some periodic convolutional codes better than any fixed code corresp some n o 2 k o 1 noncatastrophic periodic convolutional codes with memory m 4 are given that have the same free distance d infty as the best fixed code but have both a smaller number of paths of weight d infty per time instant and a smaller average number of information bit errors per such path for periods t 2 3 4 and 5 it is also shown that an n 0 k 0 code of period t is equivalent to a fixed code with parameters tn 0 tk 0

distance spectra and upper bounds on error probability for trellis codes the problem of estimating error probability for trellis codes is considered the set of all squared euclidean distances between code sequences is presented as a countable set this representation is used for calculating the generating functions for upper bounding error probability and bit error probability for trellis codes satisfying some symmetry conditions the generating functions of squared euclidean distances distance spectra are obtained by inversion of a matrix of order 2 sup spl nu it is shown that the generating functions are defined in terms of one formal variable for qam and uniform am and in terms of q 4 formal variables for q ary psk q 2 sup m where m spl ges 2 is an integer for small spl nu the generating functions may be found in closed form for larger spl nu a numerical technique for obtaining some initial terms of the power series expansion is proposed this algorithm is based on the recurrent matrix equations and the chinese remainder theorem

statistical hydrodynamics of lattice gas automata we investigate the space and time behavior of spontaneous thermohydrodynamic fluctuations in a simple fluid modeled by a lattice gas automaton and develop the statistical mechanical theory of thermal lattice gases to compute the dynamical structure factor i e the power spectrum of the density correlation function a comparative analysis of the theoretical predictions with our lattice gas simulations is presented the main results are i the spectral function of the lattice gas fluctuations is fully compatible with the spectrum obtained from experimental measurements performed in real fluids ii in the long wavelength limit the correlations of lattice gas fluctuations are well described by the landau placzek theory iii at short wavelengths and or at low densities good agreement is obtained between the lattice gas simulation results and the boltzmann theory these results provide solid support to the validity of the thermal lattice gas automaton as a consistent model system for real fluids

pseudo hermiticity versus pt symmetry iii equivalence of pseudo hermiticity and the presence of antilinear symmetries we show that a diagonalizable non hermitian hamiltonian h is pseudo hermitian if and only if it has an antilinear symmetry i e a symmetry generated by an invertible antilinear operator this implies that the eigenvalues of h are real or come in complex conjugate pairs if and only if h possesses such a symmetry in particular the reality of the spectrum of h implies the presence of an antilinear symmetry we further show that the spectrum of h is real if and only if there is a positive definite inner product on the hilbert space with respect to which h is hermitian or alternatively there is a pseudo canonical transformation of the hilbert space that maps h into a hermitian operator

calculation of the hidden symmetry operator in symmetric quantum mechanics in a recent paper it was shown that if a hamiltonian h has an unbroken symmetry then it also possesses a hidden symmetry represented by the linear operator the operator commutes with both h and the inner product with respect to is associated with a positive norm and the quantum theory built on the associated hilbert space is unitary in this paper it is shown how to construct the operator for the non hermitian symmetric hamiltonian h 1 2p2 1 2x2 ix3 using perturbative techniques it is also shown how to construct the operator for h 1 2p2 1 2x2 x4 using nonperturbative methods

an extensive search for good punctured rate k k 1 recursive convolutional codes for serially concatenated convolutional codes in many practical applications requiring variable rate coding and or high rate coding for spectral efficiency there is a need to employ high rate convolutional codes cc either by themselves or in a parallel or serially concatenated scheme for such applications in order to keep the trellis complexity of the code constant and to permit the use of a simplified decoder that can accommodate multiple rates a mother cc is punctured to obtain codes with a variety of rates this correspondence presents the results of extensive search for optimal puncturing patterns for recursive convolutional codes leading to codes of rate k k 1 k an integer to be used in serially concatenated convolutional codes sccc the code optimization is in the sense of minimizing the required signal to noise ratio snr for two target bit error rate ber and two target frame error rate fer values we provide extensive sample simulation results for rate k k 1 sccc codes employing our optimized punctured cc

is weak pseudo hermiticity weaker than pseudo hermiticity for a weakly pseudo hermitian linear operator we give a spectral condition that ensures its pseudo hermiticity this condition is always satisfied whenever the operator acts in a finite dimensional hilbert space hence weak pseudo hermiticity and pseudo hermiticity are equivalent in finite dimensions this equivalence extends to a much larger class of operators quantum systems whose hamiltonian is selected from among these operators correspond to pseudo hermitian quantum systems possessing certain symmetries

nonuniqueness of the mathcal c operator in mathcal p mathcal t symmetric quantum mechanics the operator in symmetric quantum mechanics satisfies a system of three simultaneous algebraic operator equations and these equations are difficult to solve exactly so perturbative methods have been used in the past to calculate the usual approach has been to express the hamiltonian as h h0 h1 and to seek a solution for in the form where q q q p is odd in the momentum p even in the coordinate q and has a perturbation expansion of the form q q1 3q3 5q5 in previous work it has always been assumed that the coefficients of even powers of in this expansion would be absent because their presence would violate the condition that q p q is odd in p in an earlier paper it was argued that the operator is not unique because the perturbation coefficient q1 is nonunique here the nonuniqueness of is demonstrated at a more fundamental level it is shown that the perturbation expansion for q actually has the more general form q q0 q1 2q2 in which all powers and not just odd powers of appear for the case in which h0 is the harmonic oscillator hamiltonian q0 is calculated exactly and in closed form and it is shown explicitly to be nonunique the results are verified by using powerful summation procedures based on analytic continuation it is also shown how to calculate the higher coefficients in the perturbation series for q

