on solutions of the initial value problem for the nonlinear schrodinger equations on considere le probleme aux valeurs initiales pour l equation de schrodinger non lineaire de la forme iu t u f u 2 u t x r r n u 0 x x x r n on etudie la regularite des solutions quand les fonctions initiales ne sont pas regulieres

vacuum isolating blow up threshold and asymptotic behavior of solutions for a nonlocal parabolic equation in this paper we consider a nonlocal parabolic equation associated with initial and dirichlet boundary conditions first we discuss the vacuum isolating behavior of solutions with the help of a family of potential wells then we obtain a threshold of global existence and blow up for solutions with critical initial energy furthermore for those solutions that satisfy j u0 d and i u0 0 we show that global solutions decay to zero exponentially as time tends to infinity and the norm of blow up solutions increases exponentially

global existence nonexistence and asymptotic behavior of solutions for the cauchy problem of semilinear heat equations abstract in this paper we study the cauchy problem of semilinear heat equations by introducing a family of potential wells we first prove the invariance of some sets and isolating solutions then we obtain a threshold result for the global existence and nonexistence of solutions finally we discuss the asymptotic behavior of the solution

soft output decoding of rotationally invariant codes over channels with phase noise we consider rotationally invariant ri trellis coded modulations tcms transmitted over channels affected by phase noise to describe the main ideas of this paper we first concentrate as a case study on the simplest ri scheme namely the differentially encoded m ary phase shift keying m psk signal for this problem we use the framework based on factor graphs fgs and the sum product algorithm spa to derive the exact maximum a posteriori map symbol detection algorithm by analyzing its properties we demonstrate that it can be implemented by a forward backward estimator of the phase probability density function followed by a symbol by symbol completion to produce the a posteriori probabilities of the information symbols to practically implement the forward backward phase estimator we propose a couple of schemes with different complexity the resulting algorithms exhibit an excellent performance and in one case only a limited complexity increases with respect to the algorithm that perfectly knows the channel phase the properties of the optimal decoder and the proposed practical decoding schemes are then extended to the case of a generic ri code the proposed soft output algorithms can also be used in iterative decoding schemes for concatenated codes employing ri inner components among them in the numerical results we consider repeat accumulate ra codes and other serially concatenated schemes recently proposed in the technical literature

blow up of h1 solution for the nonlinear schrodinger equation we consider the blow up of the solution in h1 for the following nonlinear schrodinger equation i tu u u p 1u x rn t 0 u 0 x u0 x x rn t 0 where n 2 and 1 4 n p min n 2 n 2 5 we prove that if the initial data u0 in h1 are radially symmetric and have negative energy then the solution of in h1 blows up in finite time we do not assume that xu0 l2 and therefore our result is the generalization of the results of glassey 4 and m tsutsumi 18 for the radially symmetric case

design of regular 2 d sub c ldpc codes over gf q using their binary images in this paper a method to design regular 2 dc ldpc codes over gf q with both good waterfall and error floor properties is presented based on the algebraic properties of their binary image first the algebraic properties of rows of the parity check matrix h associated with a code are characterized and optimized to improve the waterfall then the algebraic properties of cycles and stopping sets associated with the underlying tanner graph are studied and linked to the global binary minimum distance of the code finally simulations are presented to illustrate the excellent performance of the designed codes

complex ginzburg landau equation with nonlocal coupling a ginzburg landau type equation with nonlocal coupling is derived systematically as a reduced form of a universal class of reaction diffusion systems near the hopf bifurcation point and in the presence of another small parameter the reaction diffusion systems to be reduced are such that the chemical components constituting local oscillators are nondiffusive or hardly diffusive so that the oscillators are almost uncoupled while there is an extra diffusive component which introduces effective nonlocal coupling over the oscillators linear stability analysis of the reduced equation about the uniform oscillation is also carried out this revealed that new types of instability which can never arise in the ordinary complex ginzburg landau equation are possible and their physical implication is briefly discussed

