a matrix theoretic approach to the construction of non binary quasi cyclic ldpc codes this paper presents two simple and very flexible methods for constructing non binary nb quasi cyclic qc ldpc codes the proposed construction methods have several known ingredients including base array masking binary to non binary replacement and matrix dispersion by proper choice and combination of these ingredients nb qc ldpc codes with excellent performance can be constructed the constructed codes can be decoded with a reduced complexity iterative decoding scheme which significantly reduces the hardware implementation complexity

a cartesian grid embedded boundary method for hyperbolic conservation laws we present a second order godunov algorithm to solve time dependent hyperbolic systems of conservation laws on irregular domains our approach is based on a formally consistent discretization of the conservation laws on a finite volume grid obtained from intersecting the domain with a cartesian grid we address the small cell stability problem associated with such methods by hybridizing our conservative discretization with a stable nonconservative discretization at irregular control volumes and redistributing the difference in the mass increments to nearby cells in a way that preserves stability and local conservation the resulting method is second order accurate in l 1 for smooth problems and is robust in the presence of large amplitude discontinuities intersecting the irregular boundary

construction and encoding of qc ldpc codes using group rings quasi cyclic qc low density parity check ldpc codes which are known as qc ldpc codes have many applications due to their simple encoding implementation by the means of cyclic shift registers in this paper we construct qc ldpc codes from group rings a group ring is a free module at the same time a ring constructed in a natural way from any given ring and any given group we present a structure based on the elements of a group ring for constructing qc ldpc codes some of the previously addressed methods for constructing qc ldpc codes based on finite fields are special cases of the proposed construction method the constructed qc ldpc codes perform very well over the additive white gaussian noise channel with iterative decoding in terms of bit error probability and block error probability simulation results demonstrate that the proposed codes have competitive performance in comparison with the similar existing ldpc codes finally we propose a new encoding method for the proposed group ring based qc ldpc codes that can be implemented faster than the current encoding methods the encoding complexity of the proposed method is analyzed mathematically and indicates a significate reduction in the required number of operations even when compared to the available efficient encoding methods that have linear time and space complexities

a sharp interface immersed boundary method with improved mass conservation and reduced spurious pressure oscillations a method for reducing the spurious pressure oscillations observed when simulating moving boundary flow problems with sharp interface immersed boundary methods ibms is proposed by first identifying the primary cause of these oscillations to be the violation of the geometric conservation law near the immersed boundary we adopt a cut cell based approach to strictly enforce geometric conservation in order to limit the complexity associated with the cut cell method the cut cell based discretization is limited only to the pressure poisson and velocity correction equations in the fractional step method and the small cell problem tackled by introducing a virtual cell merging technique the method is shown to retain all the desirable properties of the original finite difference based ibm while at the same time reducing pressure oscillations for moving boundaries by roughly an order of magnitude

construction of quasi cyclic ldpc codes for awgn and binary erasure channels a finite field approach in the late 1950s and early 1960s finite fields were successfully used to construct linear block codes especially cyclic codes with large minimum distances for hard decision algebraic decoding such as bose chaudhuri hocquenghem bch and reed solomon rs codes this paper shows that finite fields can also be successfully used to construct algebraic low density parity check ldpc codes for iterative soft decision decoding methods of construction are presented ldpc codes constructed by these methods are quasi cyclic qc and they perform very well over the additive white gaussian noise awgn binary random and burst erasure channels with iterative decoding in terms of bit error probability block error probability error floor and rate of decoding convergence collectively particularly they have low error floors since the codes are qc they can be encoded using simple shift registers with linear complexity

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

a conservative immersed interface method for large eddy simulation of incompressible flows we propose a conservative second order accurate immersed interface method for representing incompressible fluid flows over complex three dimensional solid obstacles on a staggered cartesian grid the method is based on a finite volume discretization of the incompressible navier stokes equations which is modified locally in cells that are cut by the interface in such a way that accuracy and conservativity are maintained a level set technique is used for description and tracking of the interface geometry so that an extension of the method to moving boundaries and flexible walls is straightforward numerical stability is ensured for small cells by a conservative mixing procedure discrete conservation and sharp representation of the fluid solid interface render the method particularly suitable for large eddy simulations of high reynolds number flows accuracy second order grid convergence and robustness of the method is demonstrated for several test cases inclined channel flow at re 20 flow over a square cylinder at re 100 flow over a circular cylinder at re 40 re 100 and re 3900 as well as turbulent channel flow with periodic constrictions at re 10 595