a lattice boltzmann equation for diffusion the formulation of lattice gas automata lga for given partial differential equations is not straightforward and still requires some sort of magic lattice boltzmann equation lbe models are much more flexible than lga because of the freedom in choosing equilibrium distributions with free parameters which can be set after a multiscale expansion according to certain requirements here a lbe is presented for diffusion in an arbitrary number of dimensions the model is probably the simplest lbe which can be formulated it is shown that the resulting algorithm with relaxation parameter 1 is identical to an explicit finite difference efd formulation at its stability limit underrelaxation 0 1 allows stable integration beyond the stability limit of efd the time step of the explicit lbe integration is limited by accuracy and not by stability requirements

further results on high rate punctured convolutional codes for viterbi and sequential decoding the weight spectra of high rate lpunctured convolutional codes are evaluated under the hypothesis of a low rate structure this interpretation yields results slightly different from those obtained when weight spectra are evaluated assuming a true high rate structure for punctured codes the search for long memory punctured codes is extended by providing new punctured codes of rates 4 5 5 6 6 7 and 7 8 with memories ranging from 9 to 19

non self adjoint graphs on finite metric graphs we consider laplace operators subject to various classes of non self adjoint boundary conditions imposed at graph vertices we investigate spectral properties existence of a riesz basis of projectors and similarity transforms to self adjoint laplacians among other things we describe a simple way to relate the similarity transforms between laplacians on certain graphs with elementary similarity transforms between matrices defining the boundary conditions

convolutional codes under a minimal trellis complexity measure we conduct a code search restricted to the recently introduced class of generalized punctured convolutional codes under the minimal trellis complexity measure defined by mceliece and lin for the same decoding complexity and the same code rate new codes are compared to well known existing classes of convolutional codes some of the best convolutional codes in a distance spectrum sense of existing and new trellis complexities are tabulated

a decomposition approach to cpm it is shown that any continuous phase modulation cpm system can be decomposed into a continuous phase encoder and a memoryless modulator in such a way that the former is a linear modulo some integer p time invariant sequential circuit and the latter is also time invariant this decomposition is exploited to obtain alternative realizations of the continuous phase encoder and hence of cpm and also to obtain alternative forms of the optimum decoding algorithm when p is a prime p so that the encoder is linear over the finite field gf p it is shown that cascading it with an outside convolutional encoder is equivalent to a single convolutional encoder it is pointed out that the cascade of the modulator the waveform channel which it is assumed is characterized by additive white gaussian noise and the demodulator that operates over one symbol interval yield a discrete memoryless channel that can be studied without the distractions introduced by continuous phase encoding

discrete cal pt symmetric models of scattering one dimensional scattering mediated by non hermitian hamiltonians is studied a schematic set of models is used which simulates two point interactions at a variable strength and distance the feasibility of the exact construction of the amplitudes is achieved via the discretization of the coordinate by direct construction it is shown that in all our models the probability is conserved this feature is tentatively attributed to the space and time reflection symmetry also known as symmetry of our specific hamiltonians

the minimally anisotropic metric operator in quasi hermitian quantum mechanics we propose a unique way to choose a new inner product in a hilbert space with respect to which an originally non self adjoint operator similar to a self adjoint operator becomes self adjoint our c

soft information transfer for sequence detection with concatenated receivers concatenated encoders are found in many digital communication systems a concatenated receiver for such a system consists of a chain of independently working estimators ended with an outer detector each stage of the receiver chain corresponds to a certain code in the system maximum likelihood sequence detection with a concatenated receiver requires soft information consisting of symbol aposteriori probabilities to be transferred between the receiver stages in this paper the optimal inner estimator is derived and further simplified into a new asymptotically optimal one by imposing a tree structure on the inner code by mapping several suboptimal inner estimators onto the tree structure and noting which approximations they make a theoretical performance ranking is obtained the asymptotical performance of the optimal concatenated detector at high signal to noise ratios snrs is investigated the decision variables underlying the pairwise error event probability are shown to be asymptotically gaussian and consequently a free euclidean distance can be found for the optimal concatenated detector

optimization of trellis coded tfm via matched codes a matched code is a convolutional code chosen in such a way that when combined with modulation with memory the resulting receiver for the coded modulation has the smallest possible number of states in the paper the matched coding technique is applied to coded tamed frequency modulation tfm schemes and a formal procedure is developed to find the best combination of a code and a modulation the optimization criterion is the maximum free euclidean distance for a given code rate and a given number of states in the viterbi receiver used for the coded modulation a search for the best codes was carried out for code rates 1 2 and 2 3 and for receivers with up to 256 and 64 states respectively good coding gains more than 7 db for rate 1 2 were achieved some of the best codes were catastrophic yet the coded modulation was not the codes obtained using the matched coding approach were in many cases better than those obtained using traditional optimization techniques

new constructions of high performance low complexity convolutional codes in this paper new constructions of low trellis complexity convolutional codes are presented new codes are found by searching into a specific class of time varying convolutional codes which is shaped by some basic properties and search restrictions an efficient technique for obtaining minimal trellis modules for the proposed codes is provided finally new low complexity convolutional codes of various code rates and memory sizes are tabulated

