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

a discontinuous galerkin method for two temperature plasmas abstract we develop a formulation for the single fluid two temperature equations for simulating two species compressible non equilibrium plasma flows the divergence free condition of the magnetic field is enforced via the characteristic decomposition of an extended nine wave system the source terms are modified appropriately to improve energy and momentum conservation accuracy a spectral hp element algorithm is employed in the discretization combined with a discontinuous galerkin formulation for the advective and diffusive contributions the formulation is conservative and monotonicity is enforced by appropriately lowering the spectral order around discontinuities a new mhd flux introduced here is the mhd hllc harten lax van leer contact wave flux that preserves monotonicity and resolves contact discontinuities better exponential convergence is demonstrated for a magneto hydrostatic problem two tests are presented using the new mhd hllc flux also the differences between the single temperature and the two temperature models are presented for two dimensional plasma flows around bluff bodies

an efficient algorithm to find all small size stopping sets of low density parity check matrices in this work we introduce an efficient algorithm to find all stopping sets of size less than some threshold of a fixed low density parity check ldpc matrix the solution is inspired by the algorithm proposed by rosnes and ytrehus in 2005 to find an exhaustive list of all small size turbo stopping sets in a turbo code the efficiency of the proposed algorithm is demonstrated by several numerical examples for instance we have applied the algorithm to the well known 3 5 regular 155 64 tanner code and found all stopping sets of size at most 18 in about 1 min on a standard desktop computer also we have verified that the minimum stopping set size of the 4896 2474 ramanujan margulis code is indeed 24 and that the corresponding multiplicity is exactly 204 furthermore we have applied the algorithm to the ieee 802 16e ldpc codes and determined the minimum stopping set size and the corresponding multiplicity exactly for these codes finally as an application we present a greedy algorithm to find a small number of redundant parity checks to add to the original parity check matrix in order to remove all stopping sets in the corresponding tanner graph of size less than the minimum distance an extensive case study of the 155 64 tanner code illustrates the usefulness of the algorithm and we present a 110 times 155 redundant parity check matrix for this code with no stopping sets of size less than the minimum distance simulation results of iterative decoding on the binary erasure channel show performance improvements for low to medium erasure probabilities when this redundant parity check matrix is used for decoding

implicit technique for three dimensional turbulent magnetoaerodynamics a high resolution numerical procedure designed to simulate three dimensional nonideal magnetogasdynamic mgd phenomena on complex cone gurations is extended to enhance computational efe ciency and physical e delity alooselycoupledapproximatelyfactoredimplicitmethod isdevelopedtoovercometime stepsizelimitations of explicit methods a sub iteration strategy is included to recover up to second order time accuracy verie cation exercises covering wave propagation and diffusion phenomena are presented to demonstrate accuracy and characterize the efe ciency of the numerical procedure because the aerodynamic environment will exhibit relatively small electrical conductivities and large compensatory magnetic e elds a low magnetic reynolds number reae formulation and its solution procedure are described and verie ed by considering mgd control of a compressible laminar e at plate boundary layer at different interaction parameters a two equation k turbulence model with low reynolds number near wall terms is incorporated with additional expressions to reproduce the damping effect of the magnetic e eld the effect of a magnetic dipole on a supersonic turbulent e at plate boundary layer is examined an exploratory study of mgd control of e ow past a classic reentry vehicle cone guration demonstrates the capabilities of the numerical scheme

the generalized distributive law we discuss a general message passing algorithm which we call the generalized distributive law gdl the gdl is a synthesis of the work of many authors in information theory digital communications signal processing statistics and artificial intelligence it includes as special cases the baum welch algorithm the fast fourier transform fft on any finite abelian group the gallager tanner wiberg decoding algorithm viterbi s algorithm the bcjr algorithm pearl s belief propagation algorithm the shafer shenoy probability propagation algorithm and the turbo decoding algorithm although this algorithm is guaranteed to give exact answers only in certain cases the junction tree condition unfortunately not including the cases of gtw with cycles or turbo decoding there is much experimental evidence and a few theorems suggesting that it often works approximately even when it is not supposed to

normal boundary intersection a new method for generating the pareto surface in nonlinear multicriteria optimization problems this paper proposes an alternate method for finding several pareto optimal points for a general nonlinear multicriteria optimization problem such points collectively capture the trade off among the various conflicting objectives it is proved that this method is independent of the relative scales of the functions and is successful in producing an evenly distributed set of points in the pareto set given an evenly distributed set of parameters a property which the popular method of minimizing weighted combinations of objective functions lacks further this method can handle more than two objectives while retaining the computational efficiency of continuation type algorithms this is an improvement over continuation techniques for tracing the trade off curve since continuation strategies cannot easily be extended to handle more than two objectives

