on a liouville type equation with sign changing weight in this paper we study the existence nonexistence and multiplicity of non negative solutions for the family of problems u a x e f x u u h 0 where is a bounded domain in r2 and 0 is a parameter the coefficient a x is allowed to change sign the techniques used in the proofs are a combination of upper and lower solutions the trudingermoser inequality and variational methods note that when f x u 0 the equation is of liouville type

infinitely many nodal solutions for nonlinear elliptic equations with combined nonlinearities and lack of symmetry abstract we present a new approach to studying a parametric nonlinear dirichlet problem driven by a nonhomogeneous differential operator and with a reaction which is concave i e p 1 sublinear near zero and convex i e p 1 superlinear near the reaction term is not assumed to be odd we show that for all small values of the parameter 0 the problem has infinitely many nodal solutions

quantization of filter bank frame expansions through moving horizon optimization this paper describes a novel approach to quantization in oversampled filter banks the new technique is based on moving horizon optimization does not rely on an additive white noise quantization model and allows stability to be explicitly enforced in the associated nonlinear feedback loop moreover the quantization structure proposed here includes sigmadelta and linear predictive subband quantizers as a special case and in general outperforms them

linear integral equations and nonlinear difference difference equations abstract in this paper we present a systematic method to obtain various integrable nonlinear difference difference equations and the associated linear integral equations from which their solutions can be inferred it is argued that these difference difference equations can be regarded as arising from bianchi identities expressing the commutativity of backlund transformations applying an appropriate continuum limit we first obtain integrable nonlinear differential difference equations together with the associated linear integral equations and after a second continuum limit we can obtain the corresponding integrable nonlinear partial differential equations and their linear integral equations as special cases we treat the difference difference versions and the differential difference versions of the korteweg de vries equation the modified korteweg de vries equation the nonlinear schrodinger equation the isotropic classical heisenberg spin chain and the complex and real sine gordon equation

on semilinear elliptic equations involving concave convex nonlinearities and sign changing weight function abstract in this paper we study the combined effect of concave and convex nonlinearities on the number of positive solutions for semilinear elliptic equations with a sign changing weight function with the help of the nehari manifold we prove that there are at least two positive solutions for eq e f in bounded domains

a bi hamiltonian structure for the integrable discrete non linear schrodinger system abstract this paper shows that the al ablowitz ladik hierarchy of integrable equations can be explicitly viewed as a hierarchy of commuting flows which a are hamiltonian with respect to both a standard local poisson operator j and a new non local skew almost poisson operator k on the appropriate space b can be recursively generated from a recursion operator r k j 1 in addition the proof of these facts relies upon two new pivotal resolvent identities which suggest a general method for uncovering bi hamiltonian structures for other families of discrete integrable equations

decision feedback equalization via separating hyperplanes the design of finite length decision feedback equalization dfe forward and feedback filters under the assumption of genie aided feedback and independent and equally likely transmitted symbols is considered it is shown that the problem of determining dfe filters that minimize the probability of symbol error at high signal to noise ratio snr is equivalent to finding the hyperplane that maximally separates two given finite groups of points in a finite dimensional euclidean space the latter task can be formulated as a quadratic program which is readily solved numerically it is also shown that the problem of finding finite length dfe filters that minimize the probability of symbol error at any snr subject to a certain separation condition is a convex optimization problem the case where the transmitted data is coded using a runlength limited code is also investigated examples show that this criterion yields a performance that is better than zero forcing dfe on severely distorted channels at high snr

block decision feedback equalization a natural generalization of the conventional decision feedback equalizer dfe based on block processing and maximum a posteriori decisions is presented this block dfe is indexed by two parameters depending on the block length p and the number of decisions q

multilevel codes based on partitioning following v v ginzburg 1984 a hierarchy of codes is proposed to match the geometric partitioning of a signal set the authors show that coset codes including ungerboeck lattice and binary codes and indeed any codes which rely on partitioning of the signal set are all subclasses of the proposed coding scheme the combination of such codes in a multilevel scheme often leads to reduced complexity in comparison with previously published schemes a variety of decoder structures is discussed

multiple positive solutions for quasilinear problems with indefinite sublinear nonlinearity abstract we have established multiplicity of nontrivial solutions for the quasilinear elliptic problem p u h x u 1 g x u in u 0 in u 0 on where r n is a smooth bounded domain p 1 1 p h is a measurable function and g r r is a caratheodory function such that g x 0 0 which is asymptotically linear we also prove existence and nonexistence results when g x t k x t p 1

