a unified method for evaluating the error correction radius of reliability based soft decision algorithms for linear block codes this paper presents a unified method for evaluating the error correction radii of many reliability based soft decision decoding algorithms for binary linear block codes based on this unified method these decoding algorithms as well as their potential improvements can be compared directly the error correction radius for each of these decoding algorithms is determined by finding the closest point on the boundary of the decision region of the soft decision decoder to the transmitted signal sequence it is shown that this problem can be formulated as a constrained optimization problem although no general closed form expression is possible a simple algorithm that always converges to the optimum solution of this optimization problem is presented based on these results the error correction radii of some well known reliability based soft decision decoding algorithms are revisited and compared

a bounded distance decoding algorithm for the leech lattice with generalizations an algorithm is given that decodes the leech lattice with not much more than twice the complexity of soft decision decoding of the golay code the algorithm has the same effective minimum distance as maximum likelihood decoding and increases the effective error coefficient by less than a factor or two the algorithm can be recognized as a member of the class of multistage algorithms that are applicable to hierarchical constructions it is readily generalized to lattices that can be expressed in terms of binary code formulas and in particular to construction b lattices

white noise driven ostrovsky equation abstract the current paper is devoted to the cauchy problem for the white noise driven ostrovsky equation with positive dispersion we obtain the local well posedness for the initial data u 0 h s r a e which is f 0 measurable with s 3 4 and l 2 0 s l 2 0 l 2 r h s 1 2 r and the globally well posedness for the initial data u 0 l 2 r a e which is f 0 measurable and l 2 0 0 l 2 0 l 2 r h 0 1 2 r the key ingredients that we used in this paper are some bilinear estimates in x s b type spaces given in subsection 2 1 ito formula the bdg inequality and stopping time techniques as well as frequency truncated technique our method can be applied to the case 0 which is just the kdv equation thus our result improves the local well posedness result of a de bouard a debussche and y tsutsumi 1999 3

on a stochastic nonlinear equation in one dimensional viscoelasticity in this paper we discuss an initial boundary value problem for a stochastic nonlinear equation arising in one dimensional viscoelasticity we propose to use a new direct method to obtain a solution this method is expected to be applicable to a broad class of nonlinear stochastic partial differential equations

first order soliton perturbation theory for a generalized kdv model with stochastic forcing and damping we discuss an application of the expansion method to the soliton perturbation theory for a generalized kdv model with stochastic forcing and damping we find that the expansion method is a perturbation technique which allows one to retain a more representative linearization for a nonlinear differential equation than comparable methods of perturbation such as those relying on small parameters indeed one primary benefit of the method is that it tends to provide much more reasonable solutions with relatively few terms compared to standard perturbation methods due to the more accurate linearization we show that the method allows one to obtain first order perturbations in which the stochastic and nonlinear contributions separate allowing one to study each influence independently at least to first order we then apply the expansion method to the study of a stochastic generalized kdv model and we show that this procedure gives a natural extension to the perturbation theory for the traditional kdv model the actual method of computation is outlined and may be applied to a variety of generalized kdv models

local smoothing properties of dispersive equations is it possible for time evolution partial differential equations which are reversible and conservative to smooth locally the initial data for the linear wave equation for instance the answer is no however in 10 t kato found a local smoothing property of the korteweg de vries equation the solution of the initial value problem is locally one derivative smoother than the initial datum kato s proof uses in a curcial way the algebraic properties of the symbol for the korteweg de vries equation and the fact that the underlying spatial dimension is one actually judging from the way several integrations by parts and cancellations conspire to reveal a smoothing effect one would be inclined to believe this was a special property of the k dv equation this is not however the case in this paper we attempt to describe a general local smoothing effect for dispersive equations and systems the smoothing effect is due to the dispersive nature of the linear part of the equation all the physically significant dispersive equations and systems known to us have linear parts displaying this local smoothing property to mention only a few the k dv benjamin ono intermediate long wave various boussinesq and schrodinger equations are included we study thus equations and systems of the form