sequential quasi monte carlo this is a written discussion of the paper sequential quasi monte carlo sampling by m gerber and n chopin following the presentation given before the royal statistical society in london on december 10th 2014

sequentially interacting markov chain monte carlo methods we introduce a novel methodology for sampling from a sequence of probability distributions of increasing dimension and estimating their normalizing constants these problems are usually addressed using sequential monte carlo smc methods the alternative sequentially interacting markov chain monte carlo simcmc scheme proposed here works by generating interacting non markovian sequences which behave asymptotically like independent metropolis hastings mh markov chains with the desired limiting distributions contrary to smc methods this scheme allows us to iteratively improve our estimates in an mcmc like fashion we establish convergence of the algorithm under realistic verifiable assumptions and demonstrate its performance on several examples arising in bayesian time series analysis

an efficient conservative cut cell method for rigid bodies interacting with viscous compressible flows a cartesian cut cell method for viscous flows interacting with freely moving boundaries is presented the method enables a sharp resolution of the embedded boundaries and strictly conserves mass momentum and energy a new explicit runge kutta scheme pc rk is introduced by which the overall computational time is reduced by a factor of up to 2 5 the new scheme is a predictor corrector type reformulation of a popular class of runge kutta methods which substantially reduces the computational effort for tracking the moving boundaries and subsequently reinitializing the solver impairing neither stability nor accuracy the structural motion is computed by an implicit scheme with good stability properties due to a strong coupling strategy and the conservative discretization of the flow solver at the material interfaces a new formulation for the treatment of small cut cells is proposed with high accuracy and robustness for arbitrary geometries based on a weighted taylor series approach solved via singular value decomposition the efficiency and the accuracy of the new method are demonstrated for several three dimensional cases of laminar and turbulent particulate flow it is shown that the new method remains fully conservative even for large displacements of the boundaries leading to a fast convergence of the fluid solid coupling while spurious force oscillations inherent to this class of methods are effectively suppressed the results substantiate the good stability and accuracy properties of the scheme even on relatively coarse meshes an efficient cartesian cut cell method for freely moving solid boundaries is presented the new predictor corrector runge kutta scheme pc rk enables simulation speedups of up to 2 5 mass momentum and energy are strictly conserved at the sharply resolved solid fluid interfaces the method exhibits very good stability and accuracy properties even for large displacements of the boundaries spurious force oscillations inherent to this class of methods are suppressed

an immersed boundary finite volume method for simulations of flow in complex geometries abstract a new immersed boundary method for simulating flows over or inside complex geometries is developed by introducing a mass source sink as well as a momentum forcing the present method is based on a finite volume approach on a staggered mesh together with a fractional step method both momentum forcing and mass source are applied on the body surface or inside the body to satisfy the no slip boundary condition on the immersed boundary and also to satisfy the continuity for the cell containing the immersed boundary in the immersed boundary method the choice of an accurate interpolation scheme satisfying the no slip condition on the immersed boundary is important because the grid lines generally do not coincide with the immersed boundary therefore a stable second order interpolation scheme for evaluating the momentum forcing on the body surface or inside the body is proposed three different flow problems decaying vortices and flows over a cylinder and a sphere are simulated using the immersed boundary method proposed in this study and the results agree very well with previous numerical and experimental results verifying the accuracy of the present method

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

a matrix theoretic approach for analyzing quasi cyclic low density parity check codes a matrix theoretic approach for studying quasi cyclic codes based on matrix transformations via fourier transforms and row and column permutations is developed these transformations put a parity check matrix in the form of an array of circulant matrices into a diagonal array of matrices of the same size over an extension field the approach is amicable to the analysis and construction of quasi cyclic low density parity check codes since it takes into account the specific parity check matrix used for decoding with iterative message passing algorithms based on this approach the dimension of the codes and parity check matrices for the dual codes can be determined several algebraic and geometric constructions of quasi cyclic codes are presented as applications along with simulation results showing their performance over additive white gaussian noise channels decoded with iterative message passing algorithms