truncation length for viterbi decoding a bound is derived and analyzed for the bit error rate ber of a viterbi decoder with survivor truncation estimates of the snr signal to noise ratio loss on the awgn additive white gaussian noise channel due to truncation are obtained for convolutional codes larger truncation lengths are required than the smallest value that does not effectively decrease the code s free distance especially at low e sub b n sub 0

nonnegative solutions of elliptic problems with sublinear indefinite nonlinearity abstract we are concerned with existence nonexistence and multiplicity of nonnegative solutions for the elliptic problem u a x u q b x u p in u 0 on where is a bounded domain in r n r 0 q 1 p 2 1 and a b are bounded functions with b x 0 and a x changes its sign

delayed decision feedback sequence estimation the authors delayed decision feedback sequence estimation ddfse for uncoded pam signals is considered estimates on the performance of the algorithm are given and simulation results are provided for several examples a more general form of ddfse applicable to coded modulation systems is also presented as an example detection of trellis coded qpsk quadrature phase shift keyed signals over intersymbol interference channels is discussed

moving horizon estimation for hybrid systems we propose a state smoothing algorithm for hybrid systems based on moving horizon estimation mhe by exploiting the equivalence between hybrid systems modeled in the mixed logic dynamical form and piecewise affine systems we provide sufficient conditions on the time horizon and the penalties on the state at the beginning of the estimation horizon to guarantee asymptotic convergence of the mhe scheme moreover we propose two practical algorithms for the computation of penalties that allow us to implement mhe by solving a mixed integer quadratic program

multiplicity results for some elliptic problems with concave nonlinearities implies that the variational functionalassociated with 1 is bounded below and coercive coercive ellipticproblems of this type with 0 have been studied by ambrosetti andmancini 3 struwe 9 ambrosetti and lupo 2 and other authors here we prove the existence of more solutions for 0 sufficiently small

abstract critical point theorems and applications to some nonlinear problems with strong resonance at infinity critical point theorems and applications to some nonlinear problems with strong resonance at infinity p bartolo and v benci istituto di matematica applicata via re david x0 bari ital and istituto di analisi matematica palazzo ateneo l ia scolai 2 bari italy received in revised form 20 december 1952

multiple solutions for a semilinear problem with combined terms and nonlinear boundary conditions abstract we consider the problem u u f x u in u h x u q 2 u on where r n is a smooth bounded domain n 3 1 q 2 and h belongs to an appropriated lebesgue space in our main results we suppose that f is an asymptotically linear function and we obtain multiplicity of solutions when the norm of h is small we also present a multiplicity result in the case that f is nonquadratic at infinity

discrete painleve equations and their appearance in quantum gravity we discuss an algorithmic approach for both deriving discrete analogues of painleve equations as well as using such equations to characterize similarity reductions of spatially discrete integrable evolution equations as a concrete example we show that a discrete analogue of painleve i can be used to characterize similarity solutions of the kac moerbeke equation it turns out that these similarity solutions also satisfy a special case of painleve iv equation in addition we discuss a methodology for obtaining the relevant continuous limits not only at the level of equations but also at the level of solutions as an example we use the wkb method in the presence of two turning points of the third order to parametrize at the continuous limit the solution of painleve i in terms of the solution of discrete painleve i finally we show that these results are useful for investigating the partition function of the matrix model in 2d quantum gravity associated with the measure exp t1z2 t2z4 t3z6

optimal and near optimal encoders for short and moderate length tail biting trellises the results of an extensive search for short and moderate length polynomial convolutional encoders for time invariant tail biting representations of block codes at rates r 1 4 1 3 1 2 and 2 3 are reported the tail biting representations found are typically as good as the best known block codes

reduced complexity sequence estimation using state partitioning a reduced state sequence estimator rsse for linear dispersive channels is described the technique is based on partitioning the set of all channel states in a way that defines a trellis with fewer states the new technique generalizes trellises that were previously obtained by duel hallen and heegard 1989 and eyouboglu and qureshi 1988 while the approach followed by duel hallen results in powers of two state trellises the new technique generates trellises with an arbitrary number of states using the state partitioning approach one could also generalize the trellises obtained by eyouboglu therefore the approach described in this paper provides a better performance complexity tradeoff

