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 transform theory for a class of group invariant codes a binary cyclic code of length of n can be defined by a set of parity check equations that is invariant under the additive cyclic group generated by a i to i 1 modulo n a class of quasicyclic codes that have parity check equations invariant under the group generated by a subgroup of a and a subgroup of the multiplicative group m i to 2 sup k i modulo n is studied in detail the fourier transform transforms the action of the additive group and a linearized polynomial transform transforms the action of the multiplicative group the form of the transformed code equations permits a bch like bound on the minimum distance of the code the techniques are illustrated by the construction of several codes that are decodable by the berlekamp massey algorithm and that have parameters that approach or surpass those of the best codes known

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

four alternative patterns of the hilbert curve the second pattern of the hilbert curve was shown by moore in 1900 in this article we present four more patterns these patterns together with hilbert s original pattern and moore s pattern comprise a complete set of the hilbert curve

hopf structure and green ansatz of deformed parastatistics algebras deformed parabose and parafermi algebras are revised and endowed with hopf structure in a natural way the noncocommutative coproduct allows for construction of parastatistics fock like representations built out of the simplest deformed bose and fermi representations the construction gives rise to quadratic algebras of deformed anomalous commutation relations which define the generalized green ansatz

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

generation of spatial orders and space filling curves space filling curves have been found useful for many applications in diverse fields a space filling curve is a path in a 2 r 2 r raster domain which visits each location exactly once in mathematical terms space filling curves linearize a 2d integer space bijectively mapping the space to the integer line an algorithm is presented which generates a large number of space filling curves spatial orders functions are derived such that the code of each location can be calculated from its coordinates and conversely a location code can be decoded to yield the coordinates the algorithm first generates generate 4 4 spatial orders they subsequently may be scaled up to any desired domain of size 2 r 2 r the underlying theory of the algorithm the processes for scaling up encoding and decoding are described in detail the curves are generated as a set of incongruent curves followed if required by the sets of associated congruent curves a number of space filling curves are illustrated

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

on the solutions of the yang baxter equations with general inhomogeneous eight vertex r matrix relations with zamolodchikov s tetrahedral algebra we present most general one parametric solutions of the yang baxter equations ybe for one spectral parameter dependent r ij u matrices of the six and eight vertex models where the only constraint is the particle number conservation by mod 2 a complete classification of the solutions is performed we have obtained also two spectral parameter dependent particular solutions r ij u v of ybe the application of the non homogeneous solutions to construction of zamolodchikov s tetrahedral algebra is discussed

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

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

efficient region segmentation on compressed gray images using quadtree and shading representation abstract image segmentation which partitions the image into homogeneous regions is a fundamental operation in image processing suppose the input gray image with size n n has been compressed into the compressed image via quadtree and shading representation assume that the number of blocks in the representation is b commonly b n 2 due to the compression effect this paper first derives some closed forms for computing the mean variance of any block and for calculating the two statistical measures of any merged region in o 1 time it then presents an efficient o b b time algorithm for performing region segmentation on the compressed image directly where b is the inverse of the ackerman s function and is a very slowly growing function with the same time complexity our results extend the pioneering results by dillencourt and samet from the map image to the gray image in addition with four real images experimental results show that our proposed algorithm has about 55 4 execution time improvement ratio when compared to the previous fastest region segmentation algorithm by fiorio and gustedt whose o n 2 time algorithm is run on the original n n gray image

a novel two phase hilbert scan based search algorithm for block motion estimation using ctf data structure motion estimation is one of the kernel issues in mpeg series in this correspondence a novel two phase hilbert scan based search algorithm for block motion estimation is presented first in the intra phase a segmentation of the hilbert curve is applied to the current block then a novel coarse to fine data structure is developed to eliminate the impossible reference blocks in the search window of the reference frame in the inter phase a new prediction scheme for estimating the initial motion vector of the current block is presented experimental results reveal that when compared to the gapd algorithm our proposed algorithm has better execution time and estimation accuracy performance under the same estimation accuracy our proposed algorithm has better execution time performance when compared to the fs algorithm in addition when comparing with the tss algorithm our proposed algorithm has better estimation accuracy performance but has worse execution time performance