cut element based immersed boundary method for moving geometries in compressible liquid flows with cavitation the conservative immersed interface method for representing complex immersed solid boundaries or phase interfaces on cartesian grids is improved and extended to allow for the simulation of weakly compressible fluid flows through moving geometries we demonstrate that an approximation of moving interfaces by a level set field results in unphysical oscillations in the vicinity of sharp corners when dealing with weakly compressible fluids such as water by introducing an exact reconstruction of the cut cell properties directly based on a surface triangulation of the immersed boundary we are able to recover the correct flow evolution free of numerical artifacts the new method is based on cut elements it provides sub cell resolution of the geometry and handles flows through narrow closing or opening gaps in a straightforward manner we validate our method with canonical flows around oscillating cylinders we demonstrate that the method allows for an accurate prediction of flows around moving obstacles in weakly compressible liquid flows with cavitation effects in particular we show that the cavitating flow through a closing fuel injector control valve which is an example for a complex application with interaction of stationary and moving parts can be predicted by the method

near shannon limit quasi cyclic low density parity check codes this letter presents two classes of quasi cyclic low density parity check codes that perform close to the shannon limit

computation of solid liquid phase fronts in the sharp interface limit on fixed grids a finite difference formulation is applied to track solid liquid boundaries on a fixed underlying grid the interface is not of finite thickness but is treated as a discontinuity and is explicitly tracked the imposition of boundary conditions exactly on a sharp interface that passes through the cartesian grid is performed using simple stencil readjustments in the vicinity of the interface attention is paid to formulating difference schemes that are globally second order accurate in x and t error analysis and grid refinement studies are performed for test problems involving the diffusion and convection diffusion equations and for stable solidification problems issues concerned with stability and change of phase of grid points in the evolution of solid liquid phase fronts are also addressed it is demonstrated that the field calculation is second order accurate while the position of the phase front is calculated to first order accuracy furthermore the accuracy estimates hold for the cases where there is a property jump across the interface unstable solidification phenomena are simulated and an attempt is made to compare results with previously published work the results indicate the need to begin an effort to benchmark computations of instability phenomena

new classes of partial geometries and their associated ldpc codes the use of partial geometries to construct parity check matrices for binary low density parity check ldpc codes has resulted in the design of successful codes with a probability of error on the awgn channel close to the shannon capacity at bit error rate down to 10 15 such considerations have motivated this further investigation a new and simple construction of a type of partial geometries with a quasi cyclic qc structure is given and their properties are investigated two new classes of this type of partial geometries one based on prime fields and the other based on cyclic subgroups of prime orders of finite fields are constructed qc ldpc codes with good error performances are constructed based on these two new classes of partial geometries the trapping sets of the partial geometry codes were previously considered using the geometric aspects of the underlying structure to derive information on the size of allowable trapping sets this topic is further considered here finally there is a natural relationship between partial geometries and strongly regular graphs the eigenvalues of the adjacency matrices of such graphs are well known and it is of interest to determine if any of the tanner graphs derived from the partial geometries are good expanders for certain parameter sets since it can be argued that codes with good geometric and expansion properties might perform well on the awgn channel under message passing decoding

a revolving iterative algorithm for decoding algebraic cyclic and quasi cyclic ldpc codes cyclic and quasi cyclic algebraic ldpc codes constructed based on finite fields finite geometries and combinatorial designs can achieve excellent performance in terms of error rate error floor and rate of decoding convergence with iterative decoding however the relatively high density of the parity check matrix of an algebraic cyclic or quasi cyclic ldpc code makes the hardware implementation complexity of the decoder quite large which may be a critical issue in practical applications this paper presents an effective reduced complexity algorithm for decoding algebraic cyclic and quasi cyclic ldpc codes based on the block cyclic structure and cyclic grouping of the rows of their parity check matrices the decoding of a code is carried out based on a single small submatrix of the parity check matrix of the code in a revolving manner the proposed decoding algorithm significantly reduces the hardware implementation complexity and the size of memory required to store information

algebraic construction of quasi cyclic ldpc codes for the awgn and erasure channels this paper is concerned with construction of quasi cyclic qc low density parity check ldpc codes for three different types of channels the additive white gaussian noise the binary random erasure and the binary burst erasure channels two algebraic methods for systematic construction of qc ldpc codes are presented codes constructed perform well over all three types of channels

