sharp sets of permutations abstract a set of permutations is sharp if its cardinality is the product of the distinct non zero hamming distances between pairs of permutations in the set we give a number of new results and constructions for sharp sets and groups and for the more special geometric sets and groups using a mixture of algebraic and combinatorial techniques

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

codes for iterative decoding from partial geometries this paper develops codes suitable for iterative decoding using the sum product algorithm by considering a large class of combinatorial structures known as partial geometries we are able to define classes of low density parity check ldpc codes which include several previously known families of codes as special cases the existing range of algebraic ldpc codes is limited so the new families of codes obtained by generalizing to partial geometries significantly increase the range of choice of available code lengths and rates we derive bounds on minimum distance rank and girth for all the codes from partial geometries and present constructions and performance results for the classes of partial geometries which have not previously been proposed for use with iterative decoding we show that these new codes can achieve improved error correction performance over randomly constructed ldpc codes and in some cases achieve this with a significant decrease in decoding complexity

rate compatible puncturing of low density parity check codes in this correspondence we consider puncturing of low density parity check ldpc codes for additive white gaussian noise awgn channels we show that good puncturing patterns exist and that the puncturing can be performed in a rate compatible fashion furthermore rate compatible puncturing results in a small loss of performance with respect to threshold namely the punctured code is good in terms of threshold across a range of rates when compared with the optimal codes for each rate this allows one to implement a single mother encoder and decoder that is good across a wide range of rates

optical orthogonal codes with unequal auto and cross correlation constraints an optical orthogonal code ooc is a collection of binary sequences with good auto and cross correlation properties they were defined by salehi and others as a means of obtaining code division multiple access on optical networks up to now all work on oocs have assumed that the constraint placed on the autocorrelation and that placed on the cross correlation are the same we consider codes for which the two constraints are not equal specifically we develop bounds on the size of such oocs and demonstrate constriction techniques for building them the results demonstrate that a significant increase in the code size is possible by letting the autocorrelation constraint exceed the cross correlation constraint these results suggest that for a given performance requirement the optimal ooc may be one with unequal constraints this paper also views oocs with unequal auto and cross correlation constraints as constant weight unequal error protection uep codes with two levels of protection the bounds derived are interpreted from this viewpoint

exploiting coding theory for classification we propose a multiclass to binary decomposition strategy founded on coding theory we use low density parity check codes a very effective family of binary block codes exploiting the algebraic properties of the code we handle both coding and decoding two decoding rules are proposed that provide many advantages over known strategies several experiments are performed that show significant performance improvements a powerful strategy for the classification of multiple classes is to create a classifier ensemble that decomposes the polychotomy into several dichotomies the central issue when designing a multiclass to binary decomposition scheme is the definition of both the coding matrix and the decoding algorithm in this study we propose a new classification system based on low density parity check codes which is a very effective class of binary block codes the main idea is to exploit the algebraic properties of the codes to generate the codewords for the coding matrix and to define two decoding approaches which allow us to detect and recover possible errors or rejects produced by the dichotomizers experiments based on benchmark datasets demonstrated that the proposed approach provides a statistically significant improvement in terms of the classification performance compared with state of the art decomposition strategies

decay estimates of solutions for the equations of motion of compressible viscous and heat conductive gases in an exterior domain in ℝ3 we consider the equations of motion of compressible viscous and heat conductive gases in an exterior domain in 3 we give the l q l p estimates for solutions to the linearized equations and show an optimal decay estimate for solutions to the nonlinear problem

new constructions of quasi cyclic ldpc codes based on special classes of bibd s for the awgn and binary erasure channels this paper presents new methods for efficiently constructing encodable quasi cyclic low density parity check ldpc codes based on special balanced incomplete block designs bibds codes constructed perform well over both the additive white gaussian noise awgn and binary erasure channels with iterative decoding

codes and designs related to lifted mrd codes lifted maximum rank distance mrd codes which are constant dimension codes are considered it is shown that a lifted mrd code can be represented in such a way that it forms a block design known as a transversal design a slightly different representation of this design makes it similar to a q analog of a transversal design the structure of these designs is used to obtain upper bounds on the sizes of constant dimension codes which contain a lifted mrd code codes that attain these bounds are constructed these codes are the largest known constant dimension codes for the given parameters these transversal designs can also be used to derive a new family of linear codes in the hamming space bounds on the minimum distance and the dimension of such codes are given