bifurcation of eigenvalues in nonlinear problems with antilinear symmetry many physical systems can be described by eigenvalues of nonlinear equations and bifurcation problems with a linear part that is non selfadjoint e g due to the presence of loss and gain the balance of these effects is reflected in an antilinear symmetry e g the pt symmetry under the symmetry we show that the nonlinear eigenvalues bifurcating from real linear eigenvalues remain real and the corresponding nonlinear eigenfunctions remain symmetric the abstract result is applied in a number of physical models of bose einstein condensation nonlinear optics and superconductivity and numerical examples are presented

a search for good convolutional codes to be used in the construction of turbo codes recursive systematic convolutional encoders have been shown to play a crucial role in the design of turbo codes we recall some properties of binary convolutional encoders and apply them to a search for good constituent convolutional codes of turbo codes tables of the best recursive systematic convolutional encoders found are presented for various rates together with the average bit error probability performances of some turbo codes using them

generalized concatenation of encoded tamed frequency modulation a novel construction for encoded tamed frequency modulation tfm is introduced which is based on the principles of generalized concatenation the inner tfm is partitioned into nested subsystems which increases the free euclidean distances in order to obtain a large distance among the nested tfm subsystems the scrambler matrices have to be computed which transfer the original tfm into the equivalent tfm with better partitioning properties then outer convolutional codes with different error correcting capabilities are used to protect the partitioning the new concatenated and generalized concatenated constructions were simulated in an additive white gaussian noise channel a multistep decoding algorithm based on soft output demodulation was used we present various simulation results which show a significant coding gain in comparison with the best known trellis codes having the same trellis state complexity

lattice gas automata with self organization abstract self organization or dynamic phase transitions occur in computer simulations of a lattice gas model with strictly local collision dynamics conserving number of particles momentum and lattice symmetries the microscopic collision processes are biased i e they have asymmetric transition rates in this model a spatially uniform initial state is unstable at the onset of instability long wavelength sound modes drive the system into a state with very long range order with dynamics similar to spinodal decomposition the structure factor s k t and the selected wavelength for maximal growth max t are measured as a function of time the state with long range order is highly organized into moving stable spatial patterns of triangles or parallel strips of macroscopic size with two or one broken symmetry respectively the entropy suddenly drops at self organization both the onset of metastability and the detailed structure of the final patterns are explained by mean field theory

stress stress correlation functions in lattice gases beyond boltzmann s approximation the complete time dependence of the stress stress correlation functions in lattice gas cellular automata is calculated from the ring kinetic theory using numerical and analytical methods this provides corrections typically of 10 20 to the usual molecular chaos calculations where correlation functions decay exponentially the resulting correlation function crosses over from an initial exponential decay to the long time behavior calculated from mode coupling theory the present theory applied to the viscosity accounts for a substantial part of the observed difference between the boltzmann theory and simulations

on saving decoder states for some trellis codes and partial response channels it is shown that under certain conditions when convolutional codes with precoding are used in conjunction with a partial response channel the number of decoder states in a maximum likelihood decoder matched to both the code and channel is 1 2 of that predicted by j k wolf and g ungerboeck ibid vol com 34 no 7 p 751 72 1986

phase transitions in a probabilistic cellular automaton growth kinetics and critical properties we investigate a discrete time kinetic model without detailed balance which simulates the phase segregation of a quenched binary alloy the model is a variation on the rothman keller cellular automaton in which particles of type a b move toward domains of greater concentration of a b modifications include a fully occupied lattice and the introduction of a temperature like parameter which endows the system with a stochastic evolution using computer simulations we examine domain growth kinetics in the two dimensional model for long times after a quench from disorder we find that the average domain sizer t t1 3 in agreement with the prediction of lifshitz slyozov wagner theory using a variety of methods we analyze the critical properties of the associated second order transition our analysis indicates that this model does not fall within either the ising or mean field classes

supersymmetric quasi hermitian hamiltonians with point interactions on a loop we explore some aspects of pt symmetric hamiltonians with two point interactions we determine classes of point interactions for which the hamiltonians are supersymmetric we prove that these hamiltonians are quasi hermitian and find a very simple formula for the metric operator and its square root q as well further we present the quasi hermitian hamiltonian with one point interaction with a continuous spectrum

pt symmetric quantum mechanics this paper proposes to broaden the canonical formulation of quantum mechanics ordinarily one imposes the condition h h on the hamiltonian where represents the mathematical operation of complex conjugation and matrix transposition this conventional hermiticity condition is sufficient to ensure that the hamiltonian h has a real spectrum however replacing this mathematical condition by the weaker and more physical requirement h h where represents combined parity reflection and time reversal pt one obtains new classes of complex hamiltonians whose spectra are still real and positive this generalization of hermiticity is investigated using a complex deformation h p2 x2 ix e of the harmonic oscillator hamiltonian where e is a real parameter the system exhibits two phases when e 0 the energy spectrum of h is real and positive as a consequence of pt symmetry however when 1 e 0 the spectrum contains an infinite number of complex eigenvalues and a finite number of real positive eigenvalues b