performance analysis of ldpc coded diversity combining on rayleigh fading channels with impulsive noise spatial diversity is an effective method to mitigate the effects of fading and when used in conjunction with low density parity check ldpc codes it can achieve excellent error correcting performance noise added at each branch of the diversity combiner is generally assumed to be additive white gaussian noise but there are many applications where the received signal is impaired by noise with a non gaussian distribution in this paper we derive the exact bit error probability of different linear combining techniques on rayleigh fading channels with impulsive noise which is modeled using symmetric alpha stable distributions the relationship for the signal to noise ratios of these linear combiners is derived and then different non linear detectors are presented a detector based on the bi parameter cauchy gaussian mixture model is used and shows near optimal performance with a significant reduction in complexity when compared with the optimal detector furthermore the threshold signal to noise ratio of ldpc codes for different combining techniques on these channels is derived using density evolution and an estimation of the waterfall performance of ldpc codes is derived that reduces the gap between simulated and asymptotic performance

high rate quantum low density parity check codes assisted by reliable qubits quantum error correction is an important building block for reliable quantum information processing a challenging hurdle in the theory of quantum error correction is that it is significantly more difficult to design error correcting codes with desirable properties for quantum information processing than for traditional digital communications and computation a typical obstacle to constructing a variety of strong quantum error correcting codes is the complicated restrictions imposed on the structure of a code recently promising solutions to this problem have been proposed in quantum information science where in principle any binary linear code can be turned into a quantum error correcting code by assuming a small number of reliable quantum bits this paper studies how best to take advantage of these latest ideas to construct desirable quantum error correcting codes of very high information rate our methods exploit structured high rate low density parity check codes available in the classical domain and provide quantum analogues that inherit their characteristic low decoding complexity and high error correction performance even at moderate code lengths our approach to designing high rate quantum error correcting codes also allows for making direct use of other major syndrome decoding methods for linear codes making it possible to deal with a situation where promising quantum analogues of low density parity check codes are difficult to find

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

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

group theoretic analysis of cayley graph based cycle gf 2 p codes using group theory we analyze cycle gf 2p codes that use cayley graphs as their associated graphs first we show that through row and column permutations the parity check matrix h can be put in a concatenation form of row permuted block diagonal matrices encoding utilizing this form can be performed in linear time and in parallel second we derive a rule to determine the nonzero entries of h and present determinate and semi determinate codes our simulations show that the determinate and semi determinate codes have better performance than codes with randomly generated nonzero entries for gf 16 and gf 64 and have similar performance for gf 256 the constructed determinate and semi determinate codes over gf 64 and gf 256 can outperform the binary irregular counterparts of the same block lengths one distinct advantage for determinate and semi determinate codes is that they greatly reduce the storage cost of h for decoding the results in this correspondence are appealing for the implementation of efficient encoders and decoders for this class of promising ldpc codes especially when the block length is large

efficient encoding of low density parity check codes low density parity check ldpc codes can be considered serious competitors to turbo codes in terms of performance and complexity and they are based on a similar philosophy constrained random code ensembles and iterative decoding algorithms we consider the encoding problem for ldpc codes more generally we consider the encoding problem for codes specified by sparse parity check matrices we show how to exploit the sparseness of the parity check matrix to obtain efficient encoders for the 3 6 regular ldpc code for example the complexity of encoding is essentially quadratic in the block length however we show that the associated coefficient can be made quite small so that encoding codes even of length n spl sime 100000 is still quite practical more importantly we show that optimized codes actually admit linear time encoding

on min norm and min max methods of multi objective optimization this paper examines pareto optimality of solutions to multi objective problems scalarized in the min norm compromise programming generalized goal programming or unrestricted min max formulations issues addressed include among others uniqueness in solution or objective space penalization for over achievement of goals min max reformulation of goal programming inferiority in tchebycheff norm minimization strength and weakness of weighted bound optimization quasi satisficing decision making just attaining or even over passing the goals trading off by modifying weights or goals non convex pareto frontier new general necessary and sufficient conditions for both pareto optimality and weak pareto optimality are presented various formulations are compared in theoretical performance with respect to the goal point location ideas for advanced goal programming and interactive decision making are introduced

expander codes using expander graphs we construct a new family of asymptotically good linear error correcting codes these codes have linear time sequential decoding algorithms and logarithmic time parallel decoding algorithms that use a linear number of processors we present both randomized and explicit constructions of these codes experimental results demonstrate the good performance of the randomly chosen codes

error rate estimation of low density parity check codes decoded by quantized soft decision iterative algorithms this paper describes a combinatorial approach to estimate the error rate performance of low density parity check ldpc codes decoded by quantized soft decision iterative decoding algorithms the method is based on efficient enumeration of input vectors with small distances to a reference vector whose elements are selected to be the most reliable values from the input alphabet several techniques including modified cycle enumeration and the efficient derivation of problematic inputs for finer quantizers from those of coarser ones are employed to reduce the complexity of the enumeration the error rate estimate is derived by testing the input vectors of small distances followed by estimating the contribution of larger distance vectors we demonstrate by a number of examples that the proposed method provides accurate estimates of error rate with computational complexity much lower than that of monte carlo simulations especially at the error floor region

