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

regular problem for solutions of a retarded semilinear differential nonlocal equation abstract this paper deals with the regularity and existence of solutions of a retarded semilinear differential equation with nonlocal condition by using the fundamental solution in the case where the principal operators are unbounded operators

transfer matrix eigenvalues of the anisotropic multiparametric u model a multiparametric extension of the anisotropic u model is discussed which maintains integrability the r matrix solving the yang baxter equation is obtained through a twisting construction applied to the underlying u q sl 2 1 superalgebraic structure which introduces the additional free parameters that arise in the model three forms of bethe ansatz solution for the transfer matrix eigenvalues are given which we show to be equivalent

code design for iterative decoding of multilevel codes the code design problem for multilevel coded modulation with iterative decoding mlcm id has been left unsolved over a decade in this paper we define the code design criterion for mlcm id based on a novel concept parametrically mapped exit pm exit function we derive the exit functions for mlcm id and present the mathematical work by which the three area theorems of pm exit function are proved this gives theoretical support of the curve fitting techniques used in mlcm id and also provides firm proof that the pm exit function design rule allows in principle capacity achieving code assignment the simulation results perfectly match the theoretical analysis and also confirm that the design rule proposed fully exploits the flexibility of mlcm id in the choice of codes both in theory and simulations our code design is verified

rate gains in block coded modulation systems with interblock memory this paper examines the performance gains achievable by adding interblock memory to and altering the mapping of coded bits to symbols in block coded modulation systems the channel noise considered is additive gaussian and the twin design goals are to maximize the asymptotic coding gain and to minimize the number of apparent nearest neighbors in the case of the additive white gaussian noise channel these goals translate into the design of block codes of a given weighted or normalized distance whose rate is as high as possible and whose number of codewords at minimum normalized distance is low the effect of designing codes for normalized distance rather than hamming distance is to ease the problem of determining the best codes for given parameters in the cases of greatest interest and many such best codes are given

tables of sphere packings and spherical codes the theta function of a sphere packing gives the number of centers at each distance from the origin the theta functions of a number of important packings a n d n e n the leech lattice and others and tables of the first fifty or so of their coefficients are given in this paper

a class of optimum block codes in signal space by using convolutional coding coupled with expanded sets of channel signals ungerboeck showed that it is possible to obtain coding gains of several decibels at a given data rate without increasing the transmission bandwidth in this paper we construct a class of optimum signal space codes using short binary block as opposed to convolutional codes our results are compared to those obtained by ungerboeck a simplified decoding procedure that is asymptotically optimum is also presented

l2 regularity for parabolic partial integrodifferential equations with delay in the highest order derivatives abstract a partial integrodifferential equation is studied in which the derivatives of highest order also contain a discrete and a distributed delay by means of abstract regularity results global existence and uniqueness of a strict solution are obtained moreover a characterization of the infinitesimal generator of the solution operator is given

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

channel coding with multilevel phase signals a coding technique is described which improves error performance of synchronous data links without sacrificing data rate or requiring more bandwidth this is achieved by channel coding with expanded sets of multilevel phase signals in a manner which increases free euclidean distance soft maximum likelihood ml decoding using the viterbi algorithm is assumed following a discussion of channel capacity simple hand designed trellis codes are presented for 8 phase shift keying psk and 16 quadrature amplitude shift keying qask modulation these simple codes achieve coding gains in the order of 3 4 db it is then shown that the codes can be interpreted as binary convolutional codes with a mapping of coded bits into channel signals which we call mapping by set partitioning based on a new distance measure between binary code sequences which efficiently lower bounds the euclidean distance between the corresponding channel signal sequences a search procedure for more powerful codes is developed codes with coding gains up to 6 db are obtained for a variety of multilevel phase modulation schemes simulation results are presented and an example of carrier phase tracking is discussed