exact solutions for wick type stochastic coupled kadomtsev petviashvili equations the coupled kadomtsev petviashvili kp equations with variable coefficients and wick type stochastic coupled kp equations are investigated exact solutions are shown using the hermite transform the homogeneous balance principle and the f expansion method

an auto backlund transformation and exact solutions for wick type stochastic generalized kdv equations wick type stochastic generalized kdv equations are researched by using the homogeneous balance an auto backlund transformation to the wick type stochastic generalized kdv equations is derived and stochastic single soliton and stochastic multi soliton solutions are shown by using the hermite transform

numerical simulation of the stochastic korteweg de vries equation abstract in this work we numerically investigate the influence of a homogeneous noise on the evolution of solitons for the korteweg de vries equation our numerical method is based on finite elements and least squares we present numerical experiments for different values of noise amplitude and describe different types of behaviours

geometrical and performance analysis of gmd and chase decoding algorithms the overall number of nearest neighbors in bounded distance decoding bdd algorithms is given by n sub 0 eff n sub 0 n sub bdd where nbdd denotes the number of additional non codeword neighbors that are generated during the suboptimal decoding process we identify and enumerate the nearest neighbors associated with the original generalized minimum distance gmd and chase 1972 decoding algorithms after careful examination of the decision regions of these algorithms we derive an approximated probability ratio between the error contribution of a noncodeword neighbor one of n sub bdd points and a codeword nearest neighbor for chase algorithm 1 it is shown that the contribution to the error probability of a noncodeword nearest neighbor is a factor of 2 sup d 1 less than the contribution of a codeword while for chase algorithm 2 the factor is 2 sup d 2 1 d being the minimum hamming distance of the code for chase algorithm 3 and gmd a recursive procedure for calculating this ratio which turns out to be nonexponential in d is presented this procedure can also be used for specifically identifying the error patterns associated with chase algorithm 3 and gmd utilizing the probability ratio we propose an improved approximated upper bound on the probability of error based on the union bound approach simulation results are given to demonstrate and support the analytical derivations

a note on limited trial chase like algorithms achieving bounded distance decoding for the decoding of a binary linear block code of minimal hamming distance d over additive white gaussian noise awgn channels a soft decision decoder achieves bounded distance bd decoding if its squared error correction radius is equal to d a chase like algorithm outputs the best most likely codeword in a list of candidates generated by a conventional algebraic binary decoder in a few trials it is of interest to design chase like algorithms that achieve bd decoding with as least trials as possible in this paper we show that chase like algorithms can achieve bd decoding with only o d 1 2 epsiv trials for any given positive number epsiv

asymptotic optimality of the gmd and chase decoding algorithms the generalized minimum distance gmd and chase 1972 decoding algorithms are some of the most important suboptimum bounded distance decoding algorithms for binary linear block codes over an additive white gaussian noise awgn channel we compute the limitation of the ratio between the probability of decoding error for the gmd or any one of the chase decoding algorithms and that of the maximum likelihood ml decoding when the signal to noise ratio snr approaches infinity if the minimum hamming distance of the code is greater than 2 the limitation is shown to be equal to 1 and thus the gmd and chase decoding algorithms are asymptotically optimum

on the stochastic korteweg de vries equation abstract we consider a stochastic korteweg de vries equation forced by a random term of white noise type this can be a model of water waves on a fluid submitted to a random pressure we prove existence and uniqueness of solutions inh1 r in the case of additive noise and existence of martingales solutions inl2 r in the case of multiplicative noise copyright 1998 academic press nous etudions une equation de korteweg de vries stochastique comportant une force aleatoire de type bruit blanc cette equation peut decrire les ondes de surface sur un fluide soumis a un champ de pression aleatoire nous montrons l existence et l unicite de solutions dansh1 r lorsque le bruit est additif puis dans le cas du bruit multiplicatif nous etablissons l existence de solutions martingales dansl2 r