multiple solutions for some elliptic equations with a nonlinearity concave at the origin in this paper we establish the existence of multiple solutions for the semilinear elliptic problem u u q 2 u au g u in u 0o n where r n is a bounded domain with smooth boundary g r r is a function of class c 1 such that g 0 g 0 0 0i s ar eal parameter a r a nd 1 q 2

reduced state sequence estimation with set partitioning and decision feedback a reduced state sequence estimator for linear intersymbol interference channels is described the estimator uses a conventional viterbi algorithm with decision feedback to search a reduced state subset trellis that is constructed using set partitioning principles the complexity of maximum likelihood sequence estimation mlse due to the length of the channel memory and the size of the signal set is systematically reduced an error probability analysis shows that a good performance complexity tradeoff can be obtained in particular the results indicate that the required complexity to achieve the performance of mlse is independent of the size of the signal set for large enough signal sets simulation results are provided for two partial response systems a simple technique for quadrature partial response signaling qprs is described that eliminates the quasicatastrophic nature of the ml trellis

multilevel codes theoretical concepts and practical design rules this paper deals with 2 sup l ary transmission using multilevel coding mlc and multistage decoding msd the known result that mlc and msd suffice to approach capacity if the rates at each level are appropriately chosen is reviewed using multiuser information theory it is shown that there is a large space of rate combinations such that mlc and full maximum likelihood decoding mld can approach capacity it is noted that multilevel codes designed according to the traditional balanced distance rule tend to fall in the latter category and therefore require the huge complexity of mld the capacity rule the balanced distances rules and two other rules based on the random coding exponent and cutoff rate are compared and contrasted for practical design simulation results using multilevel binary turbo codes show that capacity can in fact be closely approached at high bandwidth efficiencies moreover topics relevant in practical applications such as signal set labeling dimensionality of the constituent constellation and hard decision decoding are emphasized bit interleaved coded modulation proposed by caire et al see ibid vol 44 p 927 46 1998 is reviewed in the context of mlc finally the combination of signal shaping and coding is discussed significant shaping gains are achievable in practice only if these design rules are taken into account

optimizing transmission lengths for limited feedback with nonbinary ldpc examples this paper presents a general approach for optimizing the number of symbols in increments packets of incremental redundancy in a feedback communication system with a limited number of increments this approach is based on a tight normal approximation on the rate for successful decoding applying this approach to a variety of feedback systems using nonbinary nb low density parity check ldpc codes shows that greater than 90 of capacity can be achieved with average blocklengths fewer than 500 transmitted bits one result is that the performance with ten increments closely approaches the performance with an infinite number of increments the paper focuses on binary input additive white gaussian noise bi awgn channels but also demonstrates that the normal approximation works well on examples of fading channels as well as high snr awgn channels that require larger qam constellations this paper explores both variable length feedback codes with termination vlft and the more practical variable length feedback vlf codes without termination that require no assumption of noiseless transmitter confirmation for vlf we consider both a two phase scheme and crc based scheme

performance evaluation of coded modulation schemes based on binary lattices we describe computational techniques for the evaluation of error probability of modulation schemes based on binary lattices and multilevel coding these techniques stem from the representation of a binary lattice in the form of a trellis whose structure depends on the block codes on which the binary lattice is based multilevel coded modulation schemes can also be described through a trellis by combining with this the trellis structure of the lattice constellation we obtain a single trellis that can be used for maximum likelihood decoding using the viterbi algorithm and for computing the error probability an upper bound to error probability can be obtained from the transfer function of the trellis with suitable labels and is applicable to both maximum likelihood and staged decoding

three positive solutions for semilinear elliptic problems involving concave and convex nonlinearities we study the existence and multiplicity of positive solutions for the dirichlet problem where 0 1 q p 2 2 n n 2 0 e n n 3 is a bounded domain with smooth boundary and f is a non negative continuous function on assuming that f satisfies some hypothesis we prove that the equation admits at least three positive solutions for sufficiently small