optimal control of linear retarded systems in banach spaces this paper deals with standard optimal control problems namely the fixed time integral convex cost problem and the time optimal control problem for linear retarded systems in banach spaces for the basis of optimal control theory the fundamental solution is constructed and a variation of constant formula of mild solutions is established after the controlled system description and the formulation of optimal control problems are given the retarded adjoint system is introduced for the integral convex cost problem two existence theorems of optimal controls and necessary conditions of optimality are given these conditions are precisely characterized by the solution of retarded adjoint system the pointwise maximum principle for time varying control domain is derived from the optimality conditions the bang bang principle is also established for the terminal value cost problem under some regularity condition of the adjoint system for the time optimal control problem to a target set an existence theorem is shown in the case where the target set has interior the maximum principle and the bang bang principle are established for the time optimal control finally a convergence theorem of time optimal controls to a point target set is given this paper also contains illustrative examples which give technologically important control problems

algebraic bethe ansatz for 19 vertex models with reflection conditions in this work we solve the 19 vertex models with the use of algebraic bethe ansatz for diagonal reflection matrices sklyanin k matrices the eigenvectors eigenvalues and bethe equations are given in a general form quantum spin chains of spin one derived from the 19 vertex models were also discussed

quantum spin chain with soliton non preserving boundary conditions we consider the case of an integrable quantum spin chain with soliton non preserving boundary conditions this is the first time that such boundary conditions have been considered in the spin chain framework we construct the transfer matrix of the model we study its symmetry and we find explicit expressions for its eigenvalues moreover we derive a new set of bethe ansatz equations by means of the analytical bethe ansatz method

concatenated multilevel block coded modulation encoding and decoding schemes for concatenated multilevel block codes are presented by one of these structures a real coding gain of 5 6 7 4 db for the bit error range of 10 sup 6 to 10 sup 9 is achieved for transmission through the additive white gaussian noise channel also a rather large asymptotic coding gain is obtained the new coding schemes have very low decoding complexity and increased coding gain in comparison with the conventional block and trellis coded modulation structures a few design rules for concatenated single and multilevel block codes with large coding gain are also provided

long range deformations for integrable spin chains we present a recursion relation for the explicit construction of integrable spin chain hamiltonians with long range interactions based on arbitrary shortrange e g nearest neighbor integrable spin chains it allows us to construct an infinite set of conserved long range charges we explain the moduli space of deformation parameters by different classes of generating operators the rapidity map and dressing phase in the long range bethe equations are a result of these deformations the closed chain asymptotic bethe equations for long range spin chains transforming under a generic symmetry algebra are derived notably our construction applies to generalizations of standard nearest neighbor chains such as alternating spin chains we also discuss relevant properties for its application to planar d 4 n 4 and d 3 n 6 supersymmetric gauge theories finally we present a map between long range and inhomogeneous spin chains delivering more insight into the structures of these models as well as their limitations at wrapping order

multistage decoding of multilevel block m psk modulation codes and its performance analysis multistage decoding of multilevel block multilevel phase shift keying m psk modulation codes for the additive white gaussian noise awgn channel is investigated several types of multistage decoding including a suboptimum soft decision decoding scheme are devised and analyzed upper bounds on the probability of an incorrect decoding of a code are derived for the proposed multistage decoding schemes error probabilities of some specific multilevel block 8 psk modulation codes are evaluated and simulated the computation and simulation results for these codes show that with multistage decoding significant coding gains can be achieved with large reduction in decoding complexity in one example it is shown that the difference in performance between the proposed suboptimum multistage soft decision decoding and the single stage optimum decoding is small only a fraction of a db loss in snr at the block error probability of 10 sup 6

existence and uniqueness of solutions to semilinear nonlocal parabolic equations abstract the banach contraction mapping theorem and the theory of analytic semigroups are used to prove the existence and uniqueness of solutions to nonlocal semilinear parabolic partial differential equations the equations consist of a parabolic boundary value problem and a relation connecting the initial value to values or weighted averages of values of the solution at other times

block coded modulation optimized for finite error rate on the white gaussian noise channel this correspondence examines the performance of block coded modulation bcm at finite decoded bit error rates ber we consider the optimum geometric structure to optimize coding gain at finite ber rather than asymptotic coding gain we introduce the concept of the row ber and show that this structure may be implemented by a bcm scheme in which the row bit error rates are equalized we present a design procedure for such schemes and show that significant improvements over conventional schemes are possible