an adaptive scalarization method in multiobjective optimization this paper presents a new method for the numerical solution of nonlinear multiobjective optimization problems with an arbitrary partial ordering in the objective space induced by a closed pointed convex cone this algorithm is based on the well known scalarization approach by pascoletti and serafini and adaptively controls the scalarization parameters using new sensitivity results the computed image points give a nearly equidistant approximation of the whole pareto surface the effectiveness of this new method is demonstrated with various test problems and an applied problem from medicine

non binary protograph based ldpc codes enumerators analysis and designs this paper provides a comprehensive analysis of nonbinary low density parity check ldpc codes built out of protographs we consider both random and constrained edge weight labeling and refer to the former as the unconstrained nonbinary protograph based ldpc codes u nbpb codes and to the latter as the constrained nonbinary protograph based ldpc codes c nbpb codes equipped with combinatorial definitions extended to the nonbinary domain ensemble enumerators of codewords trapping sets stopping sets and pseudocodewords are calculated the exact enumerators are presented in the finite length regime and the corresponding growth rates are calculated in the asymptotic regime an exit chart tool for computing the iterative decoding thresholds of protograph based ldpc codes is presented followed by several examples of finite length u nbpb and c nbpb codes with high performance throughout this paper we provide accompanying examples which demonstrate the advantage of nonbinary protograph based ldpc codes over their binary counterparts and over random constructions the results presented in this paper advance the analytical toolbox of nonbinary graph based codes

sumis near optimal soft in soft out mimo detection with low and fixed complexity the fundamental problem of interest here is soft input soft output multiple input multiple output mimo detection we propose a method referred to as subspace marginalization with interference suppression sumis that yields unprecedented performance at low and fixed deterministic complexity our method provides a well defined tradeoff between computational complexity and performance apart from an initial sorting step consisting of selecting channel matrix columns the algorithm involves no searching nor algorithmic branching hence the algorithm has a completely predictable run time and allows for a highly parallel implementation we numerically assess the performance of sumis in different practical settings full partial channel state information sequential iterative decoding and low high rate outer codes we also comment on how the sumis method performs in systems with a large number of transmit antennas

the stability of numerical boundary treatments for compact high order finite difference schemes the stability characteristics of various compact fourth and sixth order spatial operators are assessed with the theory of gustafsson kreiss and sundstrom g k s for the semidiscrete initial boundary value problem these results are generalized to the fully discrete case with a recently developed theory of kreiss and wu in all cases favorable comparisons are obtained between g k s theory eigenvalue determination and numerical simulation the conventional definition of stability then is sharpened to include only those spatial discretizations that are asymptotically stable bounded left half plane eigenvalues many of the higher order schemes that are g k s stable are not asymptotically stable a series of compact fourth and sixth order schemes that are both asymptotically and g k s stable for the scalar case are then developed

optimized compact difference based finite volume schemes for linear wave phenomena high order compact difference based finite volume schemes are developed analyzed and implemented for linear wave propagation phenomena with particular emphasis on computational electromagnetics in the time domain the formulation combines the primitive function approach with five point spatially sixth and fourth order methods optimization in the semi discrete case is achieved by minimizing dispersion and isotropy error the fully discrete scheme is examined by adopting the classical fourth order runge kutta technique stability bounds are established and the coefficients for the spatial discretization are readjusted for optimum performance the scheme is then formally extended to multiple dimensions consistent boundary conditions are presented for the reconstruction operator as well as flux specification several calculations in one and three dimensions confirm the properties of the method

constructing short length irregular ldpc codes with low error floor trapping sets tss are known to cause error floors in regular and irregular low density parity check ldpc codes by avoiding major error contributing tss during the code construction process codes with low error floors can effectively be built in it has been shown that tss labeled as w u are considered as being equivalent under the automorphism of the graph and are therefore contributing equally to the error floor however tss with the same label w u are not identical in general particularly for the case of irregular ldpc codes in this paper we introduce a parameter e that can identify the number of distinguishable cycles in the connected subgraph induced by an elementary trapping set further we propose a code construction algorithm namely the progressive edge growth approximate minimum cycle set extrinsic message degree peg acse method that aims to avoid small elementary trapping sets etss particularly detrimental etss we also develop theorems evaluating the minimum possible etss formed by peg construction algorithms in general we compare the characteristics of the codes built using the proposed method and those built using peg only or peg approximate minimum cycle extrinsic message degree peg ace methods results from simulations show that the codes constructed using the proposed peg acse method produce lower error rates particularly at the high signal to noise snr region compared with codes constructed using other peg based algorithms