new short constraint length convolutional code constructions for selected rational rates corresp new short constraint length convolutional code constructions are tabulated for rates r n k n k 1 2 cdots n 1 with n 2 3 cdots 8 and for constraint lengths k 3 4 cdots 8 these codes have been determined by iterative search based upon a criterion of optimizing the free distance profile specifically these codes maximize the free distance d f while minimizing the number of adversaries in the distance or weight spectrum in several instances we demonstrate the superiority of these codes over previously published code constructions at the same rate and constraint length these codes are expected to have a number of applications including combined source channel coding schemes as well as coding for burst or impulsive noise channels

maximal couplings in pt symmetric chain models with the real spectrum of energies the domain of all the coupling strengths compatible with the reality of the energies is studied for a family of non hermitian n n matrix hamiltonians h n with tridiagonal and symmetric structure at all dimensions n the coordinates are found of the extremal points at which the boundary hypersurface touches the circumscribed sphere for odd n 2m 1 or ellipsoid for even n 2k

pt symmetric models in curved manifolds we consider the laplace beltrami operator in tubular neighborhoods of curves on two dimensional riemannian manifolds subject to non hermitian parity and time preserving boundary conditions we are interested in the interplay between the geometry and spectrum after introducing a suitable hilbert space framework in the general situation which enables us to realize the laplace beltrami operator as an m sectorial operator we focus on solvable models defined on manifolds of constant curvature in some situations notably for non hermitian robin type boundary conditions we are able to prove either the reality of the spectrum or the existence of complex conjugate pairs of eigenvalues and establish similarity of the non hermitian m sectorial operators to normal or self adjoint operators the study is illustrated by numerical computations

implementation of the fchc lattice gas model on the connection machine the 4 dimensional fchc lattice gas model has been implemented on a connection machine cm 2 with 16k processors symmetries are used to reduce the collision table to a size that fits into local memory this method avoids the degradation of the reynolds coefficientr but at the price of increased computing time bit shuffling between parallel lattices is introduced to reduce the discrepancy between measured viscosities and those predicted from the boltzmann approximation thereby a model with a negative shear viscosity is obtained a fluid having a uniform initial velocity is unstable and organized nonuniform motions develop because of the buildup of very strong correlations between the parallel lattices the discrepancy with the boltzmann values decreases only very slowly with the number of parallel lattices

improved coding techniques for preceded partial response channels a coset of a convolutional code may be used to generate a zero run length limited trellis code for a 1 d partial response channel the free squared euclidean distance d sub free sup 2 at the channel output is lower bounded by the free hamming distance of the convolutional code the lower bound suggests the use of a convolutional code with maximal free hamming distance d sub max r n for given rate r and number of decoder states n in this paper we present cosets of convolutional codes that generate trellis codes with d sub free sup 2 d sub max r n for rates 1 5 spl les r spl les 7 9 and d sub free sup 2 d sub max r n for r 13 16 29 32 61 64 the tabulated convolutional codes with r spl les 7 9 were not optimized for hamming distance instead a computer search was used to determine cosets of convolutional codes that exploit the memory of the 1 d channel to increase d sub free sup 2 at the channel output the search was limited by only considering cosets with certain structural properties the r spl ges 13 16 codes were obtained using a new construction technique for convolutional codes with free hamming distance 4 newly developed bounds on the maximum zero run lengths of cosets were used to ensure a short maximum run length at the 1 d channel output

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

block and trellis codes for the binary 1 d partial response channel with simple maximum likelihood decoders we consider block and convolutional codes for improving the reliability of data transmission over the binary precoded noisy 1 d partial response channel we concentrate on a class of codes for which the maximum likelihood decoder matched to the encoder precoder and the channel has the same trellis structure as the encoder thus doubling the number of states due to the channel memory is avoided we show that the necessary and sufficient condition to belong to this class is that all codewords be of the same parity the reed muller and golay codes belong to this class

pt symmetric cubic anharmonic oscillator as a physical model there is a factor of 2 error in equation 61 of this paper correcting this error leads to minor changes in equations 62 and 63 please see pdf for details

staggered diffusivities in lattice gas cellular automata the majority of lgcas has spurious conservation laws the so called staggered invariants first discovered by kadanoff mcnamara and zanetti consequently there are additional hydrodynamic modes of diffusive type which modify mode coupling theories and the nonlinear fluid dynamic equations the diffusivities of these staggered modes are evaluated in the mean field approximation for lgcas on triangular lattices starting from the green kubo formulas for the staggered diffusivities

a network flow approach to convolutional codes presents an alternative way of looking at convolutional codes as a network of flows from this association previous known classes of nonsystematic convolutional codes are reproduced the authors also present a decomposition of the problem of finding good convolutional codes into well known and structured problems such as the maximum flow problem the knapsack problem and the modular representation of block codes a spanning tree search algorithm is also proposed for finding good codes the authors consider the class of nonsystematic convolutional codes for which the encoders satisfy an equivalent property related to the feasibility of flow finally extensive tables show the new and the previous known codes

on a class of non self adjoint periodic eigenproblems with boundary and interior singularities we prove that all the eigenvalues of a certain highly non self adjoint sturm liouville differential operator are real the results presented are motivated by and extend those recently found by various authors benilov et al 2003 3 davies 2007 7 and weir 2008 18 on the stability of a model describing small oscillations of a thin layer of fluid inside a rotating cylinder