on global existence energy decay and blow up criteria for the hall mhd system in this paper we obtain global existence and energy decay for 3d hall magnetohydrodynamics hall mhd system with u and b besides the classical energy method and besov space techniques the interpolating inequalities are crucial in the proof of decay estimates then two osgood type blow up criteria are established our results improve the corresponding theorems in 3 and 4 in addition we establish two beale kato majda blow up criterion for the generalized version of hall mhd with u and b 1

optical orthogonal codes new bounds and an optimal construction a technique for constructing optimal oocs optical orthogonal codes is presented it provides the only known family of optimal with respect to family size oocs having lambda 2 the parameters n omega lambda are respectively p sup 2m 1 p sup m 1 2 where p is any prime and the family size is p sup m 2 three distinct upper bounds on the size of an ooc are presented that for many values of the parameter set n omega lambda improve upon the tightest previously known bound

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 new construction of structured binary regular ldpc codes based on steiner systems with parameter t 2 this paper presents a novel method for constructing structured regular low density parity check ldpc codes based on a special type of combinatorial designs known as steiner systems this code design approach can be considered as a generalization of the well known method which uses the point block incidence matrix of a steiner 2 design for the code construction though the given method can be applied on any steiner system s t k v in this paper we focus only on steiner systems with t 3 furthermore we show that not only a steiner system x b itself but also its residual design with respect to an arbitrary point x x can be employed for code construction we also present a technique for constructing binary and non binary qc ldpc codes from steiner systems the tanner graph of the constructed codes is free of 4 cycles and hence the codes have girth at least six simulation results show that the so constructed codes perform well over the awgn channel with iterative message passing decoding

the beale kato majda criterion for the 3d magneto hydrodynamics equations we study the blow up criterion of smooth solutions to the 3d mhd equations by means of the littlewood paley decomposition we prove a beale kato majda type blow up criterion of smooth solutions via the vorticity of velocity only namely sup j in mathbb z int 0 t delta j nabla times u infty dt where j is the frequency localization operator in the littlewood paley decomposition

efficient erasure correcting codes we introduce a simple erasure recovery algorithm for codes derived from cascades of sparse bipartite graphs and analyze the algorithm by analyzing a corresponding discrete time random process as a result we obtain a simple criterion involving the fractions of nodes of different degrees on both sides of the graph which is necessary and sufficient for the decoding process to finish successfully with high probability by carefully designing these graphs we can construct for any given rate r and any given real number spl epsiv a family of linear codes of rate r which can be encoded in time proportional to ln 1 spl epsiv times their block length n furthermore a codeword can be recovered with high probability from a portion of its entries of length 1 spl epsiv rn or more the recovery algorithm also runs in time proportional to n ln 1 spl epsiv our algorithms have been implemented and work well in practice various implementation issues are discussed

global existence and temporal decay for the 3d compressible hall magnetohydrodynamic system abstract in this paper we are concerned with the 3d compressible hall magnetohydrodynamic system in the whole space we prove the global existence and temporal decay rates of the solutions to the system when the initial data are close to a stable equilibrium state by using a pure energy method

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

construction of low density parity check codes based on balanced incomplete block designs this correspondence presents a method for constructing structured regular low density parity check ldpc codes based on a special type of combinatoric designs known as balance incomplete block designs codes constructed by this method have girths at least 6 and they perform well with iterative decoding furthermore several classes of these codes are quasi cyclic and hence their encoding can be implemented with simple feedback shift registers

existence theorem and blow up criterion of the strong solutions to the two fluid mhd equation in r3 abstract we first give the local well posedness of strong solutions to the cauchy problem of the 3d two fluid mhd equations and then study the blow up criterion of the strong solutions by means of the fourier frequency localization and bony s paraproduct decomposition it is proved that the strong solution u b can be extended after t t if either u l t q b p 0 with 2 q 3 p 1 and b l t 1 b 0 or j l t q b p 0 with 2 q 3 p 2 where t u denotes the vorticity of the velocity and j b stands for the current density

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

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

codes on finite geometries new algebraic methods for constructing codes based on hyperplanes of two different dimensions in finite geometries are presented the new construction methods result in a class of multistep majority logic decodable codes and three classes of low density parity check ldpc codes decoding methods for the class of majority logic decodable codes and a class of codes that perform well with iterative decoding in spite of having many cycles of length 4 in their tanner graphs are presented most of the codes constructed can be either put in cyclic or quasi cyclic form and hence their encoding can be implemented with linear shift registers