a new multi edge metric constrained peg algorithm for designing binary ldpc code with improved cycle structure the progressive edge growth peg algorithm constructs an edge in each stage to maximize the variable node vn of interest s local girth in real time thus this vn s local girths after more than one edge is added to the current tanner graph tg setting may not be maximized relative to that tg setting to address this problem we define the multi edge local girth and edge trial and based on these definitions propose a new multi edge metric constrained peg algorithm mm pega to improve the design at each vn the mm pega constructs an edge in each stage that relative to the current tg setting can potentially maximize the vn of interest s local girth after a certain number up to the edge trial of edges are added to the tg setting we first analyze the properties of the multi edge local girth and then propose an algorithm for calculating the multi edge local girth we also propose a method for accelerating the mm pega moreover we generalize the mm pega for improving different peg like designs according to the theoretical analysis increasing the edge trial of the mm pega is expected to positively affect the cycle structure and the error performance of resulting low density parity check ldpc code this expectation is verified by simulations

on the order of accuracy of the immersed boundary method higher order convergence rates for sufficiently smooth problems the immersed boundary method is both a mathematical formulation and a numerical scheme for problems involving the interaction of a viscous incompressible fluid and a visco elastic structure in m c lai simulations of the flow past an array of circular cylinders as a test of the immersed boundary method ph d thesis courant institute of mathematical sciences new york university 1998 m c lai c s peskin an immersed boundary method with formal second order accuracy and reduced numerical viscosity j comput phys 160 2000 705 719 lai and peskin introduced a formally second order accurate immersed boundary method but the convergence properties of their algorithm have only been examined computationally for problems with nonsmooth solutions consequently in practice only first order convergence rates have been observed in the present work we describe a new formally second order accurate immersed boundary method and demonstrate its performance for a prototypical fluid structure interaction problem involving an immersed viscoelastic shell of finite thickness studied over a broad range of reynolds numbers we consider two sets of material properties for the viscoelastic structure including a case where the material properties of the coupled system are discontinuous at the fluid structure interface for both sets of material properties the true solutions appear to possess sufficient smoothness for the method to converge at a second order rate for fully resolved computations

reed solomon based quasi cyclic ldpc codes designs girth cycle structure and reduction of short cycles designs and constructions of quasi cyclic qc ldpc codes for the awgn channel are presented the codes are constructed based on the conventional parity check matrices of reed solomon rs codes and are referred to as rs qc ldpc codes several classes of rs qc ldpc codes are given cycle structural properties of the tanner graphs of codes in these classes are analyzed and specific methods for constructing codes with girth at least eight and reducing their short cycles are presented the designed codes perform well in both waterfall and low error rate regions

a cut cell finite volume finite element coupling approach for fluid structure interaction in compressible flow we present a loosely coupled approach for the solution of fluid structure interaction problems between a compressible flow and a deformable structure the method is based on staggered dirichlet neumann partitioning the interface motion in the eulerian frame is accounted for by a conservative cut cell immersed boundary method the present approach enables sub cell resolution by considering individual cut elements within a single fluid cell which guarantees an accurate representation of the time varying solid interface the cut cell procedure inevitably leads to non matching interfaces demanding for a special treatment a mortar method is chosen in order to obtain a conservative and consistent load transfer we validate our method by investigating two dimensional test cases comprising a shock loaded rigid cylinder and a deformable panel moreover the aeroelastic instability of a thin plate structure is studied with a focus on the prediction of flutter onset finally we propose a three dimensional fluid structure interaction test case of a flexible inflated thin shell interacting with a shock wave involving large and complex structural deformations

dynamic conditional independence models and markov chain monte carlo methods abstract in dynamic statistical modeling situations observations arise sequentially causing the model to expand by progressive incorporation of new data items and new unknown parameters for example in clinical monitoring patients and data arrive sequentially and new patient specific parameters are introduced with each new patient markov chain monte carlo mcmc might be used for continuous updating of the evolving posterior distribution but would need to be restarted from scratch at each expansion stage thus mcmc methods are often too slow for real time inference in dynamic contexts by combining mcmc with importance resampling we show how real time sequential updating of posterior distributions can be effected the proposed dynamic sampling algorithms use posterior samples from previous updating stages and exploit conditional independence between groups of parameters to allow samples of parameters no longer of interest to be discarded such as when a patient dies or is discharged we apply the

