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

conformal covariantization of moyal lax operators a covariant approach to the conformal property associated with moyal lax operators is given by identifying the conformal covariance with the second gelfand dickey flow we covariantize moyal lax operators to construct the primary fields of one parameter deformation of classical w algebras

asymmetric slepian wolf coding of nonstationarily correlated m ary sources with sliding window belief propagation asymmetric slepian wolf coding aswc of m ary sources with nonstationary correlation is a very useful model for many practical problems an effective implementation of this coding scheme is to binarize each m ary source into multiple bitplanes which are then compressed by a single binary low density parity check ldpc code though the inter bitplane correlation of m ary sources can be exploited at the decoder by the joint bitplane belief propagation jbbp algorithm accurate online estimation of varying local source correlation still remains a major challenge to tackle this problem this paper proposes an m ary counterpart of the sliding window belief propagation swbp algorithm to realize simultaneous source recovery and correlation estimation to search for the optimal sliding window size the expected rate is raised as a new criterion moreover an adaptive method is proposed to decide whether correlation reestimation is necessary the m ary swbp mswbp algorithm is then generalized to obtain its 2d form which can be used to tackle the aswc of 2d m ary sources with nonstationary correlation the developed 1d 2d mswbp algorithm inherits all merits of the original binary swbp algorithm e g near optimal coding efficiency low complexity insensitivity to initial settings etc making it a very attractive technique in practice

on the knuth bendix completion for concurrent processes abstract we consider critical pairs for replacement systems over free partially commutative monoids this is done in order to apply the knuth bendix completion procedure to concurrent processes we will see that there are one rule systems which have no finite set of critical pairs therefore we develop a sufficient and computable condition such that finite trace replacement systems have a finite set of critical pairs this condition is always satisfied in the purely free case of semi thue systems or purely commutative case of vector replacement systems in fact it generalizes and unifies both cases we will give examples of how one can use this generalization

church rosser controlled rewriting systems and equivalence problems for deterministic context free languages we use a description of deterministic context free languages dcfl by a special type of church rosser rewriting systems to extend several procedures testing the equality of two languages in a subfamilyfof dcfl to procedures testing the equality of two languages one of which is inf the other beeing a general dcfl

ldpc based lossless compression of nonstationary binary sources using sliding window belief propagation low density parity check ldpc codes have been used to implement lossless distributed or conventional source coding however block wise ldpc codes are difficult to adapt to varying source statistics as traditional symbol wise entropy coding techniques in this paper we propose the sliding window belief propagation swbp algorithm which is able to simultaneously recover the source and refine the estimate of varying source statistics the swbp is easy to implement and performs well in simulations

lambda confluence for context rewriting systems clearing restarting automata and limited context restarting automata are particular types of context rewriting systems a word w is accepted by such a system if there is a sequence of rewritings that reduces the word w to the empty word where each rewrite rule is extended by certain context conditions if each rewrite step is strictly length reducing as for example in the case of clearing restarting automata then the word problem for such a system can be solved nondeterministically in quadratic time if in addition the contextual rewritings happen to be confluent that is confluent on the congruence class of the empty word then the word problem can be solved deterministically in linear time here we show that confluence is decidable in polynomial time for limited context restarting automata of type r 2 but that this property is not even recursively enumerable for clearing restarting automata the latter follows from the fact that confluence is not recursively enumerable for finite factor erasing string rewriting systems

w gauge structures and their anomalies an algebraic approach starting from flat two dimensional gauge potentials we propose the notion of w gauge structure in terms of a nilpotent becchi rouet stora brs differential algebra the decomposition of the underlying lie algebra with respect to an sl 2 subalgebra is crucial for the discussion of conformal covariance in particular the appearance of a projective connection different sl 2 embeddings lead to different w gauge structures we present a general soldering procedure which allows one to express zero curvature conditions for the w currents in terms of conformally covariant differential operators acting on the w gauge fields and to obtain at the same time the complete nilpotent brs differential algebra generated by w currents gauge fields and the ghost fields corresponding to w diffeomorphisms as illustrations we treat the cases of sl 2 itself and the two different sl 2 embeddings in sl 3 viz the w 1 3 and w 2 3 gauge structures in some detail in these cases we determine algebraically w anomalie