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

coset codes ii binary lattices and related codes for pt i see ibid vol 34 no 5 p 1123 51 1988 the family of barnes wall lattices including d sub 4 and e sub 8 of lengths n 2 sup n and their principal sublattices which are useful in constructing coset codes are generated by iteration of a simple construction called the squaring construction the closely related reed muller codes are generated by the same construction the principal properties of these codes and lattices are consequences of the general properties of iterated squaring constructions which also exhibit the interrelationships between codes and lattices of different lengths an extension called the cubing construction generates good codes and lattices of lengths n 3 2 sup n including the golay code and leech lattice with the use of special bases for 8 space another related construction generates the nordstrom robinson code and an analogous 16 dimensional nonlattice packing these constructions are represented by trellis diagrams that display their structure and interrelationships and that lead to efficient maximum likelihood decoding algorithms

structured set partitions and multilevel concatenated coding for partial response channels we present a systematic way to construct multilevel concatenated codes for partial response pr channels using 1 a structured set partition ssp of multiple channel output sets and 2 a set of conventional block codes with different error correcting capabilities a lower bound on the minimum squared euclidean distance of the constructed codes is given this bound is based on the interset minimal euclidean distances of the ssp and the minimum hamming distances of the used block codes an example of ssp for the extended class 4 partial response channel epr4 is presented iterative suboptimal decoding which combines viterbi detection on the trellis of the pr channel with algebraic error detection correction can be applied to the constructed concatenated codes truncated versions of the iterative decoding scheme are simulated and compared with each other

solvability and pt symmetry in a double well model with point interactions the concept of point interactions offers one of the most suitable guides towards a quantitative analysis of properties of certain specific non hermitian so called symmetric quantum mechanical systems this is illustrated with a double well model the easy solvability of which is shown to lead to a clear picture of the mechanisms of the unavoided level crossing and of the spontaneous symmetry breaking at a certain strong non hermiticity boundary below this limit the model is shown to be suitable for an explicit illustration of technicalities related to the standard probabilistic physical interpretation of bound states in symmetric quantum mechanics

trellis coding for partial response channels we consider trellis coding techniques for improving the reliability of digital transmission over noisy partial response channels such channels are commonly encountered in digital communication systems and also play a role in devices for data recording concentrating on the channels with characteristics 1 mp d we study methods to obtain codes which increase free euclidean distance between permitted sequences of channel outputs and avoid the occurrence of unlimited runs of identical outputs at the expense of some loss in data rate one technique employs the concept of set partitioning the other is based on using convolutional codes designed for maximum free hamming distance in conjunction with a precoder both methods lead to essentially equivalent codes

a two parameter family of non hermitian hamiltonians with real spectrum we introduce a hamiltonian h depending on the two complex parameters and and develop a through analysis of the spectral properties of this hamiltonian and its adjoint we determine the regions in the space of the complex parameters and where h is i hermitian ii non hermitian with real spectrum and iii non hermitian but pt symmetric in the case when h is non hermitian having real spectrum we derive a closed formula for a family of the metric operators depending on two arbitrary real positive parameters which render the hamiltonian h hermitian in a particular case we calculate the hermitian counterpart of h

on n n 1 convolutional codes with low trellis complexity we show that the state complexity profile of a convolutional code c is the same as that of the reciprocal of the dual code of c in case that minimal encoders for both codes are used then we propose an optimum permutation for any given n n 1 binary convolutional code that will yield an equivalent code with the lowest state complexity with this permutation we are able to find many n n 1 binary convolutional codes which are better than punctured convolutional codes of the same code rate and memory size by either lower decoding complexity or better weight spectra

on n n 1 punctured convolutional codes and their trellis modules it is known that an n n 1 non catastrophic antipodal punctured convolutional encoder of memory m is minimal that is the corresponding code cannot be produced by an encoder of smaller memory size in this letter it is shown that the trellis module of a code produced by an n n 1 non catastrophic punctured convolutional encoder is optimum if and only if the encoder is antipodal

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

solvable non hermitian discrete square well with closed form physical inner product a new hermitizable quantum model is proposed in which the bound state energies are real and given as roots of an elementary trigonometric expression while the wave function components are expressed as superpositions of two chebyshev polynomials as an site lattice version of square well with complex robin type two parametric boundary conditions the model is unitary with respect to the hilbert space metric which becomes equal to the most common dirac s metric in the conventional textbook hermitian hamiltonian limit this metric is constructed in closed form at all

hydrodynamics and time correlation functions for cellular automata hydrodynamic excitations in lattice gas cellular automata are described in terms of equilibrium time correlation functions for the local conserved variables for large space and time scales the linearized hydrodynamic equations are obtained to navier stokes order exact expressions for the associated susceptibilities and transport coefficients are identified in terms of correlation functions the general form of the time correlation functions for conserved densities in the hydrodynamic limit is given and illustrated by some examples suitable for comparison with computer simulation the transport coefficients are related to time correlation functions for the conserved fluxes in a way analogous to the green kubo expressions for continuous fluids the general results are applied for a one component fluid and several types of binary diffusion also discussed are the effects of unphysical slow modes such as staggered particle or momentum densities

propagating staggered waves in cellular automata fluids the majority of lattice gases have apart from the physical conserved quantities of particle number momentum and energy spurious ones usually staggered in space and time at the level of linear excitations these staggered modes may be purely diffusive or damped propagating waves in the eight and nine bit model on the square lattice one finds a large number of new spurious modes and the authors derive green kubo relations for the diffusivities and damping constants and calculate them in the boltzmann approximation