trellis coded modulation with multidimensional constellations trellis coded modulation schemes using four eight or 16 dimensional constellations have a number of potential advantages over the usual two dimensional schemes a smaller constituent two dimensional constellation easier tolerance to phase ambiguities and a better trade off between complexity and coding gain a number of such schemes are presented and evaluated starting with a variety of multidimensional lattices we show how to select multidimensional constellations how to partition them into subsets how to construct trellis codes using those subsets and how to map hits to constellation points simplifications of the viterbi decoding algorithm are presented we conclude that there are multidimensional trellis coded modulation schemes that perform better for the same complexity than do two dimensional schemes

integrable spin chains associated with slq n and slp q n the hopf structure of the central extension of the uq sl n algebra is considered the intertwine matrix induces new integrable chain models we show the relation of these models and the biparametric spin chain slp q n models the cases n 2 are n 3 are discussed and for n 2 we obtain the model of dasgupta and chowdhury 1993 the case n 3 is solved by the nested bethe ansatz method and the dependence of the bethe equations on the second parameter introduced is demonstrated

approximation of solutions to history valued neutral functional differential equations in this paper we consider a class of abstract neutral functional differential equations in a separable hilbert space and study the approximation of solutions an example is also given to illustrate the applications of the abstract results

integrability of a t j model with impurities a t j model for correlated electrons with impurities is proposed the impurities are introduced in such a way that integrability of the model in one dimension is not violated the algebraic bethe ansatz solution of the model is also given and it is shown that the bethe states are highest weight states with respect to the supersymmetry algebra

new trellis codes based on lattices and cosets a new technique is proposed for constructing trellis codes which provides an alternative to ungerboeck s method of set partitioning the new codes use a signal constellation consisting of points from an n dimensional lattice lambda with an equal number of points from each coset of a sublattice lambda one part of the input stream drives a generalized convolutional code whose outputs are cosets of lambda while the other part selects points from these cosets several of the new codes are better than those previously known

diagonalisation of gl n invariant transfer matrices and quantum n wave system lee model the algebraic bethe ansatz is constructed for the gl n invariant transfer matrices with arbitrary gl n spin for this purpose the notion of vacuum subspace is introduced it is shown that the gl n magnet can be interpreted as an integrable discrete approximation of vector or matrix nonlinear schrodinger models or of the quantum n wave system

approximation of solutions to non local history valued retarded differential equations in the present work we consider a retarded differential equation and prove the existence uniqueness and convergence of approximate solutions also we consider the faedo galerkin approximations of the solution and the convergence

multilevel codes and multistage decoding h imai and s hirakawa have proposed 1977 a multilevel coding method based on binary block codes that admits a staged decoding procedure the author extends the coding method to coset codes and shows how to calculate minimum squared distance and path multiplicity in terms of the norms and multiplicities of the different cosets the multilevel structure allows the redundancy in the coset selection procedure to be allocated efficiently among the different levels it also allows the use of suboptimal multistage decoding procedures that have performance complexity advantages over maximum likelihood decoding

integrable su 3 spin chain combining different representations the general expression for the local matrix of a quantum chain with the site space in any representation of su 3 is obtained this is made by generalizing from the fundamental representation and imposing the fulfilment of the yang baxter equation then a non homogeneous spin chain combining different representations of su 3 is solved by developing a method inspired in the nested bethe ansatz the solution for the eigenvalues of the trace of the monodromy matrix is given as two coupled bethe equations a conjecture about the solution of a chain with the site states in different representations of su n is presented the thermodynamic limit of the ground state is calculated

new integrable quantum chains combining different kinds of spins a general procedure to generate new integrable hamiltonians combining to any kind of spins distributed arbitrarily on the line is given as a concrete application anisotropic chains formed by spin 1 2 and spin 1 operators at alternating sites are presented and solved exactly by the bethe ansatz ba the authors compute the ground state and excitation energies and momentum the higher order ba equations are derived depending on the choice these new hamiltonians exhibit or not conformal invariance in their low energy spectrum