distributed source coding using syndromes discus design and construction we address the problem of compressing correlated distributed sources i e correlated sources which are not co located or which cannot cooperate to directly exploit their correlation we consider the related problem of compressing a source which is correlated with another source that is available only at the decoder this problem has been studied in the information theory literature under the name of the slepian wolf 1973 source coding problem for the lossless coding case and as rate distortion with side information for the lossy coding case we provide a constructive practical framework based on algebraic trellis codes dubbed as distributed source coding using syndromes discus that can be applicable in a variety of settings simulation results are presented for source coding of independent and identically distributed i i d gaussian sources with side information available at the decoder in the form of a noisy version of the source to be coded our results reveal the promise of this approach using trellis based quantization and coset construction the performance of the proposed approach is 2 5 db from the wyner ziv 1976 bound

picard fuchs ordinary differential systems in n 2 supersymmetric yang mills theories in general picard fuchs systems in n 2 supersymmetric yang mills theories are realized as a set of simultaneous partial differential equations however if the quantum chromodynamics qcd scale parameter is used as a unique independent variable instead of moduli the resulting picard fuchs systems are represented by a single ordinary differential equation ode whose order coincides with the total number of independent periods this paper discusses some properties of these picard fuchs odes in contrast with the usual picard fuchs systems written in terms of moduli derivatives there exists a wronskian for this ordinary differential system and this wronskian produces a new relation among periods moduli and qcd scale parameter which in the case of su 2 is reminiscent of the scaling relation of prepotential on the other hand in the case of the su 3 theory there are two kinds of ordinary differential equations one of which is the equation directly constructed from periods and the other is derived

adaptive binary slepian wolf decoding using particle based belief propagation a major difficulty that plagues the practical use of slepian wolf sw coding and distributed source coding in general is that the precise correlation among sources needs to be known a priori to resolve this problem we propose an adaptive asymmetric sw decoding scheme using particle based belief propagation pbp we explain the adaptive scheme for asymmetric setup in detail and then further extend it to the non asymmetric setup based on the code partitioning approach moreover we introduce a metropolis hastings mh algorithm in the resampling step which efficiently decreases the number of simulation iterations we show through experiments that the proposed algorithm can simultaneously reconstruct the compressed sources and estimate the joint correlation among sources further comparing to the conventional sw decoder based on standard belief propagation the proposed approach can achieve higher compression under varying correlation statistics

distributed coding using punctured quasi arithmetic codes for memory and memoryless sources this correspondence considers the use of punctured quasi arithmetic qa codes for the slepian wolf problem these entropy codes are defined by finite state machines for memoryless and first order memory sources puncturing an entropy coded bit stream leads to an ambiguity at the decoder side the decoder makes use of a correlated version of the original message in order to remove this ambiguity a complete distributed source coding dsc scheme based on qa encoding with side information at the decoder is presented together with iterative structures based on qa codes the proposed schemes are adapted to memoryless and first order memory sources simulation results reveal that the proposed schemes are efficient in terms of decoding performance for short sequences compared to well known dsc solutions using channel codes

classical r matrices and compatible poisson structures for lax equations on poisson algebras given a classical r matrix on a poisson algebra we show how to construct a natural family of compatible poisson structures for the hamiltonian formulation of lax equations examples for which our formalism applies include the benny hierarchy the dispersionless toda lattice hierarchy the dispersionless kp and modified kp hierarchies the dispersionless dym hierarchy etc

monadic thue systems abstract certain infinite thue systems over a finite alphabet are studied in particular systems s e such that for each a e the set u u a s is a context freelanguage the syntactic structure of sets of ancestors and sets of descendants is considered as well as that of unions of congruence classes taken over infinite context free languages or regular sets the common descendant problem is shown to be tractable while the common ancestor problem is shown to be undecidable even for finite systems the word problem for confluent systems of this type is shown to be tractable the question of whether an infinite system of this type is confluent is shown to be undecidable as is the question of whether the congruence generated by such a system has a confluent presentation

the integrable hierarchy constructed from a pair of kdv type hierarchies and its associated w algebra for any two arbitrary positive integers n and m using them th kdv hierarchy and the n m th kdv hierarchy as building blocks we are able to construct another integrable hierarchy referred to as the n m th kdv hierarchy thew algebra associated to the second hamiltonian structure of the n m th kdv hierarchy calledw n m algebra is isomorphic via a miura map to the direct sum of aw m algebra aw n m algebra and an additionalu 1 current algebra in turn from the latter we can always construct a representation of aw algebra