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

on characterizations of the class pspace poly abstract we present several characterizations of the class pspace poly these characterizations are given in terms of pspace complete problems certain algebraic closure operations vectorial straight line programs and kolmogorov complexity to end we characterize the problems having an exponential lower bound on their nonuniform complexity measured by vectorial straight line programs

on small generators abstract yap 1983 shows that each set having small generators is in the class np poly which was introduced by karp and lipton 1980 we show here that the converse is also true i e each set in np poly has small generators this settles a question left open by yap 1983 further an argument by meyer stated in berman and hartmanis 1977 is generalized to show that a set has small generators if and only if for some sparse set s a np s

on the temporal decay for the hall magnetohydrodynamic equations abstract we establish temporal decay estimates for weak solutions to the hall magnetohydrodynamic equations with these estimates in hand we obtain algebraic time decay for higher order sobolev norms of small initial data solutions

on the regularity of weak solutions to the magnetohydrodynamic equations abstract in this paper we study the regularity of weak solution to the incompressible magnetohydrodynamic equations we obtain some sufficient conditions for regularity of weak solutions to the magnetohydrodynamic equations which is similar to that of incompressible navier stokes equations moreover our results demonstrate that the velocity field of the fluid plays a more dominant role than the magnetic field does on the regularity of solution to the magneto hydrodynamic equations

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

on the well posedness of the ideal mhd equations in the triebel lizorkin spaces in this paper we prove the local well posedness for the ideal mhd equations in the triebel lizorkin spaces and obtain a blow up criterion of smooth solutions specifically we fill a gap in a step of the proof of the local well posedness part for the incompressible euler equation in chae comm pure appl math 55 654 678 2002

cyclic and quasi cyclic ldpc codes on constrained parity check matrices and their trapping sets this paper is concerned with construction and structural analysis of both cyclic and quasi cyclic codes particularly low density parity check ldpc codes it consists of three parts the first part shows that a cyclic code given by a parity check matrix in circulant form can be decomposed into descendant cyclic and quasi cyclic codes of various lengths and rates some fundamental structural properties of these descendant codes are developed including the characterization of the roots of the generator polynomial of a cyclic descendant code the second part of the paper shows that cyclic and quasi cyclic descendant ldpc codes can be derived from cyclic finite geometry ldpc codes using the results developed in the first part of the paper this enlarges the repertoire of cyclic ldpc codes the third part of the paper analyzes the trapping set structure of regular ldpc codes whose parity check matrices satisfy a certain constraint on their rows and columns several classes of finite geometry and finite field cyclic and quasi cyclic ldpc codes with large minimum distances are shown to have no harmful trapping sets of size smaller than their minimum distances consequently their error floor performances are dominated by their minimum distances

logarithmic advice classes abstract karp and lipton 1980 introduced the notion of nonuniform complexity classes where a certain amount of additional information the advice is given for free the advice only depends on the length of the input karp and lipton initiated the study of classes with either logarithmic or polynomial advice however later yap 1983 schoning 1984 balcazar 1987 and ko and schoning 1985 concentrated on the study of classes of the form c poly where c is p np or pspace and poly denotes a polynomial size advice this paper considers classes of the form c log as a main result it is shown that in the context of an np log computation log bounded advice is equivalent to a sparse oracle in np in contrast it has been shown that a poly bounded advice to an arbitrary sparse oracle set furthermore a general theorem is presented that generalizes karp and lipton s round robin tournament method

beat noise compensation in ocdma systems using soft decoding based fec in this paper we study forward error correction fec under beat noise assumption in the context of incoherent optical code division multiple access ocdma systems due to the use of unipolar codes multiple access interference mai amount and thus beatings between different user contributions known as beat noise constitute important limitations in particular for high data rates in order to compensate for these two major limitations we propose a solution using fec based on a soft decoding algorithm for this purpose we analyze the ocdma received signal distribution and establish a new model based on a mixture of chi square distributions valuable for any ocdma code parameters and any source coherence time values from this model we establish the error probability analytical expression under beat noise assumption and determine the reliability parameters required for the fec soft decoder initialization to illustrate the performance we use low density parity check ldpc codes and show that the ldpc adapted decoder is highly efficient in reducing beat noise and mai for incoherent ocdma systems even when beat noise has a severe impact in addition we point out that this solution permits increasing data rates or number of active users