large weight code words in projective space codes abstract recently a large number of results have appeared on the small weights of the dual linear codes arising from finite projective spaces we now focus on the large weights of these linear codes for q even this study for the code c k n q reduces to the theory of minimal blocking sets with respect to the k spaces of pg n q odd blocking the k spaces for q odd in a lot of cases the maximum weight of the code c k n q is equal to q n q 1 but some unexpected exceptions arise to this result in particular the maximum weight of the code c 1 n 3 turns out to be 3 n 3 n 1 in general the problem of whether the maximum weight of the code c k n q with q 3 h h 1 is equal to q n q 1 reduces to the problem of the existence of sets of points in pg n q intersecting every k space in 2 mod 3 points

a new approach to vector median filtering based on space filling curves the availability of a wide set of multidimensional information sources in different application fields e g color cameras multispectral remote sensing imagery devices etc is the basis for the interest of image processing research on extensions of scalar nonlinear filtering approaches to multidimensional data filtering a new approach to multidimensional median filtering is presented the method is structured into two steps absolute sorting of the vectorial space based on peano space filling curves is proposed as a preliminary step in order to map vectorial data onto an appropriate one dimensional 1 d space then a scalar median filtering operation is applied the main advantage of the proposed approach is the computational efficiency of the absolute sorting step which makes the method globally faster than existing median filtering techniques this is particularly important when dealing with a large amount of data e g image sequences presented results also show that the filtering performances of the proposed approach are comparable with those of vector median filters presented in the literature

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

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

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

resolvable 2 designs for regular low density parity check codes this paper extends the class of low density parity check ldpc codes that can be algebraically constructed we present regular ldpc codes based on resolvable steiner 2 designs which have tanner graphs free of four cycles the resulting codes are 3 spl rho regular or 4 spl rho regular for any value of spl rho and for a flexible choice of code lengths

nonbinary ldpc codes on cages structural property and code optimization a v g cage is a not necessarily unique smallest v regular graph of girth g on such a graph a nonbinary 2 v regular low density parity check ldpc code can be defined such that the tanner graph has girth 2g and the code length achieves the minimum possible in this paper we focus on two aspects of this class of codes structural property and code optimization we find that in addition to those found previously many cages can be used to construct structured ldpc codes we show that all cages with even girth can be structured as protograph based codes many of which have block circulant tanner graphs we also find that four cages with odd girth can be structured as protograph based codes with block circulant tanner graphs for code optimization we develop an ontology based approach all possible inter connected cycle patterns that lead to low symbol weight codewords are identified to put together the ontology by doing so it becomes handleable to estimate and optimize distance spectrum of equivalent binary image codes we further analyze some known codes from the consultative committee for space data systems recommendation and design several new codes numerical results show that these codes have reasonably good minimum bit distance and perform well under iterative decoding

t g t a toy model for conformal field theory we study a chiral operator algebra of conformal field theory and quantum deformation of the finite dimensional lie group to obtain the definition of t g t and its representation the closeness of the kac moody algebras constituting the chiral operator algebra of a typical and generic conformal field theory model namely the wznw model and quantum deformation of corresponding finite dimensional lie groupg has become more and more evident in recent years 1 5 this in particular prompts further investigation of the differential geometry of such deformations the notion of tangent and cotangent bundles is basic in classical differential geometry it is only natural that the quantum deformations oftg andt g are to be introduced alongside those forg itself physical ideas could be useful for this goal indeed thet g can be interpreted as a phase space for a kind of a top generalizing the usual top associated withg so 3 the classical mechanics is a natural language to describe differential geometry whereas the usual quantization is nothing but the representation theory in this paper we put corresponding formulas in such a fashion that their deformation becomes almost evident given the experience in this domain as a result we get the definition of t g t and its representation t is the deformation parameter to make the exposition most simple and formulas transparent we shall work on an example ofg sl 2 and present results in such a way that the generalizations become evident we shall stick to generic complex versions real and especially compact forms requiring some additional consideration not all of which are self evident