hamming distance spectrum of dac codes for equiprobable binary sources distributed arithmetic coding dac is an effective technique for implementing slepian wolf coding swc it has been shown that a dac code partitions source space into unequal size codebooks so that the overall performance of dac codes depends on the cardinality and structure of these codebooks the problem of dac codebook cardinality has been solved by the so called codebook cardinality spectrum ccs this paper extends the previous work on ccs by studying the problem of dac codebook structure we define hamming distance spectrum hds to describe dac codebook structure and propose a mathematical method to calculate the hds of dac codes the theoretical analyses are verified by experimental results

nonstandard drinfeld sokolov reduction subject to some conditions the input data for the drinfeld sokolov construction of kdv type hierarchies is a quadruplet where the are gradations of a loop algebra and is a semisimple element of the nonzero grade a new sufficient condition on the quadruplet under which the construction works is proposed and examples are presented the proposal relies on splitting the grade zero part of into a vector space direct sum of two subalgebras this permits one to interpret certain gelfand dickey type systems associated with a nonstandard splitting of the algebra of pseudodifferential operators in the drinfeld sokolov framework

on diff s1 covariantization of pseudodifferential operator a study of diff s1 covariant properties of a pseudodifferential operator of integer degree is presented first it is shown that the action of diff s1 defines a hamiltonian flow defined by the second gelfand dickey bracket if and only if the pseudodifferential operator transforms covariantly second the covariant form of a pseudodifferential operator of degree n 0 1 is constructed by exploiting the inverse of the covariant derivative this in particular implies the existence of a primary basis for wkp n n 0 1

lossless and near lossless source coding for multiple access networks a multiple access source code masc is a source code designed for the following network configuration a pair of correlated information sequences x sub i sub i 1 sup spl infin and y sub i sub i 1 sup spl infin is drawn independent and identically distributed i i d according to joint probability mass function p m f p x y the encoder for each source operates without knowledge of the other source the decoder jointly decodes the encoded bit streams from both sources the work of slepian and wolf describes all rates achievable by mascs of infinite coding dimension n spl rarr spl infin and asymptotically negligible error probabilities p sub e sup n spl rarr 0 in this paper we consider the properties of optimal instantaneous mascs with finite coding dimension n spl infin and both lossless p sub e sup n 0 and nearlossless p sub e sup n spl rarr 0 performance the interest in near lossless codes is inspired by the discontinuity in the limiting rate region at p sub e sup n 0 and the resulting performance benefits achievable by using near lossless mascs as entropy codes within lossy mascs our central results include generalizations of huffman and arithmetic codes to the masc framework for arbitrary p x y n and p sub e sup n and polynomial time design algorithms that approximate these optimal solutions

infinite regular thue systems abstract the following new results are obtained about infinite regular thue systems s 1 if s is church rosser the word problem is solvable in linear time 2 if s is monadic church rosser it defines a nontrivial boolean algebra of dcfls 3 if s is monadic church rosser and so is another system t equivalence of s and t is decidable 4 if s is monadic it is decidable if s is church rosser 5 if s is not monadic it is undecidable if s is church rosser

improved binary dac codec with spectrum for equiprobable sources slepian wolf coding swc can be effectively implemented by distributed arithmetic coding dac codes a theoretical tool named spectrum has been developed to analyze the complexity of the full search binary dac bdac decoder for equiprobable sources following this work this paper aims at improving the coding efficiency of bdac codes to achieve this goal this paper analyzes how bdac codes partition source space into codebooks and links codebook cardinalities with the initial spectrum further by exploiting the final spectrum this paper proves that the decoding error probability of bdac codes will not tend to zero as code length goes to infinity even at rates greater than the slepian wolf limit on the basis of theoretical analyses two techniques are proposed to reduce the decoding error probability of bdac codes i e the permutation technique which removes near in the sense of hamming distance codewords in each codebook and the weighted branching technique which reduces the mis pruning risk of proper paths during the decoding the effectiveness of both techniques is well verified by experimental results