discrete mkdv and discrete sine gordon flows on discrete space curves in this paper we consider the discrete deformation of the discrete space curves with constant torsion described by the discrete mkdv or the discrete sine gordon equations and show that it is formulated as the torsion preserving equidistant deformation on the osculating plane which satisfies the isoperimetric condition the curve is reconstructed from the deformation data by using the sym tafel formula the isoperimetric equidistant deformation of the space curves does not preserve the torsion in general however it is possible to construct the torsion preserving deformation by tuning the deformation parameters further it is also possible to make an arbitrary choice of the deformation described by the discrete mkdv equation or by the discrete sine gordon equation at each step we finally show that the discrete deformation of discrete space curves yields the discrete k surfaces

solutions of a schrodinger poisson system with combined nonlinearities abstract in this paper we are concerned with the following schrodinger poisson system u v x u u k x u q 2 u f x u x r 3 u 2 lim x x 0 x r 3 where 0 is a parameter 1 q 2 and f x u is linearly bounded in u at infinity we establish the existence and multiplicity of solutions under suitable assumptions on v k and f

multiple solutions to p laplacian problems with concave nonlinearities in this paper we study the p laplacian type elliptic problems with concave nonlinearities using some asymptotic behavior of f at zero and infinity three nontrivial solutions are established

asymptotically linear schrodinger equation with potential vanishing at infinity we are concerned with the existence of bound states and ground states of the following nonlinear schrodinger equation

coset codes i introduction and geometrical classification practically all known good constructive coding techniques for bandlimited channels including lattice codes and various trellis coded modulation schemes can be characterized as coset codes a coset code is defined by a lattice partition lambda lambda and by a binary encoder c that selects a sequence of cosets of the lattice lambda the fundamental coding gain of a coset code as well as other important parameters such as the error coefficient the decoding complexity and the constellation expansion factor are purely geometric parameters determined by c lambda lambda the known types of coset codes as well as a number of new classes that systematize and generalize known codes are classified and compared in terms of these parameters

existence of three nontrivial solutions for elliptic systems with critical exponents and weights abstract in this paper an elliptic system with critical sobolev exponents and weights is studied by the linking theorem on product space and the classical minimax theorem by investigating the coefficients of the critical nonlinearities we establish the existence of three nontrivial solutions

multistep detector for linear isi channels incorporating degrees of belief in past estimates this paper formulates the channel equalization problem in the framework of constrained maximum likelihood estimation this allows us to highlight key issues including the need to summarize past data and to apply a finite alphabet constraint over a sliding optimization window the approach adopted here leads to embellishments of the usual nonadaptive decision feedback equalizer and its multistep extensions it includes a provision for degrees of belief in past estimates which addresses the problem of error propagation

decision feedback equalization using multiple hyperplane partitioning for detecting isi corrupted m ary pam signals a decision feedback equalizer scheme is derived based on multiple hyperplane partitioning of signal space for detecting m ary pulse amplitude modulation symbols transmitted through a noisy intersymbol interference channel the proposed scheme is based on the fact that the optimal bayesian decision boundary separating two neighboring signal classes is asymptotically piecewise linear and consists of several hyperplanes when the signal to noise ratio tends to infinity an algorithm is developed to determine these hyperplanes which are then used to partition the observation signal space the resulting detector can closely approximate the optimal bayesian detector at an advantage of considerably reduced detector complexity

generalized isothermic lattices we study multi dimensional quadrilateral lattices satisfying simultaneously two integrable constraints a quadratic constraint and the projective moutard constraint when the lattice is two dimensional and the quadric under consideration is the mobius sphere one obtains after the stereographic projection the discrete isothermic surfaces defined by bobenko and pinkall by an algebraic constraint imposed on the complex cross ratio of the circular lattice we derive the analogous condition for our generalized isothermic lattices using steiner s projective structure of conics and we present basic geometric constructions which encode integrability of the lattice in particular we introduce the darboux transformation of the generalized isothermic lattice and we derive the corresponding bianchi permutability principle finally we study two dimensional generalized isothermic lattices in particular geometry of their initial boundary value problem

solutions to semilinear elliptic problems with combined nonlinearities abstract we are concerned with the following nonlinear dirichlet problem u h x u q f x u 0 u h 0 1 0 where is a bounded smooth domain in rn n 1 and h x l f x s is asymptotically linear with respect to s at infinity by a variant version of mountain pass theorem we prove that there exist at least two nonnegative solutions under suitable assumptions on f x s our methods also work for the cases where f x s is superlinear or linear in s