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

ldpc codes from generalized polygons we use the theory of finite classical generalized polygons to derive and study low density parity check ldpc codes the tanner graph of a generalized polygon ldpc code is highly symmetric inherits the diameter size of the parent generalized polygon and has minimum one half diameter to girth ratio we show formally that when the diameter is four or six or eight all codewords have even hamming weight when the generalized polygon has in addition an equal number of points and lines we see that the nonregular polygon based code construction has minimum distance that is higher at least by two in comparison with the dual regular polygon code of the same rate and length a new minimum distance bound is presented for codes from nonregular polygons of even diameter and equal number of points and lines finally we prove that all codes derived from finite classical generalized quadrangles are quasi cyclic and we give the explicit size of the circulant blocks in the parity check matrix our simulation studies of several generalized polygon ldpc codes demonstrate powerful bit error rate ber performance when decoding is carried out via low complexity variants of belief propagation

t b q q analog of model space and the clebsch gordan coefficients generating matrices we study relations between the deformed cotangent bundle t b q for the borel subgroup b of a given simple lie group g the quantum lie algebra jq associated with the corresponding quantum group gq and the matrices generating clebsch gordan coefficients for jq we reveal the connection of these objects to quantum analog of the model space m and q tensor operators

an algorithm for encoding and decoding the 3 d hilbert order spatial ordering is a transformation relating an n dimensional voxel to a set of natural numbers interest in the hilbert order h order has been high because of its desirable performance when applied to image processing in this correspondence an encoding decoding algorithm for the three dimensional 3 d hilbert order is presented

hecke algebraic properties of dynamical r matrices application to related quantum matrix algebras the quantum dynamical yang baxter or gervais neveu felder equation defines an r matrix r p where p stands for a set of mutually commuting variables a family of sl n type solutions of this equation provides a new realization of the hecke algebra we define quantum antisymmetrizers introduce the notion of quantum determinant and compute the inverse quantum matrix for matrix algebras of the type r p a1a2 a1a2r it is pointed out that such a quantum matrix algebra arises in the operator realization of the chiral zero modes of the wznw model

the quantum group structure associated with non linearly extended virasoro algebras recently an infinite family of chiral virasoro vertex operators whose exchange algebra is given by the universalr matrix ofsl 2 q has been constructed in the present paper the case of non linearly w extended virasoro symmetries related to the algebrasan n 1 is considered along the same line contrary to the previous case a1 the standardr matrix ofsl n 1 q does not come out and a different solution of yang and baxter s equations is derived the associated quantum group structure is displayed

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

space filling approach for fast window query on compressed images based on the space filling approach this paper presents a fast algorithm for window query on compressed images given a query window of size n sub 1 spl times n sub 2 the proposed algorithm takes o n sub 1 logt p time to perform the window query where n sub 1 max n sub 1 n sub 2 and t spl times t is the image size p is the number of outputted codes the proposed algorithm improves the naive algorithm which needs o n sub 1 n sub 2 log t p time significantly some experimentations are carried out to demonstrate the computational advantage of the proposed algorithm from the experimental results it is observed that the proposed algorithm has about 72 98 time improvement when compared to the naive algorithm

spectral extension of the quantum group cotangent bundle the structure of a cotangent bundle is investigated for quantum linear groups gl q n and sl q n using a q version of the cayley hamilton theorem we construct an extension of the algebra of differential operators on sl q n otherwise called the heisenberg double by spectral values of the matrix of right invariant vector fields we consider two applications for the spectral extension first we describe the extended heisenberg double in terms of a new set of generators the weyl partners of the spectral variables calculating defining relations in terms of these generators allows us to derive sl q n type dynamical r matrices in a surprisingly simple way second we calculate an evolution operator for the model of the q deformed isotropic top introduced by a alekseev and l faddeev the evolution operator is not uniquely defined and we present two possible expressions for it the first one is a riemann theta function in the spectral variables the second one is an almost free motion evolution operator in terms of logarithms of the spectral variables the relation between the two operators is given by a modular functional equation for the riemann theta function