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

optimal 2 d n times m 3 2 1 optical orthogonal codes optical orthogonal codes are commonly used as signature codes for optical code division multiple access systems so far research on 2 d optical orthogonal codes has mainly concentrated on the same autocorrelation and cross correlation constraints in this paper we are concerned about optimal 2 d optical orthogonal codes with the autocorrelation a and the cross correlation 1 some combinatorial constructions for 2 d n m k a 1 optical orthogonal codes are presented when k 3 and a 2 the exact number of codewords of an optimal 2 d n m 3 2 1 optical orthogonal code is determined for any positive integers n 0 1 3 6 9 10 mod 12 and m 2 mod 4

new combinatorial construction techniques for low density parity check codes and systematic repeat accumulate codes this paper presents several new construction techniques for low density parity check ldpc and systematic repeat accumulate ra codes based on specific classes of combinatorial designs the improved code design focuses on high rate structured codes with constant column weights 3 and higher the proposed codes are efficiently encodable and exhibit good structural properties experimental results on decoding performance with the sum product algorithm show that the novel codes offer substantial practical application potential for instance in high speed applications in magnetic recording and optical communications channels

on algebraic construction of gallager and circulant low density parity check codes this correspondence presents three algebraic methods for constructing low density parity check ldpc codes these methods are based on the structural properties of finite geometries the first method gives a class of gallager codes and a class of complementary gallager codes the second method results in two classes of circulant ldpc codes one in cyclic form and the other in quasi cyclic form the third method is a two step hybrid method codes in these classes have a wide range of rates and minimum distances and they perform well with iterative decoding

on similarity and duality of computation i this paper describes what is the parallel time for sequential models what is the sequential time for parallel models and proves that the well known computational models ram vector machines turing machines uniform circuits uniform aggregates storage modification machines hardware modification machines are all similar in the sense that their parallel time their sequential time and their space complexities are polynomially related simultaneously

optical orthogonal codes design analysis and applications an optical orthogonal code ooc is a family of 0 1 sequences with good auto and cross correlation properties i e the autocorrelation of each sequence exhibits the thumbtack shape and the cross correlation between any two sequences remains low throughout the use of optical orthogonal codes enables a large number of asynchronous users to transmit information efficiently and reliably the thumbtack shaped autocorrelation facilitates the detection of the desired signal and low profile cross correlation reduces interference from unwanted signals theoretical upper and lower bounds on the maximum possible size of oocs are derived methods for the design and analysis of oocs using tools from projective geometry the greedy algorithm iterative constructions algebraic coding theory block design and various other combinational disciplines are discussed

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

the computational power of discrete hopfield nets with hidden units we prove that polynomial size discrete hopfield networks with hidden units compute exactly the class of boolean functions pspace poly i e the same functions as are computed by polynomial space bounded nonuniform turing machines as a corollary to the construction we observe also that networks with polynomially bounded interconnection weights compute exactly the class of functions p poly i e the class computed by polynomial time bounded nonuniform turing machines

a lattice based systematic recursive construction of quasi cyclic ldpc codes this paper presents a low complexity recursive and systematic method to construct good well structured low density parity check ldpc codes the method is based on a recursive application of a partial kronecker product operation on a given gamma x q q ges 3 a prime integer lattice l gamma x q the n 1 fold product of l gamma x q by itself denoted ln gamma x q represents a regular quasi cyclic qc ldpc code denoted see pdf of high rate and girth 6 the minimum distance of see pdf is equal to that of the core code see pdf introduced by l gamma x q the support of the minimum weight codewords in see pdf are characterized by the support of the same type of codewords in see pdf from performance perspective the constructed codes compete with the pseudorandom ldpc codes

construction of one coincidence sequence quasi cyclic ldpc codes of large girth one approach for designing the one coincidence sequence ocs low density parity check ldpc codes of large girth is investigated these ocs ldpc codes are quasi cyclic and their parity check matrices are composed of circulant permutation matrices generally the cycle structures in these codes are determined by the shift values of circulant permutation matrices and the existence of cycles in the corresponding tanner graph is governed by certain cycle governing equations cges therefore finding the proper shift values is the key point to increase the girth of these codes in this paper we provide an effective method to systematically find out the cges for these codes of girth 6 8 and 10 respectively then one less computation intensive algorithm is used to generate the proper shift values for constructing the ocs ldpc codes of large girth simulation results show that significant gains in signal to noise ratio over an additive white gaussian noise channel can be achieved by increasing the girth of the ocs ldpc codes