reductions of the multidimensional quadrilateral lattice the multidimensional circular lattice we apply a recently introduced 21 15 reduction method based on the dressing to construct a large class of integrable reductions of the equations characterizing the multidimensional quadrilateral lattice an n dimensional lattice in m n m whose elementary quadrilaterals are planar and whose continuous limit describes submanifolds parametrized by conjugate lines 11 we also show that generically in the limit of the small lattice parameter half of these reductions lead to the darboux equations for symmetric fields and the second half lead to the generalized lame equations describing n dimensional submanifolds of m parametrized by conjugate orthogonal systems of coordinates we finally show that a distinguished example of the second class of reductions corresponds to the multidimensional circular lattice an n dimensional lattice in m n m whose elementary quadrilaterals are inscribed in circles 7

integrable dynamics of a discrete curve and the ablowitz ladik hierarchy it is shown that the following elementary geometric properties of the motion of a discrete i e piecewise linear curve select the integrable dynamics of the ablowitz ladik hierarchy of evolution equations i the set of points describing the discrete curve lie in the sphere s3 ii the distance between any two subsequent points does not vary in time iii the equations of the dynamics do not depend explicitly on the radius of the sphere these results generalize to a discrete context the previous work on continuous curves a doliwa and p m santini phys lett a 185 373 1994 it is shown that the following elementary geometric properties of the motion of a discrete i e piecewise linear curve select the integrable dynamics of the ablowitz ladik hierarchy of evolution equations i the set of points describing the discrete curve lie in the sphere s3 ii the distance between any two subsequent points does not vary in time iii the equations of the dynamics do not depend explicitly on the radius of the sphere these results generalize to a discrete context the previous work on continuous curves a doliwa and p m santini phys lett a 185 373 1994

estimations of the transfer functions of noncatastrophic convolutional encoders a computational method which allows us to upper bound the solution of a wide class of systems of linear recurrent equations is proposed this method is used to estimate the transfer functions of noncatastrophic convolutional encoders

nontrivial solutions for neumann problems with an indefinite linear part abstract in this paper we consider a semilinear neumann problem with an indefinite linear part and a caratheodory nonlinearity which is superlinear near infinity and near zero but does not satisfy the ambrosetti rabinowitz condition using an abstract existence theorem for c 1 functions having a local linking at the origin we establish the existence of at least one nontrivial smooth solution

positive solutions for nonhomogeneous elliptic equations involving critical sobolev exponent abstract in this paper we study the existence and multiplicity of positive solutions for the dirichlet problem u f z u q 2 u g z u 2 2 u in where 0 1 q 2 2 2 n n 2 0 r n n 3 is a bounded domain with smooth boundary and f g are nonnegative continuous functions on

explicit solutions to the semi discrete modified kdv equation and motion of discrete plane curves we construct explicit solutions to continuous motion of discrete plane curves described by a semi discrete potential modified kdv equation explicit formulas in terms of the function are presented backlund transformations of the discrete curves are also discussed we finally consider the continuous limit of discrete motion of discrete plane curves described by the discrete potential modified kdv equation to motion of smooth plane curves characterized by the potential modified kdv equation

limited search trellis decoding of convolutional codes the least storage and node computation required by a breadth first tree or trellis decoder that corrects t errors over the binary symmetric channels is calculated breadth first decoders work with code paths of the same length without backtracking the viterbi algorithm is an exhaustive trellis decoder of this type other schemes look at a subset of the tree or trellis paths for random tree codes theorems about the asymptotic number of paths required and their depth are proved for concrete convolutional codes the worst case storage for t error sequences is measured in both cases the optimal decoder storage has the same simple dependence on t the m algorithm and algorithms proposed by g j foschini ibid vol it 23 p 605 9 sept 1977 and by s j simmons phd diss queens univ kingston ont canada are optimal or nearly so they are all far more efficient than the viterbi algorithm

combined effects of concave and convex nonlinearities in some elliptic problems abstract this paper deals with a class of semilinear elliptic dirichlet boundary value problems where the combined effects of a sublinear and a superlinear term allow us to establish some existence and multiplicity results

moving horizon design of discrete coefficient fir filters we show how the discrete coefficient filter design problem can be solved with a moving horizon optimization approach the computation time of this procedure is determined by the optimization horizon and does not grow exponentially with the filter length spl sigma spl delta design methods are a special case of the proposed procedure