noise adaptive ldpc decoding using particle filtering belief propagation bp is a powerful algorithm to decode low density parity check ldpc codes over additive white gaussian noise awgn channels however the traditional bp algorithm cannot adapt efficiently to the statistical change of snr in an awgn channel this paper proposes an adaptive scheme that incorporates a particle filtering pf algorithm into the bp based ldpc decoding process the proposed scheme is capable to perform online estimation of time varying snr at the bit level and enhance the bp decoding performance simultaneously

a quantum group structure in integrable conformal field theories we discuss a quantization prescription of the conformal algebras of a class ofd 2 conformal field theories which are integrable we first give a geometrical construction of certain extensions of the classical virasoro algebra known as classicalw algebras in which these algebras arise as the lie algebra of the second hamiltonian structure of a generalized korteweg de vries hierarchy this fact implies that thew algebras obtained as a reduction with respect to the nilpotent subalgebras of the kac moody algebra describe the integrability of a toda field theory subsequently we determine the coadjoint operators of thew algebras and relate these to classical yang baxter matrices the quantization of these algebras can be carried out using the concept of a so called quantum group we derive the condition under which the representations of these quantum groups admit a hilbert space completion by exploring the relation with the braid group then we consider a modification of the miura transformation which we use to define a quantumw algebra this leads to an alternative interpretation of the coset construction for kac moody algebras in terms of nonlinear integrable hierarchies subsequently we use the connection between the induced braid group representations and the representations of the mapping class group of riemann surfaces to identify an action of thew algebras on the moduli space of stable curves and we give the invariants of this action this provides a generalization of the situation for the virasoro algebra where such as invariant is given by the so called mumford form which describes the partition function of the bosonic string

performance of belief propagation for decoding ldpc codes in the presence of channel estimation error in this paper we investigate the performance of the belief propagation bp algorithm for decoding low density parity check codes over the additive white gaussian noise channel when there is an incorrect estimate of the channel signal to noise ratio snr referred to as snr mismatch at the decoder at the extremes for over and underestimation of snr the performance of bp tends to that of min sum algorithm and the channel bit error rate respectively our results for regular codes indicate that the sensitivity to mismatch increases by increasing the variable node degree and by decreasing the check node degree the effect of variable node degree however appears to be more profound such that at a given rate the codes with the smallest variable and check degrees are more robust against snr mismatch for irregular codes by comparing the thresholds of a few ensembles we demonstrate that the ensemble which performs better in the absence of mismatch can perform worse in the presence of it to obtain our asymptotic results we propose a computationally efficient method based on the gaussian approximation of density evolution in the presence of snr mismatch we also show that the asymptotic results are consistent with simulation results for codes with finite block lengths

distributed arithmetic coding for the slepian wolf problem distributed source coding schemes are typically based on the use of channels codes as source codes in this paper we propose a new paradigm named ldquodistributed arithmetic coding rdquo which extends arithmetic codes to the distributed case employing sequential decoding aided by the side information in particular we introduce a distributed binary arithmetic coder for the slepian wolf coding problem along with a joint decoder the proposed scheme can be applied to two sources in both the asymmetric mode wherein one source acts as side information and the symmetric mode wherein both sources are coded with ambiguity at any combination of achievable rates distributed arithmetic coding provides several advantages over existing slepian wolf coders especially good performance at small block lengths and the ability to incorporate arbitrary source models in the encoding process e g context based statistical models in much the same way as a classical arithmetic coder we have compared the performance of distributed arithmetic coding with turbo codes and low density parity check codes and found that the proposed approach is very competitive

zero curvature conditions and conformal covariance two dimensional zero curvature conditions with special emphasis on conformal properties are investigated in detail and the appearance of covariant higher order differential operators constructed in terms of a projective connection is elucidated the analysis is based on the kostant decomposition of simple lie algebras in terms of representations with respect to their principal sl 2 subalgebra

large chiral diffeomorphisms on riemann surfaces and w algebras the diffeomorphism action lifted on truncated chiral taylor expansion of a complex scalar field over a riemann surface is presented in the paper under the name of large diffeomorphisms after an heuristic approach we show how a linear truncation in the taylor expansion can generate an algebra of symmetry characterized by some structure functions such a linear truncation is explicitly realized by introducing the notion of forsyth frame over the riemann surface with the help of a conformally covariant algebraic differential equation the large chiral diffeomorphism action is then implemented through a becchi rouet stora brs formulation for a given order of truncation leading to a more algebraic setup in this context the ghost fields behave as holomorphically covariant jets subsequently the link with the so called w algebras is made explicit once the ghost parameters are turned from jets into tensorial ghost ones we give a general solution with the help of the structure functions pertaining to al