an adaptive version of the immersed boundary method a computational setting for the immersed boundary method employing an adaptive mesh refinement is presented enhanced accuracy for the method is attained locally by covering an immersed boundary vicinity with a sequence of nested progressively finer rectangular grid patches which dynamically follow the immersed boundary motion the set of equations describing the interaction between a non stationary viscous incompressible fluid and an immersed elastic boundary is solved by coupling a projection method specially designed for locally refined meshes to an implicit formulation of the immersed boundary method the main contributions of this work concern the formulation and the implementation of a multilevel self adaptive version of the immersed boundary method on locally refined meshes this approach is tested for a particular two dimensional model problem for which no significant difference is found between the solutions obtained on a mesh refined locally around the immersed boundary and on the associated uniform mesh built with the resolution of the finest level

quasi cyclic ldpc codes an algebraic construction this paper presents two new large classes of qc ldpc codes one binary and one non binary codes in these two classes are constructed by array dispersions of row distance constrained matrices formed based on additive subgroups of finite fields experimental results show that codes constructed perform very well over the awgn channel with iterative decoding based on belief propagation codes of a subclass of the class of binary codes have large minimum distances comparable to finite geometry ldpc codes and they offer effective tradeoff between error performance and decoding complexity when decoded with low complexity reliability based iterative decoding algorithms such as binary message passing decoding algorithms non binary codes decoded with a fast fourier transform based sum product algorithm achieve significantly large coding gains over reed solomon codes of the same lengths and rates decoded with either the hard decision berlekamp massey algorithm or the algebraic soft decision kotter vardy algorithm they have potential to replace reed solomon codes in some communication or storage systems where combinations of random and bursts of errors or erasures occur

boundary condition enforced immersed boundary lattice boltzmann flux solver for thermal flows with neumann boundary conditions a boundary condition enforced immersed boundary lattice boltzmann flux solver is proposed in this work for effective simulation of thermal flows with neumann boundary conditions in this method two auxiliary layers of lagrangian points are introduced and respectively placed inside and outside of the solid body on which the temperature corrections related to the heat source are set as unknowns to effectively consider the fluid boundary interaction these unknowns are expressed as algebraic summations of the temperature correction on eulerian points which are in turn obtained from biased distributions of unknown temperature corrections on the immersed boundary by enforcing the temperature gradient at the solid boundary being equal to that approximated by the corrected temperature field a set of algebraic equations are formed and solved to obtain all the unknowns simultaneously they are then distributed biasedly to the inner region of the auxiliary layer so that the diffusion from the smooth delta function can be reduced substantially in addition the solutions of the flow and temperature fields are obtained by the thermal lattice boltzmann flux solver with the second order of accuracy the proposed method is well validated through its applications to simulate several benchmarks of natural forced and mixed convection problems it has been demonstrated that the present solver has about 1 724 order of accuracy and the error between the present result and theoretical value for the temperature gradient on the solid surface is in the order of 10 13 which indicates that the proposed method is able to satisfy the neumann boundary condition accurately

accurate immersed boundary reconstructions for viscous flow simulations cells crossed by the immersed boundary is treated a novel interpolation method based on momentum balance and massconservationbasedon finitevolumemethodareintroducedtocorrectlypredictthevelocityandpressure fieldin the vicinity of the boundaries the assessment of the solution quality is based on calculations of taylor decaying vortices examples of laminar and turbulent flow calculations are also reported

particle filtering with invertible particle flow a key challenge when designing particle filters in high dimensional state spaces is the construction of a proposal distribution that is close to the posterior distribution recent advances in particle flow filters provide a promising avenue to avoid weight degeneracy particles drawn from the prior distribution are migrated in the state space to the posterior distribution by solving partial differential equations numerous particle flow filters have been proposed based on different assumptions concerning the flow dynamics approximations are needed in the implementation of all of these filters as a result the particles do not exactly match a sample drawn from the desired posterior distribution past efforts to correct the discrepancies involve expensive calculations of importance weights in this paper we present new filters which incorporate deterministic particle flows into an encompassing particle filter framework the valuable theoretical guarantees concerning particle filter performance still apply but we can exploit the attractive performance of the particle flow methods the filters we describe involve a computationally efficient weight update step arising because the embedded particle flows we design possess an invertible mapping property we evaluate the proposed particle flow particle filters performance through numerical simulations of a challenging multitarget multisensor tracking scenario and complex high dimensional filtering examples