trellis codes for periodic erasures this paper describes techniques for the design and analysis of trellis codes that provide reliable communication over every channel in a specified set of possible channels where each channel is characterized by additive white gaussian noise with a distinct periodic variation in signal to noise ratio an important practical application for such trellis codes is the periodic erasure channel produced by partial band interference dispersed by a block interleaver we present trellis codes that provide reliable communication over all periodic erasure patterns of a given period for which the number of unerased coded bits per period is at least equal to the number of information bits per period

on the error probability of signals in additive white gaussian noise a new upper bound to the probability of error in detecting one of m equally probable signals in additive white gaussian noise is presented this bound is easy to calculate can be applied to any signal set it is always better than the union and minimum distance bounds examples demonstrate the use of the bound

computing upper bounds to error probability of coded modulation schemes to evaluate an upper bound on error probabilities of signal constellations used for transmission over the additive white gaussian noise awgn channel enumeration of all the constellation intradistances is required these may be infinite in number for example when convolutional codes are used and the constellations are lattices truncation of the series does not necessarily provide a bound anymore and must be done with care yet the union bound is very simple as it does not require any further knowledge about the signal constellation than the distance enumerator in this paper we describe some methods that can be used to evaluate error probabilities of infinite signal constellations and that require only a finite number of terms these methods are applicable for example to convolutional codes decoded with a finite depth viterbi algorithm and to signal constellations carved from lattices coded modulations based on lattices and convolutional or block codes can also be dealt with as an example of application we analyze a variable rate 3 stage coded modulation encoder decoder which has been built and is based on a combination of convolutional codes with a single parity check block code

normalized ground states for the nls equation with combined nonlinearities abstract we study existence and properties of ground states for the nonlinear schrodinger equation with combined power nonlinearities u u u q 2 u u p 2 u in r n n 1 having prescribed mass r n u 2 a 2 under different assumptions on q p a 0 and r we prove several existence and stability instability results in particular we consider cases when 2 q 2 4 n p 2 q p i e the two nonlinearities have different character with respect to the l 2 critical exponent these cases present substantial differences with respect to purely subcritical or supercritical situations which were already studied in the literature we also give new criteria for global existence and finite time blow up in the associated dispersive equation

transformations of quadrilateral lattices motivated by the classical studies on transformations of conjugate nets we develop the general geometric theory of transformations of their discrete analogs the multidimensional quadrilateral lattices i e lattices x zn rm n m whose elementary quadrilaterals are planar our investigation is based on the discrete analog of the theory of the rectilinear congruences which we also present in detail we study in particular the discrete analogs of the laplace combescure levy radial and fundamental transformations and their interrelations the composition of these transformations and their permutability is also investigated from a geometric point of view the deep connections between transformations and discretizations is also investigated for quadrilateral lattices we finally interpret these results within the formalism

how good is quantized model predictive control with horizon one model predictive control is increasingly being used in areas where decision variables are constrained to finite or countably infinite sets well known fields include power electronics signal processing and telecommunications typically the applications utilize high speed sampling and thus there is an incentive to reduce computational burden one way of achieving this is to use small optimization horizons this raises the question as to the optimality and performance of control laws with short horizons in this paper we give necessary and sufficient conditions for horizon one quantized model predictive control to be equivalent to the use of larger horizons we also explore situations where horizon one is near optimal

variational elliptic problems which are nonquadratic at infinity p co if n 1 2 then it is well known that the weak solutions u e h 2 of p are the critical points of the c functional j u ulvul dx jcf x u dx where f x s jif x t dt in this variational setting the literature usually distinguishes between two situations for prob lem p the subquadratic situation where the potential f satisfies lim suplsl f x s s2 i c m and the superquadratic situation where f satisfies limlsl m f x s s2 00 the main goal of this paper is to present a unified approach to both situations by means of a condition of nonquadraticity at infinity on f more precisely our hypotheses are as follows

asymptotic bayesian decision feedback equalizer using a set of hyperplanes we present a signal space partitioning technique for realizing the optimal bayesian decision feedback equalizer dfe it is known that when the signal to noise ratio snr tends to infinity the decision boundary of the bayesian dfe is asymptotically piecewise linear and consists of several hyperplanes the proposed technique determines these hyperplanes explicitly and uses them to partition the observation signal space the resulting equalizer is made up of a set of parallel linear discriminant functions and a boolean mapper unlike the existing signal space partitioning technique of kim and moon 1998 which involves complex combinatorial search and optimization in design our design procedure is simple and straightforward and guarantees to achieve the asymptotic bayesian dfe