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

on the exchange matrix for wznw model the connection between the exchange algebra in thesu 2 wess zumino novikov witten model and the quantum groupsu 2 is discussed it is shown that on the quasiclassical level this connection has the simple interpretation in terms of the lie poisson action ofsu 2 on the chiral components of the fields in the wznw model

one dimensional b b polynomial and hilbert scan for graylevel image coding abstract effectiveness of one dimensional bezier bernstein polynomial has been studied for compression of graylevel images both raster and hilbert scan have been used for this purpose two different algorithms for one dimensional approximation and encoding of hilbert images provide evidence of better compression ratio compared to that for raster scanned images comparison with the result of an existing algorithm has also been performed to examine the effectiveness of our methods

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

explicit construction of families of ldpc codes with no 4 cycles low density parity check ldpc codes are serious contenders to turbo codes in terms of decoding performance one of the main problems is to give an explicit construction of such codes whose tanner graphs have known girth for a prime power q and m spl ges 2 lazebnik and ustimenko construct a q regular bipartite graph d m q on 2q sup m vertices which has girth at least 2 spl lceil m 2 spl rceil 4 we regard these graphs as tanner graphs of binary codes lu m q we can determine the dimension and minimum weight of lu 2 q and show that the weight of its minimum stopping set is at least q 2 for q odd and exactly q 2 for q even we know that d 2 q has girth 6 and diameter 4 whereas d 3 q has girth 8 and diameter 6 we prove that for an odd prime p lu 3 p is a p sup 3 k code with k spl ges p sup 3 2p sup 2 3p 2 2 we show that the minimum weight and the weight of the minimum stopping set of lu 3 q are at least 2q and they are exactly 2q for many lu 3 q codes we find some interesting ldpc codes by our partial row construction we also give simulation results for some of our 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

near optimum universal belief propagation based decoding of low density parity check codes in this paper we propose a belief propagation bp based decoding algorithm which utilizes normalization to improve the accuracy of the soft values delivered by a previously proposed simplified bp based algorithm the normalization factors can be obtained not only by simulation but also importantly theoretically this new bp based algorithm is much simpler to implement than bp decoding as it requires only additions of the normalized received values and is universal i e the decoding is independent of the channel characteristics some simulation results are given which show this new decoding approach can achieve an error performance very close to that of bp on the additive white gaussian noise channel especially for low density parity check ldpc codes whose check sums have large weights the principle of normalization can also be used to improve the performance of the max log map algorithm in turbo decoding and some coding gain can be achieved if the code length is long enough

rational top and its classical r matrix we construct a rational integrable system the rational top on a co adjoint orbit of sl n lie group it is described by the lax operator with spectral parameter and classical non dynamical skew symmetric r matrix in the case of the orbit of minimal dimension the model is gauge equivalent to the rational calogero moser cm system to obtain the results we represent the lax operator of the cm model in two different factorized forms without spectral parameter related to the spinless case and another one with the spectral parameter the latter gives rise to the rational top while the first one is related to generalized cremmer gervais r matrices the gauge transformation relating the rational top and cm model provides the classical rational version of the irf vertex correspondence from the geometrical point of view it describes the modification of bundles over degenerated elliptic curve in view of the symplectic hecke correspondence the rational top is related to the rational spin cm model possible applications and generalizations of the suggested construction are discussed in particular the obtained r matrix defines a class of kzb equations

minimum pseudoweight and minimum pseudocodewords of ldpc codes in this correspondence we study the minimum pseudoweight and minimum pseudocodewords of low density parity check ldpc codes under linear programming lp decoding first we show that the lower bound of kelley sridhara xu and rosenthal on the pseudoweight of a nonzero pseudocodeword of an ldpc code whose tanner graph has girth greater than is tight if and only if this pseudocodeword is a real multiple of a codeword then the lower bound of kashyap and vardy on the stopping distance of an ldpc code is proved to be also a lower bound on the pseudoweight of a nonzero pseudocodeword of an ldpc code whose tanner graph has girth and this lower bound is tight if and only if this pseudocodeword is a real multiple of a codeword using these results we further obtain that for some ldpc codes there are no other minimum pseudocodewords except the real multiples of minimum weight codewords this means that the lp decoding for these ldpc codes is asymptotically optimal in the sense that the ratio of the probabilities of decoding errors of lp decoding and maximum likelihood decoding approaches as the signal to noise ratio snr tends to infinity finally some ldpc codes are listed to illustrate these results