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

4 cycle free ldpc codes based on difference sets difference sets are used to give a novel method for constructing structured regular quasi cyclic low density parity check codes let fq be a field with q elements and assume that d d1 dk is a v k 1 difference set for zv with d1 d2 dk depending on v q 1 v 2dk or v 2dk 1 three code construction methods are given that produce regular 4 cycle free codes that is codes with girth at least 6 simulation results show that the constructed codes perform well over the awgn channel with an iterative sum product message passing decoding algorithm

large families of asymptotically optimal two dimensional optical orthogonal codes nine new two dimensional optical orthogonal codes 2 d oocs are presented here all sharing the common feature of a code size that is much larger in relation to the number of time slots than those of constructions appearing previously in the literature each of these constructions is either optimal or asymptotically optimal with respect to either the original johnson bound or else a nonbinary version of the johnson bound introduced in this paper the first five codes are constructed using polynomials over finite fields the first construction is optimal while the remaining four are asymptotically optimal the next two codes are constructed using rational functions in place of polynomials and these are asymptotically optimal the last two codes also asymptotically optimal are constructed by composing two of the above codes with a constant weight binary code also presented is a three dimensional optical orthogonal code 3 d ooc that exploits the polarization dimension finally phase encoded optical cdma is considered and construction of two efficient codes are provided

complex rotary codes revisited a low complexity high performance decoding approach in this paper based on a belief propagation decoding strategy a class of generalized parity check codes called complex rotary codes is investigated it is shown that by using iterative sum product decoding the complex rotary codes have a much lower decoding complexity than turbo codes but have almost the same performance for the high code rate and short frame case frame length 500 bits it is also shown that the prime block size of complex rotary codes is essential to achieve better performance because of its uniform checking characteristic

some estimates of solutions for the equations of motion of compressible viscous fluid in the three dimensional exterior domain abstract we consider the equations of motion of compressible viscous fluid in an exterior domain in r 3 we give the l q l p estimates for solutions to the linearized equations and show an optimal decay estimate for solutions to the nonlinear problem in particular we shall give l 1 estimates which implies the diffusion wave of compressible navier stokes flow

time invariant quasi cyclic spatially coupled ldpc codes based on packings this paper presents two packings derived from balanced incomplete block designs to construct quasi cyclic spatially coupled ldpc convolutional codes sc ldpc ccs the construction gives time invariant codes since the sub blocks corresponding to each time instant of the parity check matrix are identical moreover it provides flexible design rates and constraint lengths simulation results show that the proposed packing based sc ldpc ccs outperform the existing time invariant codes and perform closely to the time varying protograph based codes

crc handbook of combinatorial designs balanced incomplete block designs and t designs2 v k l designs of small orderbibds with small block sizet designs t 3steiner systemssymmetric designsresolvable and near resolvable designslatin squares mols and orthogonal arrayslatin squaresmutually orthogonal latin squares mols incomplete molsorthogonal arrays of index more than oneorthogonal arrays of strength more than twopairwise balanced designspbds and gdds the basicspbds recursive constructionspbd closurepairwise balanced designs as linear spacespbds and gdds of higher indexpbds frames and resolvabilityother combinatorial designsassociation schemesbalanced part ternary designsbalanced tournament designsbhaskar rao designscomplete mappings and sequencings of finite groupsconfigurationscostas arrayscoveringscycle systemsdifference familiesdifference matricesdifference sets abeliandifference sets nonabeliandifference triangle setsdirected designsd optimal matricesembedding partial quasigroupsequidistant permutation arraysfactorial designsfrequency squaresgeneralized quadranglesgraph decompositions and designsgraphical designshadamard matrices and designshall triple systemshowell designsmaximal sets of molsmendelsohn designsthe oberwolfach problemordered designs and perpendicular arraysorthogonal designsorthogonal main effect planspackingspartial geometriespartially balanced incomplete block designsquasigroupsquasi symmetric designs r l designsroom squaresself orthogonal latin squares sols sols with a symmetric orthogonal mate solssom sequences with zero autocorrelationskolem sequencesspherical t designsstarterstrades and defining sets t m s netstuscan squarest wise balanced designsuniformly resolvable designsvector space designsweighing matrices and conference matriceswhist tournamentsyouden designs generalizedyouden squaresapplicationscodescomputer science selected applicationsapplications of designs to cryptographyderandomizationoptimality and efficiency comparing block designsgroup testingscheduling a tournamentwinning the lotteryrelated mathematics and computational methodsfinite groups and designsnumber theory and finite fieldsgraphs and multigraphsfactorizations of graphsstrongly regular graphstwo graphsclassical geometriesprojective planes nondesarguesiancomputational methods in design theoryindex