a variational approach to discontinuous problems with critical sobolev exponents abstract we employ variational techniques to study the existence and multiplicity of positive solutions of semilinear equations of the form u h x h u a uq u2 1 in rn where a 0 are parameters h x is both nonnegative and integrable on rn h is the heaviside function 2 is the critical sobolev exponent and 0 q

existence of solutions for quasilinear elliptic equations abstract using variational methods we study the existence and multiplicity of solutions of the dirichlet problem for the equation div a u p u p 2 u f x u

non uniformly asymptotically linear p laplacian problems abstract we relax conditions on uniform convergences of f x s s p 2 s which are essential in many results on multiplicity for asymptotically linear p laplacian problems

universal trellis codes for diagonally layered space time systems foschini s diagonally layered space time transmission system known as d blast is an architecture designed for a rayleigh fading environment using multiple element antenna arrays at both the transmit and receive sites to achieve very high spectral efficiencies in this paper we propose a simple coding technique for d blast that uses a single trellis code with finite traceback viterbi decoding we examine the performance of universal trellis codes that are designed to have a distance structure that is matched to the periodic signal to noise ratio snr variation of the channel created by d blast under the assumption that the channel is static during one burst but may change from burst to burst we show that a universal 64 state trellis code on a 2 spl times 2 d blast system with long enough block lengths displays universal behavior working on almost every 2 spl times 2 channel with at least the mutual information required by a standard 64 state awgn trellis code the only 2 spl times 2 channel where more mutual information is required is a certain rotation of the zero eigenvalue channel we also present 4 spl times 4 and 8 spl times 8 examples

geometrically uniform codes a signal space code c is defined as geometrically uniform if for any two code sequences in c there exists an isometry that maps one sequence into the other while leaving the code c invariant geometrical uniformity a strong kind of symmetry implies such properties as a the distance profiles from code sequences in c to all other code sequences are all the same and b all voronoi regions of code sequences in c have the same shape it is stronger than ungerboeck zehavi wolf symmetry or calderbank sloane regularity nonetheless most known good classes of signal space codes are shown to be generalized coset codes and therefore geometrically uniform including a lattice type trellis codes based on lattice partitions lambda lambda such that z sup n lambda lambda 4z sup n is a lattice partition chain and b phase shift keying psk type trellis codes based on up to four way partitions of a 2 sup n psk signal set

an optimal circular viterbi decoder for the bounded distance criterion we propose a viterbi type decoder for tailbiting trellis codes that works by traversing the tailbiting circle somewhat more than once the traversal is the least possible for any bounded distance viterbi decoder procedures are given that compute this minimum unlike previous decoders of the type the new scheme does not suffer limit cycles or from pseudocodewords the bit error rate is compared to that of bahl cocke jelinek raviv and maximum likelihood decoding

radial solutions of dirichlet problems with concave convex nonlinearities abstract we prove the existence of a double infinite sequence of radial solutions for a dirichlet concave convex problem associated with an elliptic equation in a ball of r n we are interested in relaxing the classical positivity condition on the weights by allowing the weights to vanish the idea is to develop a topological method and to use the concept of rotation number the solutions are characterized by their nodal properties

conditions for optimality of naive quantized finite horizon control this paper presents properties of a control law which quantizes the unconstrained solution to a unitary horizon quadratic programme this naive quantized control law underlies many popular algorithms such as converters and decision feedback equalities and is easily shown to be globally optimal for horizon one however the question arises as to whether it is also globally optimal for horizons greater than one i e whether it solves a finite horizon quadratic programme where decision variables are restricted to belonging to a quantized set by using dynamic programming we develop sufficient conditions for this to hold the present analysis is restricted to first order plants however this case already raises a number of highly non trivial issues the results can be applied to arbitrary horizons and quantized sets which may contain a finite or an infinite though countable number of elements

multidimensional signal space partitioning using a minimal set of hyperplanes for detecting isi corrupted symbols a signal space partitioning technique is presented for detecting symbols transmitted through intersymbol interference channels the decision boundary is piecewise linear and is made up of several hyperplanes the goal here is to minimize the number of hyperplanes for a given performance measure namely the minimum distance between any signal and the decision boundary unlike in voronoi partitioning individual hyperplanes are chosen to separate signal clusters rather than signal pairs the convex regions associated with individual signals which together form the overall decision region generally overlap or coincide among in class signals the technique leads to an asymptotically optimum detector when the target distance is set at half the minimum distance associated with the maximum likelihood sequence detector complexity and performance can be easily traded as the target distance is a flexible design parameter