design of regular 2 d sub c ldpc codes over gf q using their binary images in this paper a method to design regular 2 dc ldpc codes over gf q with both good waterfall and error floor properties is presented based on the algebraic properties of their binary image first the algebraic properties of rows of the parity check matrix h associated with a code are characterized and optimized to improve the waterfall then the algebraic properties of cycles and stopping sets associated with the underlying tanner graph are studied and linked to the global binary minimum distance of the code finally simulations are presented to illustrate the excellent performance of the designed codes

bounds on the size of parity check matrices for quasi cyclic low density parity check codes in this paper we investigate the cycle properties of quasi cyclic low density parity check qc ldpc codes using the sequence representation of a parity check matrix for a qc ldpc code we analyze a necessary and sufficient condition for a cycle of a given length to exist we then derive bounds which are necessary conditions for a qc ldpc code to have a given girth in terms of its parameters we also give a bound which is a sufficient condition for a qc ldpc code of a given girth to be constructed by a greedy algorithm the bounds derived here are applicable to any regular or irregular qc ldpc codes as well as they improve the existing bounds in many classes of regular ldpc codes

comparison of constructions of irregular gallager codes the low density parity check codes whose performance is closest to the shannon limit are gallager codes based on irregular graphs we compare alternative methods for constructing these graphs and present two results first we find a super poisson construction which gives a small improvement in empirical performance over a random construction second whereas gallager codes normally take n sup 2 time to encode we investigate constructions of regular and irregular gallager codes that allow more rapid encoding and have smaller memory requirements in the encoder we find that these fast encoding gallager codes have equally good performance

computing linear transformations with unreliable components we consider the problem of computing a binary linear transformation when all circuit components are unreliable two models of unreliable components are considered probabilistic errors and permanent errors we introduce the encoded technique that ensures that the error probability of the computation of the linear transformation is kept bounded below a small constant independent of the size of the linear transformation even when all logic gates in the computation are noisy by deriving a lower bound we show that in some cases the computational complexity of the encoded technique achieves the optimal scaling in error probability further we examine the gain in energy efficiency from the use of a voltage scaling scheme where gate energy is reduced by lowering the supply voltage we use a gate energy reliability model to show that tuning gate energy appropriately at different stages of the computation dynamic voltage scaling in conjunction with encoded can lead to orders of magnitude energy savings over the classical uncoded approach finally we also examine the problem of computing a linear transformation when noiseless decoders can be used providing upper and lower bounds to the problem

progressive transmission of images over fading channels using rate compatible ldpc codes in this paper we propose a combined source channel coding scheme for transmission of images over fading channels the proposed scheme employs rate compatible low density parity check codes along with embedded image coders such as jpeg2000 and set partitioning in hierarchical trees spiht the assignment of channel coding rates to source packets is performed by a fast trellis based algorithm we examine the performance of the proposed scheme over correlated and uncorrelated rayleigh flat fading channels with and without side information simulation results for the expected peak signal to noise ratio of reconstructed images which are within 1 db of the capacity upper bound over a wide range of channel signal to noise ratios show considerable improvement compared to existing results under similar conditions we also study the sensitivity of the proposed scheme in the presence of channel estimation error at the transmitter and demonstrate that under most conditions our scheme is more robust compared to existing schemes

high order numerical method for magnetohydrodynamic control of shock induced separation magnetic fields significantly affect the flow of ionized gases and may be exploited for the control of separation transition and turbulence the wave structure of ionized gas high speed flows under the influence of magnetic fields is more involved than the waves of ordinary gas dynamics and high resolution is required to accurately compute the complex wave interactions of such flows with discontinuities numerical solutions of the nonlinear ideal and viscous magnetohydrodynamic equations are obtained with a high order accurate shock capturing scheme the numerical method is tested for flows containing strong magnetohydrodynamic discontinuities and smooth flow features to ensure that it maintains high order accuracy for the smooth parts of the flow it preserves numerical stability and eliminates nonphysical features that result from the violation of the divergence free condition for the magnetic field problems with exact solutions such as the convection of smooth waves caused by magnetic fields are also solved numerically to validate the method the numerical method is applied to simulate separation control at the interaction region of an oblique shock with a laminar boundary layer under the influence of magnetic fields

an implicit scheme for nonideal magnetohydrodynamics a new implicit algorithm is developed for solving the time dependent nonideal magnetohydrodynamic equations it can also be used as an efficient relaxation scheme for steady state solutions the algorithm is a finite volume scheme that uses an approximate riemann solver for the hyperbolic fluxes and central differencing applied on nested control volumes for the parabolic fluxes that arise from the non ideal terms i e resistivity and viscosity in one dimension the scheme is second order accurate in space and time in two or three dimensions the accuracy is between first and second order for the class of problems considered the implicit formulation is stable for any size time step thus allowing efficient tracking of slower transients the implicit operator is inverted using a lower upper symmetric gauss seidel iteration results from several test cases are presented that show good agreement with analytical solutions and illustrate the advantages of the scheme

