get a piecewise quadratic polynomial approximation to the exact scalar variable finally optimal convergence rates and accuracy improvement with respect to the lower order formulation are shown by numerical examples

design of repeat accumulate codes for iterative detection and decoding extrinsic information transfer exit charts are used to design systematic and nonsystematic repeat accumulate ra codes for iterative detection and decoding the convergence problems of nonsystematic ra codes are solved by introducing a biregular or doped layer of check nodes as examples such nonsystematic codes are designed for multi input multi output mimo fading channels and are shown to operate close to capacity

monotonicity of control volume methods robustness of numerical methods for multiphase flow problems in porous media is important for development of methods to be used in a wide range of applications here we discuss monotonicity for a simplified problem of single phase flow but where the simulation grids and media are allowed to be general posing challenges to control volume methods we discuss discrete formulations of the maximum principle and derive sufficient criteria for discrete monotonicity for arbitrary nine point control volume discretizations for conforming quadrilateral grids in 2d these criteria are less restrictive than the m matrix property it is shown that it is impossible to construct nine point methods which unconditionally satisfy the monotonicity criteria when the discretization satisfies local conservation and exact reproduction of linear potential fields numerical examples are presented which show the validity of the criteria for monotonicity further the impact of nonmonotonicity is studied different behavior for different discretization methods is illuminated and simple ideas are presented for improvement in terms of monotonicity

a mimetic discretization of the stokes problem with selected edge bubbles a new mimetic finite difference method for the stokes problem is proposed and analyzed the mimetic discretization methodology can be understood as a generalization of the finite element method to meshes with general polygons polyhedrons in this paper the mimetic generalization of the unstable p 1 p 0 and the conditionally stable q1 p0 finite element is shown to be fully stable when applied to a large range of polygonal meshes moreover we show how to stabilize the remaining cases by adding a small number of bubble functions to selected mesh edges a simple strategy for selecting such edges is proposed and verified with numerical experiments

spectral efficiency of cdma with random spreading the cdma channel with randomly and independently chosen spreading sequences accurately models the situation where pseudonoise sequences span many symbol periods furthermore its analysis provides a comparison baseline for cdma channels with deterministic signature waveforms spanning one symbol period we analyze the spectral efficiency total capacity per chip as a function of the number of users spreading gain and signal to noise ratio and we quantify the loss in efficiency relative to an optimally chosen set of signature sequences and relative to multiaccess with no spreading white gaussian background noise and equal power synchronous users are assumed the following receivers are analyzed a optimal joint processing b single user matched filtering c decorrelation and d mmse linear processing

a monotone finite volume method for advection diffusion equations on unstructured polygonal meshes we present a new second order accurate monotone finite volume fv method for the steady state advection diffusion equation the method uses a nonlinear approximation for both diffusive and advective fluxes and guarantees solution non negativity the interpolation free approximation of the diffusive flux uses the nonlinear two point stencil proposed in lipnikov 23 approximation of the advective flux is based on the second order upwind method with a specially designed minimal nonlinear correction the second order convergence rate and monotonicity are verified with numerical experiments

finite field spreading for multiple access channel as a generalization of the binary spreading scheme in conventional direct sequence code division multiple access ds cdma and interleave division multiple access idma a finite field spreading scheme is proposed for a synchronous multiple access channel mac with gaussian noise and equal power users for each user each information symbol over a finite field is spread into a length l field vector by l field multiplications at the receiver an iterative multi user decoding algorithm on a factor graph is developed to recover each user s information symbol to estimate the bit error rate performance of an uncoded finite field spreading system an extrinsic information transfer analysis of the finite field despreading is given this analysis shows that in addition to overcoming multi user interference the finite field spreading scheme can also provide an additional coding gain to overcome gaussian noise compared with the conventional spreading scheme this coding gain increases with the field order the finite field spreading serially concatenated with a nonbinary low density parity check ldpc code with field order 64 approaches the mac capacity within 0 26 db at a sum rate of 0 25