non differentiable functionals and applications to elliptic problems with discontinuous nonlinearities abstract multiple critical points theorems for non differentiable functionals are established applications both to elliptic variational hemivariational inequalities and eigenvalue problems with discontinuous nonlinearities are then presented

decision depths of convolutional codes the decision depth function of a convolutional code l sub d w is the first trellis depth at which all unmerged incorrect subset paths exceed weight w the authors tabulate this function for most codes in common use l sub d w specifies the path memory length of a decoder it follows a clear asymptotic growth rule

triple solutions for nonlinear elliptic problems driven by a non homogeneous operator abstract some multiplicity results for a parametric nonlinear dirichlet problem involving a nonhomogeneous differential operator of p laplacian type are given via variational methods the article furnishes new contributions and completes some previous results obtained for problems considering other types of differential operators and or nonlinear terms satisfying different asymptotic conditions

reliability output decoding of tail biting convolutional codes we present extensions to raghavan and baum s reliability output viterbi algorithm rova to accommodate tail biting convolutional codes these tail biting reliability output algorithms compute the exact word error probability of the decoded codeword after first calculating the posterior probability of the decoded tail biting codeword s starting state one approach employs a state estimation algorithm that selects the maximum a posteriori state based on the posterior distribution of the starting states another approach is an approximation to the exact tail biting rova that estimates the word error probability a comparison of the computational complexity of each approach is discussed in detail the presented reliability output algorithms apply to both feedforward and feedback tail biting convolutional encoders these tail biting reliability output algorithms are suitable for use in reliability based retransmission schemes with short blocklengths in which terminated convolutional codes would introduce rate loss

techniques of bounding the probability of decoding error for block coded modulation structures two techniques for upper bounding the average probability of decoding error in coded modulation structures are presented the first bound which is applicable to the additive white gaussian noise awgn channel is tighter than the well known union bound and the minimum distance bound especially for low signal to noise ratio it is shown that for the leech lattice this upper bound is very close to a sphere lower bound for the second upper bound which is applicable to any memoryless channel not necessarily awgn a method of random coset coding is presented for the awgn channel a tighter upper bound is obtained by employing the method of random coset coding for calculating the average spectrum of distances of the code which is required for the computation of the first upper bound

multiple solutions of an even order nonlinear problem with convex concave nonlinearity abstract we study multiple solutions of an even order nonlinear partial differential equation with a dirichlet boundary condition a related class of nonlinear systems is investigated

brief constrained linear state estimation a moving horizon approach this article considers moving horizon strategies for constrained linear state estimation additional information for estimating state variables from output measurements is often available in the form of inequality constraints on states noise and other variables formulating a linear state estimation problem with inequality constraints however prevents recursive solutions such as kalman filtering and consequently the estimation problem grows with time as more measurements become available to bound the problem size we explore moving horizon strategies for constrained linear state estimation in this work we discuss some practical and theoretical properties of moving horizon estimation we derive sufficient conditions for the stability of moving horizon state estimation with linear models subject to constraints on the estimate we also discuss smoothing strategies for moving horizon estimation our framework is solely deterministic

computing upper bounds to error probability of soft decision decoding of reed solomon codes based on the ordered statistics algorithm this correspondence presents performance analysis of symbol level soft decision decoding of q ary maximum distance separable mds codes based on the ordered statistics algorithm the method we present is inspired by the one recently proposed by agrawal and vardy 2000 who approximately evaluate the performance of generalized minimum distance decoding the correspondence shows that in our context the method allows us to compute the exact value of the probability that the transmitted codeword is not one of the candidate codewords this leads to a close upper bound on the performance of the decoding algorithm application of the ordered statistics algorithm to mds codes is not new nevertheless its advantages seem not to be fully explored we show an example where the decoding algorithm is applied to singly extended 16 ary reed solomon rs codes in a 128 dimensional multilevel coded modulation scheme that approaches the sphere lower bound within 0 5 db at the word error probability of 10 sup 4 with manageable decoding complexity