some exact wick type stochastic generalized boussinesq equation solutions the resolution of the stochastic generalized boussinesq equation driven by a white noise is undertaken explicit solutions are found thanks to a white noise functional approach and the f expansion method among these solutions periodic and solitonic ones are pointed out

white noise functional solutions of wick type stochastic generalized hirota satsuma coupled kdv equations generalized hirota satsuma coupled kdv equations with variable coefficients and wick type stochastic generalized hirota satsuma coupled kdv equations are investigated white noise functional solutions are shown by hermite transform homogeneous balance principle and f expansion method

the stochastic korteweg de vries equation inl2 r abstract we present here two results of global existence and uniqueness of the cauchy problem concerning the korteweg de vries equation forced by a random term of white noise type in the functional framework of weighted spaces on l 2 r this work is motivated by both physical experiments where a forced generation of weakly nonlinear waves by localized disturbances was observed 1 15 and a result of uniqueness in weighted space in the homogeneous case 8 14

stochastic production frontiers and panel data a latent variable framework abstract this paper deals with the issue of estimating production frontier and measuring efficiency from a panel data set first it proposes an alternate method for the estimation of a production frontier on a short panel data set the method is based on the so called mean and covariance structure analysis which is closely related to the generalized method of moments one advantage of the method is that it allows us to investigate the presence of correlations between individual effects and exogenous variables without the requirement of some available instruments uncorrelated with the individual effects as in instrumental variable estimation another advantage is that the method is well suited to a panel data set with a short number of periods second the paper considers the question of recovering individual efficiency levels from the estimates obtained from the mean and covariance structure analysis since individual effects are here viewed as latent variables they can be estimated as factor scores i e weighted sums of the observed variables we illustrate the proposed methods with the estimation of a stochastic production frontier on a short panel data of french fruit growers

well posedness and blow up solution for the stochastic dullin gottwald holm equation in this paper to describe the uncertainty from external environment we propose a stochastic dullin gottwald holm sdgh equation by adding an additive noise to the well known dgh equation using regularization the local existence and uniqueness of the solution of sdgh are proved by means of a priori estimates we find that the local solution may blow up in a finite time if the initial value satisfies certain conditions in this paper to describe the uncertainty from external environment we propose a stochastic dullin gottwald holm sdgh equation by adding an additive noise to the well known dgh equation using regularization the local existence and uniqueness of the solution of sdgh are proved by means of a priori estimates we find that the local solution may blow up in a finite time if the initial value satisfies certain conditions

three types of exact solutions to wick type generalized stochastic korteweg de vries equation a wick type generalized stochastic korteweg de vries equation is researched by means of hermite transformation white noise theory and riccati equation mapping method three types of exact solutions to the generalized stochastic korteweg de vries equation which include the functional solutions of hyperbolic exponential type trigonometric exponential type and exponential type are derived

on the stochastic benjamin ono equation abstract we discuss the cauchy problem for the stochastic benjamin ono equation in the function class h s r s 3 2 when there is a zero order dissipation we also establish the existence of an invariant measure with support in h 2 r many authors have discussed the cauchy problem for the deterministic benjamin ono equation but our results are new for the stochastic benjamin ono equation our goal is to extend known results for the deterministic equation to the stochastic equation