construction of structured regular ldpc codes a design theoretic approach a new combinatorial technique for constructing girth 6 structured binary regular low density parity check ldpc codes based on special types of t designs is given a very large number of well known t designs can be used by this method for code construction based on this method a t v k design d x b can be exploited for code construction if it satisfies the following three conditions 1 b1 b2 t for any two blocks b1 b2 b and b1 b2 2 1 and 3 k t though the technique works for any t design satisfying these conditions we focus only on the utilization of simple triple systems super simple bibds steiner systems and large sets lss of t designs we also construct binary and non binary girth 6 qc ldpc codes from the t designs satisfying these conditions by using matrix dispersion method experimental results show that the constructed non binary qc ldpc codes can provide good practical performance under iterative decoding using the fast fourier transform based q ary sum product algorithm fft qspa and they can achieve acceptable coding gains over random like codes of comparable parameters decoded with sum product algorithm spa

a logarithmic improvement of regularity criterion for the mhd equations in terms of the pressure abstract in this paper we prove a logarithmic improvement of regularity criterion only in terms of the pressure in morrey campanato spaces for the cauchy problem to the incompressible mhd equations

bifurcation analysis of magnetic reconnection in hall mhd systems abstract the influence of the hall term on the width of the magnetic islands of the tearing mode is examined we applied the center manifold cmf theory to a magnetohydrodynamic mhd system the mhd system was chosen to be incompressible and includes in addition to viscosity the hall term in ohm s law for certain values of physical parameters the corresponding center manifold is two dimensional and therefore the original partial differential equations could be reduced to a two dimensional system of ordinary ones this amplitude equations exhibit a pitchfork bifurcation which corresponds to the occurrence of the tearing mode eigenvalue problems and linear equations due to the center manifold reduction were solved numerically with the arpack library an important result of this analysis is the growth of the tearing mode island width by increasing the hall parameter a feature which has been observed in recent numerical simulations of collisionless reconnection

constructions of optimal 2 d optical orthogonal codes via generalized cyclotomic classes optical orthogonal codes oocs are widely used as spreading codes in optical fiber networks in this paper a bound on the code size of 2 d oocs with both at most one pulse per wavelength am oppw and at most one pulse per time slot am oppts is derived accordingly two constructions of optimal 2 d oocs with both am oppw and am oppts are proposed via the generalized cyclotomic classes furthermore optimal 2 d ooc with am oppw can be also constructed by adding more codewords into the 2 d oocs with both am oppw and am oppts

on the construction of structured ldpc codes free of small trapping sets we present a method to construct low density parity check ldpc codes with low error floors on the binary symmetric channel codes are constructed so that their tanner graphs are free of certain small trapping sets these trapping sets are selected from the trapping set ontology for the gallager a b decoder they are selected based on their relative harmfulness for a given decoding algorithm we evaluate the relative harmfulness of different trapping sets for the sum product algorithm by using the topological relations among them and by analyzing the decoding failures on one trapping set in the presence or absence of other trapping sets we apply this method to construct structured ldpc codes to facilitate the discussion we give a new description of structured ldpc codes whose parity check matrices are arrays of permutation matrices this description uses latin squares to define a set of permutation matrices that have disjoint support and to derive a simple necessary and sufficient condition for the tanner graph of a code to be free of four cycles

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

on the notion of infinite pseudorandom sequences abstract three definitions of infinite pseudorandom sequences with respect to polynomial time and space complexity are introduced and compared with each other it is shown that the first two definitions based on martin lof s notion of sequential tests and levin and schnorr s notion of monotonic operator complexity are equivalent with respect to polynomial space complexity while both are strictly stronger than the third definition which is derived from von mises s notion of collectives

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

construction of low density parity check codes by superposition this paper presents a superposition method for constructing low density parity check ldpc codes several classes of structured ldpc codes are constructed codes in these classes perform well with iterative decoding and their tanner graphs have girth at least six

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

new construction of multiwavelength optical orthogonal codes we investigate multiwavelength optical orthogonal codes mwoocs for optical code division multiple access particularly we present a new construction method for mn spl lambda 2 spl lambda mwoocs with the number of available wavelengths m codeword length n and constant hamming weight spl lambda 2 that have autocorrelation and cross correlation values not exceeding spl lambda in the proposed scheme there is no constraint on the relationship between the number of available wavelengths and the codeword length and it is also possible to use an arbitrary spl lambda we show that the constructed code is optimal especially for spl lambda 1 finally we analyze the bit error rate of the new code and compare it with that of other optical codes