on finding bipartite graphs with a small number of short cycles and large girth the problem of finding bipartite tanner graphs with given degree sequences that have large girth and few short cycles is of great interest in many applications including construction of good low density parity check ldpc codes in this paper we prove that for given integers alpha beta and gamma and degree sequences pi and pi the problem of determining whether there exists a simple bipartite graph with degree sequences pi pi that has at most alpha beta and gamma cycles of length four six and eight respectively is np complete this is proved by a two step polynomial time reduction from the 3 partition problem on the other hand using connections to linear hypergraphs we prove that given the degree sequence pi a polynomial time algorithm can be devised to determine whether there exists a bipartite graph whose degree sequence on one side of the bipartition is pi and has a girth of at least six in addition to these complexity results we devise a quasi polynomial time algorithm that can construct a bipartite graph with given irregular degree sequences and a girth that increases logarithmically with the size of the graph compared to the well known progressive edge growth peg algorithm the proposed method in some cases results in tanner graphs with larger girth particularly for scenarios where the degree sequences of the graph are strictly enforced

a multi level non linear multi objective decision making under fuzziness this paper studies a three level non linear multi objective decision making tln modm problem with linear or non linear constraints and in which the objective function at every level are non linear functions which are to be maximized this paper makes an extension work of abo sinna j operat res soc india opsearch 38 5 2001 484 495 which deal with a bi level non linear multi objective decision making problem under fuzziness the three level programming tlp problem whether from the stand point of the three planner stackelberg behavior or from the interactive organizational behavior is a very practical problem and encountered frequently in actual practice this paper proposes a three planner multi objective decision making model and solution method for solving this problem this method uses the concepts of tolerance membership function and multi objective optimization at each level to develop a fuzzy max min decision model for generating pareto optimal satisfactory solution for tln modm problem the first level decision maker fldm specifies his her objective functions and decisions with possible tolerances which are described by membership functions of fuzzy set theory then the second level decision maker sldm specifies his her objective functions and decisions in the view of the fldm with possible tolerances which are described by membership functions of fuzzy set theory finally the third level decision maker tldm uses the preference information for the fldm and sldm to solves his her problem subject to the two upper level decision makers restrictions an illustrative numerical example is given to demonstrate the obtained results

optimal erasure selection of m ary pam signaling for errors and erasures decoding algorithms erasure selection for errors and erasures decoding algorithms is investigated and analyzed where declaring erasures provides additional gain for hard decision decoding to derive an analytical criterion for optimal erasure selection we first investigate erasure effects on decoding performance by which a metric function for erasure selection is derived from the derived metric a suboptimal threshold is defined which can be used for errors and erasures decoding of large code distance channel codes moreover application to m ary m 2 pam constellation is also described for verification of the proposed erasure threshold simulation results with popular channel codes are included

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

minimum distance bounds by graph analysis the parity check matrix of a linear code is used to define a bipartite code constraint tanner graph in which bit nodes are connected to parity check nodes the connectivity properties of this graph are analyzed using both local connectivity and the eigenvalues of the associated adjacency matrix a simple lower bound on the minimum distance of the code is expressed in terms of the two largest eigenvalues for a more powerful bound local properties of the subgraph corresponding to a minimum weight word in the code are used to create an optimization problem whose solution is a lower bound on the code s minimum distance linear programming gives one bound the technique is illustrated by applying it to sparse block codes with parameters 7 3 4 and 42 23 6

reliability based joint detection decoding algorithm for nonbinary ldpc coded modulation systems this paper studies an extension and improvement of the joint detection decoding algorithm for nonbinary ldpc coded modulation systems the iterative joint detection decoding ijdd algorithm in 1 combines nonbinary ldpc decoding with signal detection based on the hard message passing strategy resulting in significantly reduced decoding complexity however it applies only to majority logic decodable nonbinary ldpc codes with high column weight for nonbinary ldpc codes with low column weight a noticeable performance loss will be incurred to handle this problem we propose a reliability based iterative joint detection decoding also termed improved ijdd algorithm which combines the accumulated reliability of symbols based on the one step majority logic decoding mlgd algorithm and a chase like local list decoding algorithm simulation results show that the improved ijdd algorithm outperforms the ijdd algorithm by about 0 3 db using nonbinary ldpc codes with high column weight and by about 3 db using nonbinary ldpc codes with low column weight d v 4 while maintaining the low complexity of decoding compared to the fft qspa the proposed algorithm has a performance degradation of 0 5 db in the high column weight regime and about 1 db in the low column weight regime

systematic design of low density parity check code ensembles for binary erasure channels we propose a systematic method to design irregular low density parity check ldpc codes for binary erasure channels bec compared to the existing methods which are based on the application of asymptotic analysis tools such as density evolution or extrinsic information transfer exit charts in an optimization process the proposed method is much simpler and faster through a number of examples we demonstrate that the codes designed by the proposed method perform very closely to the best codes designed by optimization an important property of the proposed designs is the flexibility to select the number of constituent variable node degrees p the proposed designs include existing systematic designs as a special case with p n 1 where n is the maximum variable node degree compared to the existing systematic designs for a given rate and a given 0 the designed ensembles can have a threshold in neighborhood of the capacity upper bound with smaller values of p and n they can also achieve the capacity of the bec as n and correspondingly p and the maximum check node degree tend to infinity