construction of regular and irregular ldpc codes geometry decomposition and masking two algebraic methods for systematic construction of structured regular and irregular low density parity check ldpc codes with girth of at least six and good minimum distances are presented these two methods are based on geometry decomposition and a masking technique numerical results show that the codes constructed by these methods perform close to the shannon limit and as well as random like ldpc codes furthermore they have low error floors and their iterative decoding converges very fast the masking technique greatly simplifies the random like construction of irregular ldpc codes designed on the basis of the degree distributions of their code graphs

an embedded boundary formulation for large eddy simulation of turbulent flows interacting with moving boundaries a non boundary conforming formulation for simulating complex turbulent flows with dynamically moving boundaries on fixed cartesian grids is proposed the underlying finite difference solver for the filtered incompressible navier stokes equations is based on a second order fractional step method on a staggered grid to satisfy the boundary conditions on an arbitrary immersed interface the velocity field at the grid points near the interface is reconstructed using momentum forcing without smearing the sharp interface the concept of field extension is also introduced to treat the points emerging from a moving solid body to the fluid laminar flow cases and large eddy simulations les are presented to demonstrate the formal accuracy and range of applicability of the method in particular simulations of laminar flow induced by the harmonic in line oscillation of a circular cylinder in quiescent fluid and from a transversely oscillating cylinder in a free stream are presented and compared to reference simulations and experiments les of turbulent flow over a traveling wavy wall and transitional flow through a bileaflet prosthetic heart valve are also shown all results are in very good agreement with reference results in the literature

efficient encoding of quasi cyclic low density parity check codes efficient encoding of quasi cyclic low density parity check codes quasi cyclic qc low density parity check ldpc codes form an important subclass of ldpc codes these codes have encoding advantage over other types of ldpc codes this paper addresses the issue of efficient encoding of qc ldpc codes two methods are presented to find the generator matrices of qc ldpc codes in systematic circulant form from their parity check matrices given in circulant form based on the systematic circulation form of the generator matrix of a qc ldpc code various types of encoding circuits using simple shift registers are devised it is shown that the encoding complexity of a qc ldpc code is linearly proportional to the number of parity bits of the code for serial encoding and to the length of the code for high speed parallel encoding

immersed boundary method for flow around an arbitrarily moving body for the simulation of flow around an arbitrarily moving body an immersed boundary method is developed in a non inertial reference frame that is fixed to the body the navier stokes equation is formulated in a conservative form such that the force terms due to the rotation and the translational and rotational accelerations are included in the nonlinear term in order to satisfy the no slip condition on the body surface momentum forcing and mass source sink are applied on the body surface or inside the body the numerical method is based on a finite volume approach on a staggered mesh together with a fractional step method the present numerical method is applied to both the forced motion and fluid structure interaction problems in the latter we solve fully coupled navier stokes and dynamic equations for the moving body without introducing any iteration four different flow problems are tested and the results are in excellent agreements with previous numerical and experimental ones

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

quasicyclic low density parity check codes from circulant permutation matrices in this correspondence the construction of low density parity check ldpc codes from circulant permutation matrices is investigated it is shown that such codes cannot have a tanner graph representation with girth larger than 12 and a relatively mild necessary and sufficient condition for the code to have a girth of 6 8 10 or 12 is derived these results suggest that families of ldpc codes with such girth values are relatively easy to obtain and consequently additional parameters such as the minimum distance or the number of redundant check sums should be considered to this end a necessary condition for the codes investigated to reach their maximum possible minimum hamming distance is proposed

regular article an accurate cartesian grid method for viscous incompressible flows with complex immersed boundaries a cartesian grid method has been developed for simulating two dimensional unsteady viscous incompressible flows with complex immersed boundaries a finite volume method based on a second order accurate central difference scheme is used in conjunction with a two step fractional step procedure the key aspects that need to be considered in developing such a solver are imposition of boundary conditions on the immersed boundaries and accurate discretization of the governing equation in cells that are cut by these boundaries a new interpolation procedure is presented which allows systematic development of a spatial discretization scheme that preserves the second order spatial accuracy of the underlying solver the presence of immersed boundaries alters the conditioning of the linear operators and this can slow down the iterative solution of these equations the convergence is accelerated by using a preconditioned conjugate gradient method where the preconditioner takes advantage of the structured nature of the underlying mesh the accuracy and fidelity of the solver is validated by simulating a number of canonical flows and the ability of the solver to simulate flows with very complicated immersed boundaries is demonstrated