high rate punctured convolutional codes structure properties and construction technique the authors present some properties of punctured convolutional codes providing a construction method and a list of new good high rate long memory punctured codes the structure of punctured codes is examined and an upper bound on the free distance of punctured codes is derived indicating that punctured codes are good codes a construction method that generates the low rate original codes which duplicate given known high rate codes through perforation is proposed tables of punctured codes that duplicate the best known nonsystematic codes of rates 2 3 and 3 4 with memory lengths ranging from 3 to 23 and from 3 to 9 respectively are given together with the best known systematic codes for rates ranging from 2 3 to 7 8 with very long memory m 44 through 48

on the reality of the eigenvalues for a class of symmetric oscillators we study the eigenvalue problem with the boundary conditions that decays to zero as z tends to infinity along the rays where is a real polynomial and we prove that if for some we have for all then the eigenvalues are all positive real we then sharpen this to a larger class of polynomial potentials

relaxation and transport in fchc lattice gases fchc lattice gases are the basic models for studying flow problems in three dimensional systems this paper presents a self contained theoretical analysis and some computer simulations of such lattice gases extended to include an arbitrary number of rest particles with special emphasis on non semi detailed balance nsdb models the special fchc lattice symmetry guarantees isotropy of the navier stokes equations and enumerates the 12 spurious conservation laws staggered momenta the kinetic theory is based on the mean field approximation or the nonlinear boltzmann equation it is shown how calculation of the eigenvalues of the linearized boltzmann equation offers a simple alternative to the chapman enskog method or the multi time scale methods for calculating transport coefficients and relaxation rates the simulated values for the speed of sound in nsdb models slightly disagree with the boltzmann prediction

pseudo hermiticity versus pt symmetry ii a complete characterization of non hermitian hamiltonians with a real spectrum we give a necessary and sufficient condition for the reality of the spectrum of a non hermitian hamiltonian admitting a complete set of biorthonormal eigenvectors

non hermitian multi particle systems from complex root spaces we provide a general construction procedure for antilinearly invariant complex root spaces the proposed method is generic and may be applied to any weyl group allowing us to take any element of the group as a starting point for the construction worked out examples for several specific weyl groups are presented focusing especially on those cases for which no solutions were found previously when applied to the defining relations of models based on root systems this usually leads to non hermitian models which are nonetheless physically viable in a self consistent sense as they are antilinearly invariant by construction we discuss new types of calogero models based on these complex roots in addition we propose an alternative construction leading to q deformed roots we employ the latter type of roots to formulate a new version of affine toda field theories based on non simply laced root systems these models exhibit on the classical level a strong weak duality in the coupling constant equivalent to a lie algebraic duality which is known for the quantum version of the undeformed case

good convolutional codes for the precoded 1 d 1 d sup n partial response channels we extend the coding technique for the 1 d channel due to wolf and ungerboeck to the case of the 1 d 1 d sup n channel the technique employs a convolutional encoder a precoder and the channel in cascade a computer aided search for channel codes with large minimum free squared euclidean distance d sub free sup 2 is introduced the search is limited to a class of convolutional encoders for which an encoder with constraint length spl nu generates a decoder trellis with 2 sup spl nu states only as opposed to 2 sup spl nu n 1 states obtained when a general convolutional encoder is used these channel codes are said to be totally trellis matched ttm to the 1 d 1 d sup n channel a limitation on the maximum zero run length l sub max is attained by choosing a nontrivial coset of the convolutional code a class of coset representatives from which the resulting run length limited channel codes are ttm is determined while minimal encoders generate channel codes containing no flawed codewords it is shown that some nonminimal encoders do the same while achieving larger dg sub free sup 2 both types of encoders are considered in the search many new channel codes for the 1 d 1 d sup 2 and the 1 d 1 d sup 3 channels with diverse rates and decoding complexities are tabulated the codes have relatively low decoding complexity for rates up to 0 8 two of the new channel codes are compared to a matched spectral null msn code with the same decoding complexity and code rate one of these two new channel codes has a smaller d sub free sup 2 and larger l sub max than the msn code however with slightly higher decoding complexity the second new channel code outperforms the msn code

multilevel coded cpfsk systems for awgn and fading channels in this paper we introduce multilevel coded continuous phase frequency shift keying cpfsk systems for both additive white gaussian noise and fading channels based on multilevel coding and multistage decoding techniques these schemes are designed under the constraint m spl ges 2p for m ary cpfsk with modulation index j p in order to maintain the phase continuity property after multilevel coding we use some specific set partitioning rules we construct examples to show that the proposed systems outperform the corresponding conventional one level schemes for the fading case we consider an ideal fading channel where adjacent fading symbols are assumed to be independent and a correlated fading channel where bit interleavers are needed at each coding level the computer simulation results show that the proposed systems have bit error performance and decoder complexity advantages over the corresponding reference codes taken from the literature it is also shown that there is only a slight degradation on the bit error performance for correlated fading compared to the ideal fading case

punctured convolutional codes for the 1 d partial response channel a coded 1 d system containing a punctured convolutional encoder is analyzed in general a punctured encoder with 2 sup v states results in a decoder trellis with 2 sup v 1 states and a periodically time varying branch structure a class c of punctured convolutional encoders for which the decoder trellis has a fixed branch structure with 2 sup v states is described an encoder in this class can be combined with a precoder to form a new punctured convolutional encoder that generates the output from the precoder the author determines the set of good variable rate trellis codes for selectable rate encoding and viterbi decoding a set of variable rate trellis codes is generated by a variable rate punctured convolutional encoder in c the author also determines punctured convolutional encoders in c that generate a single good high rate trellis code