multiobjective bilevel optimization in this work nonlinear non convex multiobjective bilevel optimization problems are discussed using an optimistic approach it is shown that the set of feasible points of the upper level function the so called induced set can be expressed as the set of minimal solutions of a multiobjective optimization problem this artificial problem is solved by using a scalarization approach by pascoletti and serafini combined with an adaptive parameter control based on sensitivity results for this problem the bilevel optimization problem is then solved by an iterative process using again sensitivity theorems for exploring the induced set and the whole efficient set is approximated for the case of bicriteria optimization problems on both levels and for a one dimensional upper level variable an algorithm is presented for the first time and applied to two problems a theoretical example and a problem arising in applications

regular and irregular progressive edge growth tanner graphs we propose a general method for constructing tanner graphs having a large girth by establishing edges or connections between symbol and check nodes in an edge by edge manner called progressive edge growth peg algorithm lower bounds on the girth of peg tanner graphs and on the minimum distance of the resulting low density parity check ldpc codes are derived in terms of parameters of the graphs simple variations of the peg algorithm can also be applied to generate linear time encodeable ldpc codes regular and irregular ldpc codes using peg tanner graphs and allowing symbol nodes to take values over gf q q 2 are investigated simulation results show that the peg algorithm is a powerful algorithm to generate good short block length ldpc codes

stochastic multiobjective problems with complementarity constraints and applications in healthcare management abstract we consider a class of stochastic multiobjective problems with complementarity constraints smopccs in this paper we derive the first order optimality conditions including the clarke mordukhovich strong type stationarity in the pareto sense for the smopcc since these first order optimality systems involve some unknown index sets we reformulate them as nonlinear equations with simple constraints then we introduce an asymptotic method to solve these constrained equations furthermore we apply this methodology results to a patient allocation problem in healthcare management

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

correctness of local probability propagation in graphical models with loops graphical models such as bayesian networks and markov networks represent joint distributions over a set of variables by means of a graph when the graph is singly connected local propagation rules of the sort proposed by pearl 1988 are guaranteed to converge to the correct posterior probabilities recently a number of researchers have empirically demonstrated good performance of these same local propagation schemes on graphs with loops but a theoretical understanding of this performance has yet to be achieved for graphical models with a single loop we derive an analytical relationship between the probabilities computed using local propagation and the correct marginals using this relationship we show a category of graphical models with loops for which local propagation gives rise to provably optimal maximum a posteriori assignments although the computed marginals will be incorrect we also show how nodes can use local information in the messages they receive in order to correct their computed marginals we discuss how these results can be extended to graphical models with multiple loops and show simulation results suggesting that some properties of propagation on single loop graphs may hold for a larger class of graphs specifically we discuss the implication of our results for understanding a class of recently proposed error correcting codes known as turbo codes

ldpc decoding scheduling for faster convergence and lower error floor this paper presents a maximum mutual information increase m 2 i 2 based algorithm that can be used to arrange low density parity check ldpc decoding schedules for faster convergence where the increase is used to guide the arrangement of the fixed decoding schedule the predicted mutual information for the messages to be updated is used in the calculation of the increase by looking ahead for several decoding stages a high order prediction can be realized which can then be used to devise a schedule with an even faster convergence for a single received frame different decoding results can be obtained using different schedules and hence schedule diversity that lowers the error floor resultant from the dominant trapping sets is proposed by adopting the m 2 i 2 based schedule together with the schedule diversity both the convergence speed in the waterfall region and the error rate in the floor region can be improved

linear time encodable and decodable error correcting codes we present a new class of asymptotically good linear error correcting codes these codes can be both encoded and decoded in linear time they can also be encoded by logarithmic depth circuits of linear size and decoded by logarithmic depth circuits of size o nlogn we present both randomized and explicit constructions of these codes

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

shock capturing approach and nonevolutionary solutions in magnetohydrodynamics shock capturing methods have become an effective tool for the solution of hyperbolic partial differential equations both upwind and symmetric tvd schemes in the framework of the shock capturing approach are thoroughly investigated and applied with great success to a number of complicated multidimensional gasdynamic problems the extension of these schemes to magnetohydrodynamic mhd equations is not a simple task first the exact solution of the mhd riemann problem is too multivariant to be used in regular calculations on the other hand the extensions of roe s approximate riemann problem solvers for mhd equations in general case are nonunique and need further investigation that is why some simplified approaches should be constructed in this work the second order of accuracy in time and space high resolution lax friedrichs type scheme is suggested that gives a drastic simplification of the numerical algorithm comparing to the precise characteristic splitting of jacobian matrices the necessity is shown to solve the full set of mhd equations for modeling of multishocked flows even when the problem is axisymmetric to obtain evolutionary solutions for the numerical example the mhd riemann problem is used with the initial data consisting of two constant states lying to the right and to the left from the centerline of the computational domain if the problem is solved as purely coplanar a slow compound wave appears in the self similar solution obtained by any shock capturing scheme if the full set of mhd equations is used and a small uniform tangential disturbance is added to the magnetic field vector a rotational jump splits from the compound wave and it degrades into a slow shock the reconstruction process of the nonevolutionary compound wave into evolutionary shocks is investigated presented results should be taken into account in the development of shock capturing methods for mhd flows