integrability of the frobenius algebra valued kadomtsev petviashvili hierarchy we introduce a frobenius algebra valued kadomtsev petviashvili kp hierarchy and show the existence of frobenius algebra valued function for this hierarchy in addition we construct its hamiltonian structures by using the adler dickey gelfand method as a byproduct of these constructions we show that the coupled kp hierarchy defined by casati and ortenzi j geom phys 56 418 449 2006 has at least n basic different local bi hamiltonian structures finally via the construction of the second hamiltonian structures we obtain some local matrix or frobenius algebra valued generalizations of classical w algebras

dac spectrum of binary sources with equally likely symbols though distributed arithmetic coding dac is an effective implementation of slepian wolf coding its performance which is closely linked with its decoding complexity has not received a thorough analysis with binary sources with equally likely symbols as the research object this paper develops the dac spectrum and makes use of it as a tool to answer the complexity problem of the ideal dac decoder based on an in depth analysis on dac decoding process we define the dac spectrum and propose to find it by a recursive formulation firstly the initial dac spectrum is constrained by a functional equation and the fourier transform is utilized to obtain its general explicit form secondly an equation is given through which stage i 1 dac spectrum can be deduced from stage i dac spectrum a numerical method is also proposed for calculating dac spectrum whose convergency is proved to measure the complexity of the ideal dac decoder we define the expansion factor and relate it to dac spectrum it is proved that if binary symbols 0 and 1 are mapped onto partially overlapped intervals 0 q and 1 q 1 respectively the expansion factor will converge to 2q i e the complexity of the ideal rate dac decoder is approximately o 2 n 1

classical a n w geometry by analyzing theextrinsic geometry of two dimensional surfaces chirally embedded incp n thecp n w surface 1 we give exact treatments in various aspects of the classical w geometry in the conformal gauge first the basis of tangent and normal vectors are defined at regular points of the surface such that their infinitesimal displacements are given by connections which coincide with the vector potentials of the conformal a n toda lax pair since the latter is known to be intrinsically related with the w symmetries this gives the geometrical meaning of thea n w algebra second w surfaces are put in one to one correspondence with solutions of the conformally reduced wznw model which is such that the toda fields give the cartan part in the gauss decomposition of its solutions third the additional variables of the toda hierarchy are used as coordinates ofcp n this allows us to show that w transformations may be extended as particular diffeomorphisms of this target space higher dimensional generalizations of the wznw equations are derived and related with the zakharov shabat equations of the toda hierarchy fourth singular points are studied from a global viewpoint using our earlier observation 1 that w surfaces may be regarded as instantons the global indices of the w geometry which are written in terms of the toda fields are shown to be the instanton numbers for associated mappings of w surfaces into the grassmannians the relation with the singularities of w surface is derived by combining the toda equations with the gauss bonnet theorem

non local matrix generalizations of w algebras there is a standard way to define two symplectic hamiltonian structures the first and second gelfand dikii brackets on the space of ordinarymth order linear differential opeatorsl d m u1dm 1 u2dm 2 u m in this paper i consider in detail the case where theu k aren n matrix valued functions with particular emphasis on the more interesting second gelfand dikii bracket of particular interest is the reduction to the symplectic submanifoldu1 0 this reduction gives rise to matrix generalizations of the classical version of thenon linear w m algebras calledv n m algebras the non commutativity of the matrices leads tonon local terms in thesev n m algebra s i show that these algebras contain a conformal virasoro subalgebra and that combinationsw k of theu k can be formed that aren n matrices of conformally primary fields of spink in analogy with the scalar casen 1 in general however thev m n algebras have a much richer structure than thew m algebras as can be seen on the examples of thenon linear andnon local poisson brackets u2 ab u2 cd u2 ab w3 cd and w3 ab w3 cd which i work out explicitly for allm andn a matrix miura transformations is derived mapping these complicated second gelfand dikii brackets of theu k to a set of much simpler poisson brackets providing the analogoue of the free field representation of thew m algebras