some extended results on the search for good convolutional codes we provide useful results on two classes of convolutional codes binary codes and nonbinary codes the best codes or the best known codes for these two classes of convolutional codes are found by computer search some of them are better than those found in the past we specify these codes by their transfer function matrices distance spectra and information weight spectra furthermore we derive an upper bound on the free distances of binary to m ary codes and q ary to m ary codes numerical values of this bound closely fit the computer searched values

non hermitian hamiltonians of lie algebraic type we analyse a class of non hermitian hamiltonians which can be expressed in terms of bilinear combinations of generators in the lie algebra or their isomorphic su 1 1 counterparts the hamiltonians are prototypes for solvable models of lie algebraic type demanding a real spectrum and the existence of a well defined metric we systematically investigate the constraints these requirements impose on the coupling constants of the model and the parameters in the metric operator we compute isospectral hermitian counterparts for some of the original non hermitian hamiltonians alternatively we employ a generalized bogoliubov transformation which allows us to compute explicitly real energy eigenvalue spectra for these type of hamiltonians together with their eigenstates we compare the two approaches

rational rate punctured convolutional codes for soft decision viterbi decoding we present rational rate k n punctured convolutional codes n up to 8 k 1 spl middot spl middot spl middot n 1 and constraint length spl nu up to 8 with good performance many of these codes improve the free distance and or weight spectra over previously reported codes with the same parameters the tabulated codes are found by an exhaustive or a random search

rate k k 1 punctured convolutional encoders g d forney 1970 1975 defined a minimal encoder as a polynomial matrix g such that g generates the code and g has the least constraint length among all generators for the code any convolutional code can be generated by a minimal encoder high rate k k 1 punctured convolutional codes were introduced to simplify viterbi decoding an ordinary convolutional encoder g can be obtained from any punctured encoder a punctured encoder is minimal if the corresponding ordinary encoder g is minimal and the punctured and ordinary encoders have the same constraint length it is shown that any rate k k 1 noncatastrophic antipodal punctured encoder is a minimal encoder

calculation of the metric in the hilbert space of a cal p cal t symmetric model via the spectral theorem in a previous paper 1 we introduced a very simple symmetric non hermitian hamiltonian with a real spectrum and derived a closed formula for the metric operator relating the problem to a hermitian one in this paper we propose an alternative formula for the metric operator which we believe is more elegant and whose construction based on a backward use of the spectral theorem for self adjoint operators provides new insights into the nature of the model

complete set of inner products for a discrete pt symmetric square well hamiltonian a discrete n point runge kutta version h n of one of the simplest non hermitian square well hamiltonians with real spectrum is studied its possible hermitizations mediated by nontrivial often called non dirac metrics i are considered as a source of nonequivalent standard probabilistic interpretations of this quantum model a complete set of these alternative multiparametric metrics a b n defining all the eligible hamiltonian dependent representations of the physical hilbert space of states is constructed in closed form for any coupling 1 1 and for any matrix dimension n

binary convolutional codes with application to magnetic recording calderbank heegard and ozarow 1 have suggested a method of designing codes for channels with intersymbol interference such as the magnetic recording channel these codes are designed to exploit intersymbol interference the standard method is to minimize intersymbol interference by constraining the input to the channel using run length limited sequences calderbank heegard and ozarow considered an idealized model of an intersymbol interference channel that leads to the problem of designing codes for a partial response channel with transfer function 1 d n 2 where the channel inputs are constrained to be pm 1 this problem is considered here channel inputs are generated using a nontrivial coset of a binary convolutional code the coset is chosen to limit the zero run length of the output of the channel and so maintain clock synchronization the minimum squared euclidean distance between outputs corresponding to distinct inputs is bounded below by the free distance of a second convolutional code which we call the magnitude code an interesting feature of the analysis is that magnitude codes that are catastrophic may perform better than those that are noncatastrophic

a linear algebra approach to minimal convolutional encoders the authors review the work of g d forney jr on the algebraic structure of convolutional encoders upon which some new results regarding minimal convolutional encoders rest an example is given of a basic convolutional encoding matrix whose number of abstract states is minimal over all equivalent encoding matrices however this encoding matrix can be realized with a minimal number of memory elements neither in controller canonical form nor in observer canonical form thus this encoding matrix is not minimal according to forney s definition of a minimal encoder to resolve this difficulty the following three minimality criteria are introduced minimal basic encoding matrix minimal encoding matrix and minimal encoder it is shown that all minimal basic encoding matrices are minimal and that there exist minimal encoding matrices that are not minimal basic several equivalent conditions are given for an encoding matrix to be minimal it is proven that the constraint lengths of two equivalent minimal basic encoding matrices are equal one by one up to a rearrangement all results are proven using only elementary linear algebra

biased lattice gases with correlated equilibrium states the approach to and structure of the equilibrium state is studied for a 7 bit lattice gas with biased forward and backward transition rates by means of mean field theory and computer simulations if the rate constants obey the factorizability and the detailed balance conditions the occupations of different velocity directions are uncorrelated anh theorem is valid and a nonuniversal equilibrium state exists that depends explicitly on the transition rates in case the above conditions are not satisfied theh theorem is no longer valid and mean field theory also predicts nontrivial velocity correlations in postcollision states the simulations are mainly concentrated on the time dependence of pre and postcollision velocity correlations on a single node and on slowly increasing fluctuations that might indicate metastable behavior