searching for binary and nonbinary block and convolutional ldpc codes a unified approach to search for and optimize codes determined by their sparse parity check matrices is presented replacing the nonzero elements of a binary parity check matrix the base or parent matrix either by circulants or by companion matrices of elements from a finite field gf 2 m we obtain quasi cyclic low density parity check ldpc block codes and binary images of nonbinary ldpc block codes respectively by substituting monomials of a formal variable d we obtain the polynomial description of an ldpc convolutional code a set of performance measures applicable to different classes of ldpc codes is considered and a greedy algorithm for code performance optimization is presented the heart of the new optimization algorithm is a fast procedure for searching for ldpc codes with large girth of their tanner graphs for a few classes of ldpc codes examples of codes combining good error correcting performance with compact representation are obtained in particular we present optimized convolutional ldpc codes and conclude that the ldpc block codes are still superior to their convolutional counterparts if both decoding complexity and coding delay are considered moreover a specific channel model can easily be embedded into the optimization loop thereby the code can be optimized for a specific channel the efficiency of such an optimization is demonstrated via an example of faster than nyquist ftn signaling using ldpc codes the ftn strategy combined with a rate r 1 2 ldpc code of length 64 800 optimized for effective data rate r 3 4 gains more than 0 5 db compared with the standard ldpc codes of the same rate and length the obtained gain corresponds to transmission at the capacity of the binary input additive white gaussian noise channel in most numerical examples we consider codes with bidiagonal structure of the parity check matrix this restriction preserves low encoding complexity and allows fair comparison with codes selected for communication standards

an algorithm for counting short cycles in bipartite graphs let g u spl cup w e be a bipartite graph with disjoint vertex sets u and w edge set e and girth g this correspondence presents an algorithm for counting the number of cycles of length g g 2 and g 4 incident upon every vertex in u spl cup w the proposed cycle counting algorithm consists of integer matrix operations and its complexity grows as o gn sup 3 where n max u w

pseudo wave decomposition high order method for magnetogasdynamics a new characteristics based decomposition of the ideal magnetogasdynamic equations is derived this formulation consists in representing the temporal variation of the physical quantities pressure velocity magnetic field and entropy as a linear combination of the generic advective terms corresponding to each wave type occurring in the medium the flux terms can then be handled with existing high order upwind dispersion relation preserving schemes those being specifically chosen in our case to increase numerical accuracy and improve stability another feature of the new formulation of the non ideal governing equations is that the boundary conditions are exactly satisfied at the frontiers of the computational domain the accuracy of the method is assessed by comparison between numerical and exact solutions good agreement is obtained between computed and exact solutions

an algorithm based on particle swarm optimization for multiobjective bilevel linear problems improved mopso for multiobjective at the upper level bilevel linear problems a hybrid scheme for the selection of the global best particles is proposed an adaptive mutation is also introduced the incorporation of these mechanisms led to significantly better results this paper presents an improved multiple objective particle swarm optimization mopso algorithm to solve bilevel linear programming problems with multiple objective functions at the upper level the algorithm aims to produce a good approximation of the entire pareto front of the problem we have previously designed a mopso algorithm for the same class of problems in which several techniques for the global best selection were tested including a new one the algorithm revealed a good convergence towards the pareto front but the diversity of the solutions was a drawback the algorithm we propose herein uses a hybrid strategy for the global best selection and an adaptive mutation operator the incorporation of these mechanisms led to an improved algorithm which also showed better overall performance than considering alternative options usually employed in mopso algorithms the algorithm and computational results are presented

design of low rate irregular ldpc codes using trellis search a simple design method using trellis search is proposed for good low density parity check ldpc codes with relatively low code rates by applying a trellis search technique to the design of a pre assigned part of the parity check matrix that allows a simple encoding we improve the distribution of cycles formed by the entries contained in the parity check part of the parity check matrix in addition we extend the proposed algorithm to a class of structured ldpc codes which have been recently preferred in many practical applications simulation results show that the codes designed by the proposed method outperform those constructed by conventionally used greedy design algorithms