generalized minimum distance decoding of euclidean space codes and lattices it is shown that multistage generalized minimum distance gmd decoding of euclidean space codes and lattices can provide an excellent tradeoff between performance and complexity we introduce a reliability metric for gaussian channels that is easily computed from an inner product and prove that a multistage gmd decoder using this metric is a bounded distance decoder up to the true packing radius the effective error coefficient of multistage gmd decoding is determined two simple modifications in the gmd decoding algorithm that drastically reduce this error coefficient are proposed it is shown that with these modifications gmd decoding achieves the error coefficient of maximum likelihood decoding for block codes and for generalized construction a lattices multistage gmd decoding of the lattices d sub 4 e sub 8 k sub 12 bw sub 16 and spl lambda sub 24 is investigated in detail for k sub 12 bw sub 16 and spl lambda sub 24 the gmd decoders have considerably lower complexity than the best known maximum likelihood or bounded distance decoding algorithms and appear to be the most practically attractive decoders available for high dimensional codes and lattices spl ges 64 dimensions maximum likelihood decoding becomes infeasible while gmd decoding algorithms remain quite practical as an example we devise a multistage gmd decoder for a 128 dimensional sphere packing with a nominal coding gain of 8 98 db that attains an effective error coefficient of 1365760 this decoder requires only about 400 real operations in addition to algebraic errors and erasures decoding of certain bch and hamming codes it therefore appears to be practically feasible to implement algebraic multistage gmd decoders for high dimensional sphere packings and thus achieve high effective coding gains

a series of exact solutions for 2 1 dimensional wick type stochastic generalized broer kaup system via a modified variable coefficient projective riccati equation mapping method abstract a modified variable coefficient projective riccati equation mapping method is applied to 2 1 dimensional wick type stochastic generalized broer kaup system with the help of hermit transformation we obtain a series of new exact stochastic solutions to the stochastic broer kaup system in the white noise environment

white noise driven korteweg de vries equation abstract we consider a stochastic korteweg de vries equation on the real line the noise is additive we use function spaces similar to those introduced by bourgain to prove well posedness results for the korteweg de vries equation in l 2 r we are able to handle a noise which is locally white in space and time more precisely it is a space time white noise multiplied by an l 2 function of the space variable due to the lack of a priori estimates we can only get a local existence result in time however we obtain the global existence of l 2 r solutions when the covariance operator of the noise is hilbert schmidt in l 2 r

a bounded distance decoding algorithm for binary linear block codes achieving the minimum effective error coefficient a new bounded distance bd decoding algorithm is presented for binary linear n k d block codes on additive white gaussian noise channels the algorithm is based on the generalized minimum distance gmd decoding algorithm of forney 1989 using the acceptance criterion of taipale and pursley gmd tp proposed in 1991 it is shown that the gmd tp decoding algorithm is a bd decoding algorithm with effective error coefficient sup n sub d it is also shown that the decision regions of gmd tp are good inner approximations of those of full gmd decoding and therefore full gmd decoding is bd and has an effective error coefficient that is well approximated by sup n sub d moreover by adding a d erasure correction step to gmd decoding the effective error coefficient can be reduced to a sub d the number of minimum weight codewords which is the same as the effective error coefficient of maximum likelihood decoding the decoding algorithm is mainly based on algebraic errors and erasures decoding and therefore has polynomial rather than exponential complexity

well posedness of the initial value problem for the korteweg de vries equation 1 1 itu axu u1xu o x t e r u x 0 uo x the kdv equation which was first derived as a model for unidirectional propagation of nonlinear dispersive long waves 21 has been considered in different contexts namely in its relation with the inverse scattering method in plasma physics and in algebraic geometry see 24 and references therein our purpose is to study local and global well posedness of the ivp 1 1 in classical sobolev spaces hs r we shall say that the ivp 1 1 is locally resp globally well posed in the function space x if it induces a dynamical system on x by generating a continuous local resp global flow it was established in the works of bona and smith 3 bona and scott 2 saut and temam 30 and kato 1 5 that the ivp 1 1 is locally resp globally well posed in hs with s 3 2 resp s 2 roughly speaking global well posedness in hs depends on the available local theory and on the conservation laws satisfied by solutions of 1 1 namely

martingale and stationary solutions for stochastic navier stokes equations we prove the existence of martingale solutions and of stationary solutions of stochastic navier stokes equations under very general hypotheses on the diffusion term the stationary martingale solutions yield the existence of invariant measures when the transition semigroup is well defined the results are obtained by a new method of compactness