unbounded mathcal c symmetries and their nonuniqueness it is shown that if the operator for a symmetric hamiltonian with simple eigenvalues is not unique then it is unbounded the fact that the operator is unbounded is significant because while there is a formal equivalence between a symmetric hamiltonian and a conventionally hermitian hamiltonian in the sense that the two hamiltonians are isospectral the hilbert spaces are inequivalent this is so because the mapping from one hilbert space to the other is unbounded this shows that symmetric quantum theories are mathematically distinct from conventional hermitian quantum theories this article is part of a special issue of journal of physics a mathematical and theoretical devoted to quantum physics with non hermitian operators

woven coded cpfsk with hierarchical code structure we introduce hierarchical woven coded continuous phase frequency shift keying hierarchical wccpfsk as the serial concatenation of different outer convolutional codes and inner cpfsk we compare it to wccpfsk with identical outer convolutional codes with the proposed code combinations hierarchical wccpfsk achieves superior decoding capability simulations show that it performs better at medium snrs

pseudospectra in non hermitian quantum mechanics we propose giving the mathematical concept of the pseudospectrum a central role in quantum mechanics with non hermitian operators we relate pseudospectral properties to quasi hermiticity similarity to self adjoint operators and basis properties of eigenfunctions the abstract results are illustrated by unexpected wild properties of operators familiar from pt symmetric quantum mechanics

new short constraint length rate n 1 n punctured convolutional codes for soft decision viterbi decoding punctured convolutional codes with good performance are reported for rates n 1 n with n 5 6 7 8 and constraint lengths k 2 3 6 the tabulated codes are nonsystematic binary convolutional codes with maximum free distance and minimum information weight for use with soft decision viterbi decoding

closed formula for the metric in the hilbert space of a symmetric model we introduce a very simple exactly solvable symmetric non hermitian model with a real spectrum and derive a closed formula for the metric operator which relates the problem to a hermitian one

metric operators for non hermitian quadratic su 2 hamiltonians a class of non hermitian quadratic su 2 hamiltonians having an anti linear symmetry is constructed this is achieved by analysing the possible symmetries of such systems in terms of automorphisms of the algebra in fact different realizations for this type of symmetry are obtained including the natural occurrence of charge conjugation together with parity and time reversal once specified the underlying anti linear symmetry of the hamiltonian the former if unbroken leads to a purely real spectrum and the latter can be mapped to a hermitian counterpart by amongst other possibilities a similarity transformation here lie algebraic methods which were used to investigate the generalized swanson hamiltonian assis and fring 2009 j phys a math theor 42 015203 are employed to identify the class of quadratic hamiltonians that allow for such a mapping to the hermitian counterpart whereas for the linear su 2 system every hamiltonian of this type can be mapped to a hermitian counterpart by a transformation which is itself an exponential of a linear combination of su 2 generators the situation is more complicated for quadratic hamiltonians therefore the possibility of more elaborate similarity transformations including quadratic exponents is also explored in detail the existence of finite dimensional representations for the su 2 hamiltonian as opposed to the su 1 1 studied before allows for comparison with explicit diagonalization results for finite matrices finally the similarity transformations constructed are compared with the analogue of swanson s method for exact diagonalization of the problem establishing a simple relation between both approaches

low viscosity lattice gases a class of lattice gas models are studied which are variants of the fchc model the aim is to achieve the highest possible reynolds coefficient inverse dimensionless viscosity for efficient simulations of the three dimensional incompressible navier stokes equations the models include an arbitrary number of rest particles and violation of semi detailed balance within the framework of the boltzmann approximation exact expressions are obtained for the reynolds coefficients the minimization of the viscosity is done by solving a hitchcock type optimization problem for the fine tuning of the collision rules when the number of rest particles exceeds one there is a range of densities at which the viscosity takes negative values various optimal models with up to 26 bits per node have been implemented on a cray 2 and their true transport coefficients have been measured with good accuracy fairly large discrepancies with boltzmann values are observed when semi detailed balance is violated in particular no negative viscosity is obtained still the best model has a reynolds coefficient of 13 5 twice that of the best previously implemented model and thus is about 16 times more efficient computationally suggestions are made for further improvements it is proposed to use models with very high reynolds coefficients for sub grid scale modeling of turbulent flows

unveiling turbo codes some results on parallel concatenated coding schemes a parallel concatenated coding scheme consists of two simple constituent systematic encoders linked by an interleaver the input bits to the first encoder are scrambled by the interleaver before entering the second encoder the codeword of the parallel concatenated code consists of the input bits to the first encoder followed by the parity check bits of both encoders this construction can be generalized to any number of constituent codes parallel concatenated schemes employing two convolutional codes as constituent codes in connection with an iterative decoding algorithm of complexity comparable to that of the constituent codes have been previously shown to yield remarkable coding gains close to theoretical limits they have been named and are known as turbo codes we propose a method to evaluate an upper bound to the bit error probability of a parallel concatenated coding scheme averaged over all interleavers of a given length the analytical bounding technique is then used to shed some light on some crucial questions which have been floating around in the communications community since the proposal of turbo codes