quasi cyclic ldpc codes on cyclic subgroups of finite fields a new class of quasi cyclic ldpc codes whose parity check matrices are arrays of circulant permutation matrices constructed based on cyclic subgroups of finite fields is presented this class of codes contains several known classes of algebraic quasi cyclic ldpc codes as subclasses experimental results show that the codes constructed perform very well over the awgn channel when decoded with iterative decoding based on belief propagation this class of new qc ldpc codes contains a subclass of codes which have large minimum distances combinatorial expressions for the ranks of the parity check matrices of a subclass of codes constructed based on fields of characteristic two are given

algebraic quasi cyclic ldpc codes construction low error floor large girth and a reduced complexity decoding scheme this paper presents a simple and very flexible method for constructing quasi cyclic qc low density paritycheck ldpc codes based on finite fields the code construction is based on two arbitrary subsets of elements from a given field some well known constructions of qc ldpc codes based on finite fields and combinatorial designs are special cases of the proposed construction the proposed construction in conjunction with a technique known as masking results in codes whose tanner graphs have girth 8 or larger experimental results show that codes constructed using the proposed construction perform well and have low error floors also presented in the paper is a reduced complexity iterative decoding scheme for qc ldpc codes based on the section wise cyclic structure of their parity check matrices the proposed decoding scheme is an improvement of an earlier proposed reduced complexity iterative decoding scheme

a two dimensional conservation laws scheme for compressible flows with moving boundaries the generalized riemann problem grp scheme for the hydrodynamic conservation laws is extended to a two dimensional moving boundary tracking mbt configuration aimed at treating time dependent compressible flows with moving impermeable boundary surfaces a strang type operator splitting is employed for the integration of the conservation laws the boundary motion is also split into cartesian components that are taken with the respective operator split integration phases the conservation laws in boundary cells are integrated by a finite volume scheme that accounts for changing mesh geometry cell volume and side area through which mass momentum and energy fluxes are taken the central feature of the scheme is the algorithms for evaluating the changing mesh geometry at boundary cells these algorithms are based on a decomposition rule for evaluating polygon intersection area which has been used extensively for rezoning in hydrocodes over the past decades the decomposition rule is combined with the cartesian splitting of the boundary motion producing algorithms for the integration of conservation laws in boundary cells that are both consistent and simple consistency is taken to mean that the scheme produces an exact solution in the case of a uniform motion of the fluid and the boundary common velocity an illustrative example of shock lifting of a light weight cylinder is presented

an accurate moving boundary formulation in cut cell methods a cut cell method for cartesian meshes to simulate viscous compressible flows with moving boundaries is presented we focus on eliminating unphysical oscillations occurring in cartesian grid methods extended to moving boundary problems in these methods cells either lie completely in the fluid or solid region or are intersected by the boundary for the latter cells the time dependent volume fraction lying in the fluid region can be so small that explicit time integration schemes become unstable and a special treatment of these cells is necessary when the boundary moves a fluid cell may become a cut cell or a solid cell may become a small cell at the next time level this causes an abrupt change in the discretization operator and a suddenly modified truncation error of the numerical scheme this temporally discontinuous alteration is shown to act like an unphysical source term which deteriorates the numerical solution i e it generates unphysical oscillations in the hydrodynamic forces exerted on the moving boundary we develop an accurate moving boundary formulation based on the varying discretization operators yielding a cut cell method which avoids these discontinuities results for canonical two and three dimensional test cases evidence the accuracy and robustness of the newly developed scheme

uep constructions of quasi cyclic low density parity check codes via masking in this paper the algebraic constructions of quasi cyclic low density parity check qc ldpc codes with the unequal error protection uep property are considered a criterion for constructing such codes via the masking technique is proposed based on which explicit conditions on the base parity check matrices and masking matrices to achieve uep are provided we also give three specific constructions of uep qc ldpc codes furthermore a sufficient condition to ensure strict uep is presented simulation results demonstrate the superiority of our constructed codes over time sharing schemes the constructed codes also have competitive error performance against randomly constructed equal error protection ldpc codes and irregular uep ldpc codes designed based on the degree distribution