accumulate repeat accumulate codes in this paper we propose an innovative channel coding scheme called accumulate repeat accumulate ara codes this class of codes can be viewed as serial turbo like codes or as a subclass of low density parity check ldpc codes and they have a projected graph or protograph representation this allows for high speed iterative decoding implementation using belief propagation an ara code can be viewed as precoded repeat accumulate ra code with puncturing or as precoded irregular repeat accumulate ira code where simply an accumulator is chosen as the precoder the amount of performance improvement due to the precoder will be called precoding gain using density evolution on their associated protographs we find some rate 1 2 ara codes with a maximum variable node degree of 5 for which a minimum bit snr as low as 0 08 db from channel capacity threshold is achieved as the block size goes to infinity such a low threshold cannot be achieved by ra ira or unstructured irregular ldpc codes with the same constraint on the maximum variable node degree furthermore by puncturing the inner accumulator we can construct families of higher rate ara codes with thresholds that stay close to their respective channel capacity thresholds uniformly iterative decoding simulation results are provided and compared with turbo codes in addition to iterative decoding analysis we analyzed the performance of ara codes with maximum likelihood ml decoding by obtaining the weight distribution of these codes and through existing tightest bounds we have shown that the ml snr threshold of ara codes also approaches very closely to that of random codes these codes have better interleaving gain than turbo codes

an iterative multiuser decoder for near capacity communications the combination of forward error correction fec coding and random interleaving is shown to overcome the limitations of multiuser detectors decoders when the user cross correlations are high in particular one can asymptotically achieve single user performance in a highly correlated multiuser system in addition an optimal iterative multiuser detector is derived from iterative techniques for cross entropy minimization a practical suboptimal implementation of this algorithm is presented and simulations demonstrate that even with highly correlated users it achieves optimal asymptotic efficiency the effects of the theoretical limits on channel capacity are evident in many of the simulation results the complexity of the suboptimal algorithm is approximately o 2 sup k o 2 sup spl kappa per bit per iteration where k is the number of users and spl kappa is the code constraint length

well posedness for the heat flow of harmonic maps and the liquid crystal flow with rough initial data we investigate the well posedness of 1 the heat flow of harmonic maps from mathbb r n to a compact riemannian manifold n without boundary for initial data in bmo and 2 the hydrodynamic flow u d of nematic liquid crystals on mathbb r n for initial data in bmo 1 bmo

global strong and weak solutions to inhomogeneous nematic liquid crystal flow in two dimensions abstract we consider the strong and weak solutions to the cauchy problem of the inhomogeneous incompressible nematic liquid crystal equations in two dimensions we first establish the local existence and uniqueness of strong solutions by using the standard domain expanding method and then extend such a local strong solution to be a global one provided the initial density is away from vacuum and the initial direction field satisfies some geometric structure the size of the initial data can be large based on such global existence results by using the compactness argument we obtain the global existence of weak solutions with nonnegative initial density

strong solutions to the density dependent incompressible nematic liquid crystal flows abstract in this paper we investigate the density dependent incompressible nematic liquid crystal flows in n dimensional n 2 or 3 bounded domain the local existence and uniqueness of strong solutions are obtained when the viscosity coefficient of fluid depends on density furthermore one establishes blowup criterions for the regularity of the strong solutions in dimensions two and three respectively in particular we build a blowup criterion just in terms of the gradient of density if the initial direction field satisfies some geometric configuration for these results the initial density need not be strictly positive

global strong solution to the 2d nonhomogeneous incompressible mhd system abstract in this paper we first prove the unique global strong solution with vacuum to the two dimensional nonhomogeneous incompressible mhd system as long as the initial data satisfies some compatibility condition as a corollary the global existence of strong solution with vacuum to the 2d nonhomogeneous incompressible navier stokes equations is also established our main result improves all the previous results where the initial density need to be strictly positive the key idea is to use some critical sobolev inequality of logarithmic type which is originally due to brezis and wainger 1980 7