short non binary low density parity check codes for phase noise channels this paper considers the design of short non binary low density parity check ldpc codes over finite fields of order m for channels with phase noise in particular m ary differential phase shift keying dpsk modulated code symbols are transmitted over an additive white gaussian noise awgn channel with the wiener phase noise at the receiver side non coherent detection takes place with the help of a multi symbol detection algorithm followed by a non binary decoding step both the detector and the decoder operate on a joint factor graph as a benchmark finite length bounds and information rate expressions are computed and compared with the codeword error rate cer performance as well as the iterative threshold of the obtained codes as a result performance within 1 2 db from finite length bounds is obtained down to a cer of 10 3

channel coding rate in the finite blocklength regime this paper investigates the maximal channel coding rate achievable at a given blocklength and error probability for general classes of channels new achievability and converse bounds are given which are tighter than existing bounds for wide ranges of parameters of interest and lead to tight approximations of the maximal achievable rate for blocklengths n as short as 100 it is also shown analytically that the maximal rate achievable with error probability isclosely approximated by c v n q 1 where c is the capacity v is a characteristic of the channel referred to as channel dispersion and q is the complementary gaussian cumulative distribution function

finite time blow up and global existence for the nonlocal complex ginzburg landau equation abstract in this paper we consider the cauchy problem for a family of nonlocal complex ginzburg landau equation e i u t u 1 x n u p u p 2 u u on r n where 2 2 and r first the local well posedness in lebesgue spaces is established by a fixed point argument then we set up the h 2 regularity and derive the energy identities by constructing some invariant sets we further find some sufficient conditions on finite time blow up and global existence for solutions which in particular determines a sharp threshold of initial date when 0 in addition we estimate the lifespan of solutions as a function of and obtain the lower bound of the maximal existence time for r

stable and unstable manifolds for the nonlinear wave equation with dissipation on considere la stabilite pour des solutions solitons stationnaires du probleme de cauchy sur r n u tt u t u f u 0 u x 0 u t x 0 donnes

design of repeat accumulate codes for iterative detection and decoding extrinsic information transfer exit charts are used to design systematic and nonsystematic repeat accumulate ra codes for iterative detection and decoding the convergence problems of nonsystematic ra codes are solved by introducing a biregular or doped layer of check nodes as examples such nonsystematic codes are designed for multi input multi output mimo fading channels and are shown to operate close to capacity

strong instability of standing waves for a nonlocal schrodinger equation abstract variational methods are used to prove that the solutions of the nonlocal schrodinger equation i t p 2 v x p 0 x r n must blow up for a class of initial data with nonnegative energy and some restriction on p then using this we prove that the standing wave must be h 1 r n strongly unstable with respect to the nonlocal nonlinear schrodinger equation

design and analysis of nonbinary ldpc codes for arbitrary discrete memoryless channels we present an analysis under the iterative decoding of coset low density parity check ldpc codes over gf q designed for use over arbitrary discrete memoryless channels particularly nonbinary and asymmetric channels we use a random coset analysis to produce an effect that is similar to output symmetry with binary channels we show that the random selection of the nonzero elements of the gf q parity check matrix induces a permutation invariance property on the densities of the decoder messages which simplifies their analysis and approximation we generalize several properties including symmetry and stability from the analysis of binary ldpc codes we show that under a gaussian approximation the entire q 1 dimensional distribution of the vector messages is described by a single scalar parameter like the distributions of binary ldpc messages we apply this property to develop extrinsic information transfer exit charts for our codes we use appropriately designed signal constellations to obtain substantial shaping gains simulation results indicate that our codes outperform multilevel codes at short block lengths we also present simulation results for the additive white gaussian noise awgn channel including results within 0 56 db of the unrestricted shannon limit i e not restricted to any signal constellation at a spectral efficiency of 6 bits s hz