design of efficiently encodable moderate length high rate irregular ldpc codes this paper presents a new class of irregular low density parity check ldpc codes of moderate length 10 sup 3 spl les n spl les 10 sup 4 and high rate r spl ges 3 4 codes in this class admit low complexity encoding and have lower error rate floors than other irregular ldpc code design approaches it is also shown that this class of ldpc codes is equivalent to a class of systematic serial turbo codes and is an extension of irregular repeat accumulate codes a code design algorithm based on the combination of density evolution and differential evolution optimization with a modified cost function is presented moderate length high rate codes with no error rate floors down to a bit error rate of 10 sup 9 are presented although our focus is on moderate length high rate codes the proposed coding scheme is applicable to irregular ldpc codes with other lengths and rates

finding the exhaustive list of small fully absorbing sets and designing the corresponding low error floor decoder this work provides an efficient exhaustive search algorithm for finding all small fully absorbing sets fass of any arbitrary low density parity check ldpc code the proposed algorithm is based on the branch bound principle for solving np complete problems in particular given any ldpc code the problem of finding all fass of size less than t is formulated as an integer programming problem for which a new branch bound algorithm is devised with new node selection and tree trimming mechanisms the resulting algorithm is capable of finding all fass of size 7 for ldpc codes of length 1000 when limiting the fass of interest to those with the number of violated parity check nodes 3 the proposed algorithm is capable of finding all such fass of size 14 for ldpc codes of lengths 1000 the resulting exhaustive list of small fass is then used to devise a new efficient post processing low error floor ldpc decoder the numerical results show that by exploiting the exhaustive list of small fass the proposed post processing decoder can significantly lower the error floor performance of a given ldpc code for various example codes of length 3000 the proposed post processing decoder lowers the error floor by a couple of orders of magnitude when compared to the standard belief propagation decoder and by an order of magnitude when compared to other existing low error floor decoders

higher order solution procedure for three dimensional nonideal magnetogasdynamics a high resolution scheme developed for use in multidisciplinary applications is applied to solve the equations governingthethree dimensionale owofanonidealcompressibleconductinge uidinamagnetice eld both4th order and 6th order spatially implicit schemes are considered in conjunction with up to 10th order e lters the fourthorderclassicalrunge kuttaschemeisemployedfortimeintegration theaccuracyandversatility ofthealgorithm and the accompanying code are explored by solving a wide variety of problems discretized with uniform as well as curvilinear grids with particular emphasis on the unique physical phenomena arising in conducting e uids these

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

low density parity check codes from transversal designs with improved stopping set distributions this paper examines the construction of low density parity check ldpc codes from transversal designs based on sets of mutually orthogonal latin squares mols by transferring the concept of configurations in combinatorial designs to the level of latin squares we thoroughly investigate the occurrence and avoidance of stopping sets for the arising codes stopping sets are known to determine the decoding performance over the binary erasure channel and should be avoided for small sizes based on large sets of simple structured mols we derive powerful constraints for the choice of suitable subsets leading to improved stopping set distributions for the corresponding codes we focus on ldpc codes with column weight 4 but the results are also applicable for the construction of codes with higher column weights finally we show that a subclass of the presented codes has quasi cyclic structure which allows low complexity encoding

efficient algorithm for finding dominant trapping sets of ldpc codes this paper presents an efficient algorithm for finding the dominant trapping sets of a low density parity check ldpc code the algorithm can be used to estimate the error floor of ldpc codes or as a tool to design ldpc codes with low error floors for regular codes the algorithm is initiated with a set of short cycles as the input for irregular codes in addition to short cycles variable nodes with low degree and cycles with low approximate cycle extrinsic message degree ace are also used as the initial inputs the initial inputs are then expanded recursively to dominant trapping sets of increasing size at the core of the algorithm lies the analysis of the graphical structure of dominant trapping sets and the relationship of such structures to short cycles low degree variable nodes and cycles with low ace the algorithm is universal in the sense that it can be used for an arbitrary graph and that it can be tailored to find a variety of graphical objects such as absorbing sets and zyablov pinsker trapping sets known to dominate the performance of ldpc codes in the error floor region over different channels and for different iterative decoding algorithms simulation results on several ldpc codes demonstrate the accuracy and efficiency of the proposed algorithm in particular the algorithm is significantly faster than the existing search algorithms for dominant trapping sets

improved low density parity check codes using irregular graphs we construct new families of error correcting codes based on gallager s 1973 low density parity check codes we improve on gallager s results by introducing irregular parity check matrices and a new rigorous analysis of hard decision decoding of these codes we also provide efficient methods for finding good irregular structures for such decoding algorithms our rigorous analysis based on martingales our methodology for constructing good irregular codes and the demonstration that irregular structure improves performance constitute key points of our contribution we also consider irregular codes under belief propagation we report the results of experiments testing the efficacy of irregular codes on both binary symmetric and gaussian channels for example using belief propagation for rate 1 4 codes on 16000 bits over a binary symmetric channel previous low density parity check codes can correct up to approximately 16 errors while our codes correct over 17 in some cases our results come very close to reported results for turbo codes suggesting that variations of irregular low density parity check codes may be able to match or beat turbo code performance