on the completeness of the set of classical w algebras obtained from ds reductions we clarify the notion of the ds generalized drinfeld sokolov reduction approach to classical cal w algebras we first strengthen an earlier theorem which showed that an sl 2 embedding cal s subset cal g can be associated to every ds reduction we then use the fact that a cal w algebra must have a quasi primary basis to derive severe restrictions on the possible reductions corresponding to a given sl 2 embedding in the known ds reductions found to date for which the cal w algebras are denoted by cal w s g algebras and are called canonical the quasi primary basis corresponds to the highest weights of the sl 2 here we find some examples of noncanonical ds reductions leading to cal w algebras which are direct products of cal w s g algebras and lq lq free field algebras with conformal weights delta in 0 1 over 2 1 we also show that if the conformal weights of the generators of a cal w algebra obtained from ds reduction are nonnegative delta geq 0 which is the case for all ds reductions known to date then the delta geq 3 over 2 subsectors of the weights are necessarily the same as in the corresponding cal w s g algebra these results are consistent with an earlier result by bowcock and watts on the spectra of cal w algebras derived by different means we are led to the conjecture that up to free fields the set of cal w algebras with nonnegative spectra delta geq 0 that may be obtained from ds reduction is exhausted by the canonical ones

undecidable questions related to church rosser thue systems abstract the following four properties are shown undecidable for finite thue systems s is s equivalent to a finite church rosser respectively almost confluent preperfect system does s generate a church rosser congruence

undecidable properties of monoids with word problem solvable in linear time let c1 be the class of finitely presented monoids with word problem solvable in linear time let p be a markov property of monoids related to class c1 in some sense it is undecidable given a monoid in c1 whether it satisfies p let c and c be classes of finitely presented monoids with word problem solvable in some time bounds if c contains c1 and c properly contains c then it is undecidable given a monoid in c whether it belongs to c

classical w algebras we reconsider the relation between classicalw algebras and deformations of differential operators emphasizing the consistency with diffeomorphisms generators of thew algebra that arek differentials are constructed by a systematic procedure the method extends following drinfeld and sokolov tow algebras based on arbitrary simple lie algebras

maximum likelihood laplacian correlation channel estimation in layered wyner ziv coding the distributed source coding theory teaches that efficient compression can be achieved by exploiting the correlation between encoded sources at the decoder only a critical issue in this coding paradigm is how to accurately estimate the correlation statistics at the decoder this paper proposes a novel correlation channel estimation method designed for generic layered wyner ziv wz coding driven by real life applications i e video coding the correlation noise is assumed to be memoryless zero mean laplacian with a block stationary behavior unlike existing methods the proposed technique derives a novel maximum likelihood estimate of the noise scaling parameter per stationarity block adhering to layered coding the derived estimate is successively refined as more stages are decoded the cramer rao lower bound crlb for our estimator is derived and the mean squared error performance of the proposed successive refinement algorithm is evaluated through simulations apart from achieving an accuracy close to the derived crlb the proposed algorithm is shown to yield a wz rate distortion performance approaching the ideal but unrealistic scenario where the decoder knows a priori the correlation statistics moreover the proposed technique has been integrated into our latest wz video codec for wireless capsule endoscopy experimentation reveals that the proposed method delivers improved compression performance compared to state of the art techniques while simultaneously reducing the overall decoding complexity

particle filters for joint blind equalization and decoding in frequency selective channels this paper introduces new algorithms for joint blind equalization and decoding of convolutionally coded communication systems operating on frequency selective channels the proposed method is based on particle filters pf recursively approximating maximum a posteriori map estimates of the transmitted data without explicitly determining channel parameters further elaborating on previous works we assume that both the channel order and the noise variance are unknown random variables and develop a new formulation for pf weight propagation which allows these quantities to be analytically integrated out we verify via numerical simulations that the proposed methods lead to near optimal performance closely approximating that of algorithms that require exact knowledge of all channel parameters