efficient algorithms for coding hilbert curve of arbitrary sized image and application to window query previously several efficient hilbert scan based operations were presented but they all suffer from the constraint that the image size must be 2 rx2 r considering an image with arbitrary size i 1xi 2 this paper first presents an efficient snake scan based algorithm for coding the hilbert curve of the given image the proposed coding algorithm takes o k logu time to code the hilbert order of one pixel where k denotes the number of the quadrants and u min i 1 i 2 next a memory saving hilbert curve representation called hcgl is presented for representing the encoded hilbert curve and it can be constructed in o l 2logl time where l max i 1 i 2 based on the hcgl representation of arbitrary sized image an application to window query is presented and the proposed window query algorithm takes o mlogl p time where m denotes the number of generated maximal quadtree blocks and p denotes the number of output codes under the same psnr peak signal to noise ratio experimental results demonstrate that our proposed hcgl representation outperforms some existing related algorithms in terms of execution time and bpp bit per pixel in addition our proposed window query algorithm has been justified in the gis geographical information system application

iterative list decoding of some ldpc codes we present an iterative list decoding algorithm for low density parity check ldpc codes in particular we apply this decoder to a class of ldpc codes from finite geometries and show that the 73 45 10 projective geometry code can be maximum likelihood ml decoded with low complexity moreover the list decoding approach enables us to give a theoretical analysis of the performance we also consider list bit flipping bf decoding of longer ldpc codes

incidence structures from the blown up plane and ldpc codes in this paper new regular incidence structures are presented they arise from sets of conics in the affine plane blown up at its rational points the ldpc codes given by these incidence matrices are studied these sparse incidence matrices turn out to be redundant which means that their number of rows exceeds their rank such a feature is absent from random ldpc codes and is in general interesting for the efficiency of iterative decoding the performance of some codes under iterative decoding is tested some of them turn out to perform better than regular gallager codes having similar rate and row weight

fock representations of quantum fields with generalized statistics we develop a rigorous framework for constructing fock representations of quantum fields obeying generalized statistics the main features of these representations are investigated various aspects of the underlying mathematical structure are illustrated by means of explicit examples

space filling curves and their use in the design of geometric data structures we are given a two dimensional square grid of size n n where n 2n and n 0 a space filling curve sfc is a numbering of the cells of this grid with numbers from c 1 to c n2 for some c 0 we call a sfc recursive rsfc if it can be recursively divided into four square rsfcs of equal size examples of well known rsfcs include the hilbert curve the z curve and the gray code

manipulation and presentation of multidimensional image data using the peano scan a fractal curve first discussed by giuseppe peano has useful statistical properties in image processing the curve can act as a transform between a line and n dimensional space retaining some of the spatially associative properties of the space applications of the curve include multispectral image display compression in the color and spa tial domain classification and color display the technique enables the display of high quality color images on a frame store capable of displaying only 256 colors simultaneously a logically ordered and complete set of colors for false color work can be selected an im provement in compression by about 3x for color images can be ob tained by using this method in conjunction with an existing spatial compression technique a simple algorithm for constructing the curves is shown

new solvable lattice models in three dimensions in this paper we establish a remarkable connection between two seemingly unrelated topics in the area of solvable lattice models the first is the zamolodchikov model which is the only nontrivial model on a three dimen sional lattice so far solved the second is the chiral potts model on the square lattice and its generalization associated with theu q sl n algebra which is of current interest due to its connections with high genus algebraic curves and with representations of quantum groups at roots of unity we show that this last sl n generalized chiral potts model can be interpreted as a model on a threedimensional simple cubic lattice consisting ofn square lattice layers with ann valued n 2 spin at each site further in then 2 case this three dimen sional model reduces after a modification of the boundary conditions to the zamolodchikov model we mentioned above

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

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

twisted yang baxter equations for linear quantum super groups we consider the modified or twisted yang baxter equations for the groups and supergroups the general solutions for these equations are presented in the case of the linear quantum super groups the introduction of spectral parameters in the twisted yang baxter equation and its solutions are also discussed