analysis of the monotonicity conditions in the mimetic finite difference method for elliptic problems the maximum principle is one of the most important properties of solutions of partial differential equations its numerical analog the discrete maximum principle dmp is one of the most difficult properties to achieve in numerical methods especially when the computational mesh is distorted to adapt and conform to the physical domain or the problem coefficients are highly heterogeneous and anisotropic violation of the dmp may lead to numerical instabilities such as oscillations and to unphysical solutions such as heat flow from a cold material to a hot one in this work we investigate sufficient conditions to ensure the monotonicity of the mimetic finite difference mfd method on two and three dimensional meshes these conditions result in a set of general inequalities for the elements of the mass matrix of every mesh element efficient solutions are devised for meshes consisting of simplexes parallelograms and parallelepipeds and orthogonal locally refined elements as those used in the amr methodology on simplicial meshes it turns out that the mfd method coincides with the mixed hybrid finite element methods based on the low order raviart thomas vector space thus in this case we recover the well established conventional angle conditions of such approximations instead in the other cases a suitable design of the mfd method allows us to formulate a monotone discretization for which the existence of a dmp can be theoretically proved moreover on meshes of parallelograms we establish a connection with a similar monotonicity condition proposed for the multi point flux approximation mpfa methods numerical experiments confirm the effectiveness of the considered monotonicity conditions

uniform well posedness and low mach number limit to the compressible nematic liquid crystal flows in a bounded domain abstract we prove global in time and uniform in of the strong solutions to the 3 d compressible nematic liquid crystal flows in a bounded domain where is the mach number consequently we obtain the strong solution of compressible nematic liquid crystal model that converges to that of incompressible nematic liquid crystal model this is the first result on the low mach number limit for compressible nematic liquid crystal flows in 3 d bounded domain our proof relies on the dedicated estimates on the solutions and the subtle use of the boundary conditions

achievable information rates and the coding spreading tradeoff in finite sized synchronous cdma systems in this letter we compute achievable information rates for finite sized synchronous code division multiple access cdma systems and low density parity check ldpc codes are adopted to approach the achievable rates the associated coding spreading tradeoff problem is also considered using these results we assume binary random spreading sequences and the computed achievable rates are averaged over ensembles of spreading sequences unlike most prior papers which analyze the spectral efficiency of large cdma systems under gaussianity assumptions channel inputs and or multiple access interference we make no such assumptions in order to display the coding spreading tradeoff we plot the minimum required signal to noise ratio for reliable transmission as a function of information rate it is shown that the coding spreading tradeoff favors all coding i e no spreading when the optimal joint multiuser detector decoder is employed whereas for systems with a suboptimal multiuser detector and single user decoders there generally exists an optimal balance between coding and spreading we also provide simulation results on the performance of ldpc coded synchronous cdma systems which approach the information theoretic limits we have computed

flux reconstruction and solution post processing in mimetic finite difference methods abstract we present a post processing technique for the mimetic finite difference solution of diffusion problems in mixed form our post processing method yields a piecewise linear approximation of the scalar variable that is second order accurate in the l2 norm on quite general polyhedral meshes including non convex and non matching elements the post processing is based on the reconstruction of vector fields projected onto the mimetic space of vector variables this technique is exact on constant vector fields and is shown to be independent of the mimetic scalar product choice if a local consistency condition is satisfied the post processing method is computationally inexpensive optimal performance is confirmed by numerical experiments

strong solutions of the compressible nematic liquid crystal flow abstract we study strong solutions of the simplified ericksen leslie system modeling compressible nematic liquid crystal flows in a domain r 3 we first prove the local existence of a unique strong solution provided that the initial data 0 u 0 d 0 are sufficiently regular and satisfy a natural compatibility condition the initial density function 0 may vanish on an open subset i e an initial vacuum may exist we then prove a criterion for possible breakdown of such a local strong solution at finite time in terms of blow up of the quantities l t l x and d l t 3 l x