analysis on tailed distributed arithmetic codes for uniform binary sources distributed arithmetic coding dac is a variant of ac that can realize slepian wolf coding in a nonlinear way in our previous work we defined codebook cardinality spectrum ccs and hamming distance spectrum hds for dac in this paper we make use of ccs and hds to analyze tailed dac which is a form of dac that as traditional ac maps the last few symbols of each source block onto non overlapped intervals first we derive the exact hds formula for tailless dac a form of dac that maps all the symbols of each source block onto overlapped intervals and show that the hds formula previously given is in fact approximation then the hds formula is extended to tailed dac using ccs we also deduce the average codebook cardinality which is closely related to decoding complexity and rate loss of tailed dac the effects of tail length are extensively analyzed it is revealed that by increasing tail length to a value not close to the bitstream length closely spaced codewords within the same codebook can be removed at the cost of a higher decoding complexity and a larger rate loss finally theoretical analyses are verified by experiments

the constrained modified kp hierarchy and the generalized miura transformations in this letter we consider the second hamiltonian structure of the constrained modified kp hierarchy after mapping the lax operator to a pure differential operator the second structure becomes the sum of the second and the third gelfand dickey brackets defined by this differential operator we simplify this hamiltonian structure by factorizing the lax operator into linear terms

on the gelfand dickey algebra gd sln and the wn symmetry i the bosonic case the algebra of nonlinear local and nonlocal differential operators acting on the ring of analytic functions is studied it is shown in particular that this space splits into 3 2 special subalgebras jr j 0 1 r 1 each subalgebra is completely specified by quantum numbers s and p q describing the conformal spin and the lowest and the highest degrees respectively the algebra and its dual of local pure nonlocal differential operators is used to calculate the general expression of the gelfand dickey bracket and the wn symmetry poisson one in terms of a set of spin j canonical fields uj 2 j n and a nonlinear u cubic dependent differential operator d n i j z u the explicit form of this operator is worked out other remarkable features are also discussed

rate compatible punctured low density parity check codes with short block lengths we consider the problem of rate compatible puncturing of low density parity check ldpc codes over additive white gaussian noise awgn channels in previous work it was shown that good puncturing distributions exist for ldpc codes but the code length was large in this correspondence we give a procedure for determining the puncturing distributions for ldpc codes with short block lengths a few thousand bits and show that careful puncturing can produce good performance we compare the performance of the rate compatible punctured ldpc codes with dedicated ldpc codes across a range of rates and see that the rate compatible codes have a favorable complexity performance tradeoff

classical extended conformal algebras associated with constrained kp hierarchy the conformal property of the second hamiltonian structure of constrained kp hierarchy derived by oevel and strampp is examined it is found that it naturally gives a family of nonlocal extended conformal algebras two examples of such algebras are given and it is found that they are similar to bilal s v algebra by taking a gauge transformation one can map the constrained kp hierarchy to kupershmidt s nonstandard lax hierarchy the second hamiltonian structure in this representation is considered it is shown that after mapping the lax operator to a pure differential operator the second structure becomes the sum of the second and the third gelfand dickey brackets defined by this differential operator the corresponding conformally covariant form of this differential operator is also given

bihamiltonian hierarchies in 2d topological field theory at one loop approximation we compute the genus one correction to the integrable hierarchy describing coupling to gravity of a 2d topological field theory the bihamiltonian structure of the hierarchy is given by a classical w algebra we compute the central charge of this algebra we also express the generating function of elliptic gromov witten invariants via tau function of the isomonodromy deformation problem arising in the theory of wdvv equations of associativity

a matrix integral solution to two dimensional w p gravity thep th gel fand dickey equation and the string equation l p 1 have a common solution expressible in terms of an integral overn n hermitean matrices for largen the integrand being a perturbation of a gaussian generalizing kontsevich s integral beyond the kdv case it is equivalent to showing that is a vacuum vector for aw generated from the coefficients of the vertex operator this connection is established via a quadratic identity involving the wave function and the vertex operator which is a disguised differential version of the fay identity the latter is also the key to the spectral theory for the two compatible symplectic structures of kdv in terms of the stress energy tensor associated with the virasoro algebra given a differential operator l d p q 2 t d p 2 cdots q p t with d frac partial dx t t 1 t 2 t 3 x equiv t 1 consider the deformation equations1 0 1 begin gathered frac partial l partial t n l n p l n 1 2 n 0 mod p hfill p reduced kp equation hfill end gathered ofl for which there exists a differential operatorp possibly of infinite order such that 0 2 l p 1 string equation in this note we give a complete solution to this problem in section 1 we give a brief survey of useful facts about thei function t the wave function t z solution of t n l n p x andl 1 p z and the corresponding infinitedimensional planev 0 of formal power series inz for largez v 0 span psi t z for all t in mathbb c infty in sato s grassmannian the three theorems below form the core of the paper their proof will be given in subseuqent sections each of which lives on its own right