decoding algorithms for nonbinary ldpc codes over gf q in this letter we address the problem of decoding nonbinary low density parity check ldpc codes over finite fields gf q with reasonable complexity and good performance in the first part of the letter we recall the original belief propagation bp decoding algorithm and its fourier domain implementation we show that the use of tensor notations for the messages is very convenient for the algorithm description and understanding in the second part of the letter we introduce a simplified decoder which is inspired by the min sum decoder for binary ldpc codes we called this decoder extended min sum ems we show that it is possible to greatly reduce the computational complexity of the check node processing by computing approximate reliability measures with a limited number of values in a message by choosing appropriate correction factors or offsets we show that the ems decoder performance is quite good and in some cases better than the regular bp decoder the optimal values of the factor and offset correction are obtained asymptotically with simulated density evolution our simulations on ultra sparse codes over very high order fields show that nonbinary ldpc codes are promising for applications which require low frame error rates for small or moderate codeword lengths the ems decoder is a good candidate for practical hardware implementations of such codes

on the information rate and repeat accumulate code design for phase noise channels we investigate the information rate of channels affected by phase noise aiming at predicting the ultimate performance limits in this scenario moreover a closed form upper bound is also derived for phase shift keying psk modulations finally we consider the design of nonsystematic irregular repeat accumulate ra codes for this channel trying to give new insights on the codes to be employed for such an application

sharp thresholds of blow up and global existence for the coupled nonlinear schrodinger system in this paper we establish two new types of invariant sets for the coupled nonlinear schrodinger system in the euclidean n space rn and derive two sharp thresholds of blow up and global existence for its solutions some analogous results for the nonlinear schrodinger system posed on the hyperbolic space hn and on the standard 2 sphere s2 are also presented our arguments and constructions are improvements of some previous works on this direction at the end we give some heuristic analysis about the strong instability of the solitary waves the relation between the two types of thresholds is a very interesting problem and we leave it as an open problem for further study

ldpc codes over rings for psk modulation this paper describes the design and analysis of low density parity check ldpc codes over rings and shows how these codes when mapped onto appropriate signal constellations can be used to effect bandwidth efficient modulation specifically ldpc codes are constructed over the integer rings spl zopf sub m and g sub m sup 2 and mapped onto phase shift keying psk type signal sets to yield geometrically uniform signal space codes this paper identifies and addresses the design issues that affect code performance examples of codes over spl zopf sub 8 and g sub 64 mapped onto 8 ary and 64 ary signal sets at a spectral efficiency of 1 5 and 2 0 bits per second per hertz b s hz illustrate the approach simulation of these codes over the additive white gaussian noise awgn channel demonstrates that this approach is a good alternative to bandwidth efficient techniques based on binary ldpc codes e g bit interleaved coded modulation

invariant sets and the blow up threshold for a nonlocal equation of parabolic type abstract in this paper we consider a nonlocal equation of parabolic type on a bounded smooth domain with dirichlet boundary condition first the well posedness in lebesgue spaces is established by using the banach fixed point theorem then we set up the regularity of the solution more interestingly we find the invariant sets for the initial boundary value problem and derive a threshold of blow up and global existence for its solution

bounds on the error probability of block codes over the q ary erasure channel in this paper tight bounds on the block error probability of linear block codes over order q finite fields for the q ary erasure channel under maximum likelihood ml decoding are developed upper bounds are obtained for uniform parity check ensembles sparse parity check ensembles general parity check ensembles e g gallager regular nonbinary low density parity check ensembles and for any given linear code with known distance spectrum the tightness of the upper bounds is confirmed both by the comparison with simple lower bounds and for gallager low density parity check ensembles by extensive monte carlo simulations exploiting the derived bounds it is shown how already for short blocks and small q 2 sparse ensembles attain block error probabilities close to those of idealized maximum distance separable mds codes down to low error probabilities whereas in the same regime binary codes show visible losses with respect to the singleton bound thanks to the accurate performance estimates the developed bounds can support the design of near optimum erasure correcting codes with short and moderate lengths