a versatile sharp interface immersed boundary method for incompressible flows with complex boundaries a sharp interface immersed boundary method for simulating incompressible viscous flow past three dimensional immersed bodies is described the method employs a multi dimensional ghost cell methodology to satisfy the boundary conditions on the immersed boundary and the method is designed to handle highly complex three dimensional stationary moving and or deforming bodies the complex immersed surfaces are represented by grids consisting of unstructured triangular elements while the flow is computed on non uniform cartesian grids the paper describes the salient features of the methodology with special emphasis on the immersed boundary treatment for stationary and moving boundaries simulations of a number of canonical two and three dimensional flows are used to verify the accuracy and fidelity of the solver over a range of reynolds numbers flow past suddenly accelerated bodies are used to validate the solver for moving boundary problems finally two cases inspired from biology with highly complex three dimensional bodies are simulated in order to demonstrate the versatility of the method

combined immersed boundary finite difference methods for three dimensional complex flow simulations a second order accurate highly efficient method is developed for simulating unsteady three dimensional incompressible flows in complex geometries this is achieved by using boundary body forces that allow the imposition of the boundary conditions on a given surface not coinciding with the computational grid the governing equations therefore can be discretized and solved on a regular mesh thus retaining the advantages and the efficiency of the standard solution procedures two different forcings are tested showing that while the quality of the results is essentially the same in both cases the efficiency of the calculation strongly depends on the particular expression a major issue is the interpolation of the forcing over the grid that determines the accuracy of the scheme this ranges from zeroth order for the most commonly used interpolations up to second order for an ad hoc velocity interpolation the present scheme has been used to simulate several flows whose results have been validated by experiments and other results available in the literature finally in the last example we show the flow inside an ic piston cylinder assembly at high reynolds number to our knowledge this is the first example in which the immersed boundary technique is applied to a full three dimensional complex flow with moving boundaries and with a reynolds number high enough to require a subgrid scale turbulence model

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

approximations of the optimal importance density using gaussian particle flow importance sampling abstractrecently developed particle flow algorithms provide an alternative to importance sampling for drawing particles from a posterior distribution and a number of particle filters based on this principle have been proposed samples are drawn from the prior and then moved according to some dynamics over an interval of pseudo time such that their final values are distributed according to the desired posterior in practice implementing a particle flow sampler requires multiple layers of approximation with the result that the final samples do not in general have the correct posterior distribution in this article we consider using an approximate gaussian flow for sampling with a class of nonlinear gaussian models we use the particle flow within an importance sampler correcting for the discrepancy between the target and actual densities with importance weights we present a suitable numerical integration procedure for use with this flow and an accompanying step size control algorithm in a filtering co

a unified approach to the construction of binary and nonbinary quasi cyclic ldpc codes based on finite fields a unified approach for constructing binary and nonbinary quasi cyclic ldpc codes under a single framework is presented six classes of binary and nonbinary quasi cyclic ldpc codes are constructed based on primitive elements additive subgroups and cyclic subgroups of finite fields numerical results show that the codes constructed perform well over the awgn channel with iterative decoding

a representation of curved boundaries for the solution of the navier stokes equations on a staggered three dimensional cartesian grid a method is presented for representing curved boundaries for the solution of the navier stokes equations on a non uniform staggered three dimensional cartesian grid the approach involves truncating the cartesian cells at the boundary surface to create new cells which conform to the shape of the surface we discuss in some detail the problems unique to the development of a cut cell method on a staggered grid methods for calculating the fluxes through the boundary cell faces for representing pressure forces and for calculating the wall shear stress are derived and it is verified that the new scheme retains second order accuracy in space in addition a novel cell linking method is developed which overcomes problems associated with the creation of small cells while avoiding the complexities involved with other cell merging approaches techniques are presented for generating the geometric information required for the scheme based on the representation of the boundaries as quadric surfaces the new method is tested for flow through a channel placed oblique to the grid and flow past a cylinder at re 40 and is shown to give significant improvement over a staircase boundary formulation finally it is used to calculate unsteady flow past a hemispheric protuberance on a plate at a reynolds number of 800 good agreement is obtained with experimental results for this flow

quasi cyclic ldpc codes an algebraic construction rank analysis and codes on latin squares quasi cyclic ldpc codes are the most promising class of structured ldpc codes due to their ease of implementation and excellent performance over noisy channels when decoded with message passing algorithms as extensive simulation studies have shown in this paper an approach for constructing quasi cyclic ldpc codes based on latin squares over finite fields is presented by analyzing the parity check matrices of these codes combinatorial expressions for their ranks and dimensions are derived experimental results show that with iterative decoding algorithms the constructed codes perform very well over the awgn and the binary erasure channels