adaptive bayesian multiuser detection for synchronous cdma with gaussian and impulsive noise we consider the problem of simultaneous parameter estimation and data restoration in a synchronous cdma system in the presence of either additive gaussian or additive impulsive white noise with unknown parameters the impulsive noise is modeled by a two term gaussian mixture distribution bayesian inference of all unknown quantities is made from the superimposed and noisy received signals the gibbs sampler a markov chain monte carlo procedure is employed to calculate the bayesian estimates the basic idea is to generate ergodic random samples from the joint posterior distribution of all unknown and then to average the appropriate samples to obtain the estimates of the unknown quantities adaptive bayesian multiuser detectors based on the gibbs sampler are derived for both the gaussian noise synchronous cdma channel and the impulsive noise synchronous cdma channel a salient feature of the proposed adaptive bayesian multiuser detectors is that they can incorporate the a priori symbol probabilities and they produce as output the a posteriori symbol probabilities that is they are soft input soft output algorithms hence these methods are well suited for iterative processing in a coded system which allows the adaptive bayesian multiuser detector to refine its processing based on the information from the decoding stage and vice versa a receiver structure termed the adaptive turbo multiuser detector

classical n 2 w superalgebras from superpseudodifferential operators we study the supersymmetric gelfand dickey algebras associated with the superpseudodifferential operators of positive as well as negative leading order we show that upon the usual constraint these algebras contain the n 2 super virasoro algebra as a subalgebra when the leading order is odd the decompositions of the coefficient functions into n 1 primary fields are then obtained by covariantizing the superpseudodifferential operators we discuss the problem of identifying n 2 supermultiplets and work out a couple of supermultiplets by explicit computations

source coding with side information at the decoder and uncertain knowledge of the correlation this paper considers the problem of lossless source coding with side information at the decoder when the correlation model between the source and the side information is uncertain four parametrized models representing the correlation between the source and the side information are introduced the uncertainty on the correlation appears through the lack of knowledge on the value of the parameters for each model we propose a practical coding scheme based on non binary low density parity check codes and able to deal with the parameter uncertainty at the encoder the choice of the coding rate results from an information theoretical analysis then we propose decoding algorithms that jointly estimate the source vector and the parameters as the proposed decoder is based on the expectation maximization algorithm which is very sensitive to initialization we also propose a method to produce first a coarse estimate of the parameters

poisson algebras associated with constrained dispersionless modified kadomtsev petviashvili hierarchies we investigate the bi hamiltonian structures associated with constrained dispersionless modified kadomtsev petviashvili kp hierarchies which are constructed from truncations of the lax operator of the dmkp hierarchy after transforming their second hamiltonian structures to those of the gelfand dickey type we obtain the poisson algebras of the coefficient functions of the truncated lax operators then we study the conformal property and free field realizations of these poisson algebras some examples are worked out explicitly to illustrate the obtained results

superconformal covariantization of superdifferential operator on 1 1 superspace and classical n 2 w superalgebras a study of the superconformal covariantization of superdifferential operators defined on 1 1 superspace is presented it is shown that a superdifferential operator with a particular type of constraint can be covariantized only when it is of odd order in such a case the action of superconformal transformation on the superdifferential operator is nothing but a hamiltonian flow defined by the corresponding supersymmetric second gelfand dickey bracket the covariant form of a superdifferential operator of odd order is given

testing for the church rosser property abstract it is shown that there is a polynomial time algorithm to determine whether a finite thue system is church rosser

w algebras for generalized toda theories the generalized toda theories obtained in a previous paper by the conformal reduction of wznw theories possess a new class of w algebras namely the algebras of gauge invariant polynomials of the reduced theories an algorithm for the construction of base elements for the w algebras of all such generalized toda theories is found and the w algebras for the maximal sl n r generalized toda theories are constructed explicitly the primary field basis being identified 1992 springer verlag