numerical calculation of equivalent grid block permeability tensors for heterogeneous porous media a numerical procedure for the determination of equivalent grid block permeability tensors for heterogeneous porous media is presented the method entails solution of the fine scale pressure equation subject to periodic boundary conditions to yield upon appropriate averaging of the fine scale velocity field the coarse scale or equivalent grid block permeability when the region over which this coarse scale permeability is computed constitutes a representative elementary volume rev the resulting equivalent permeability may be interpreted as the effective permeability of the region solution of the pressure equation on the fine scale is accomplished through the application of an accurate triangle based finite element numerical procedure which allows for the modeling of geometrically complex features the specification of periodic boundary conditions is shown to yield symmetric positive definite equivalent permeability tensors in all cases the method is verified through application to a periodic model problem and is then applied to the scale up of areal and cross sections with fractally generated permeability fields the applicability and limitations of the method for these more general heterogeneity fields are discussed

multiscale phenomena green s functions the dirichlet to neumann formulation subgrid scale models bubbles and the origins of stabilized methods abstract an approach is developed for deriving variational methods capable of representing multiscale phenomena the ideas are first illustrated on the exterior problem for the helmholtz equation this leads to the well known dirichlet to neumann formulation next a class of subgrid scale models is developed and the relationships to bubble function methods and stabilized methods are established it is shown that both the latter methods are approximate subgrid scale models the identification for stabilized methods leads to an analytical formula for the intrinsic time scale whose origins have been a mystery heretofore

an adaptive gmsfem for high contrast flow problems in this paper we derive an a posteriori error indicator for the generalized multiscale finite element method gmsfem framework this error indicator is further used to develop an adaptive enrichment algorithm for the linear elliptic equation with multiscale high contrast coefficients the gmsfem which has recently been introduced in 13 allows solving multiscale parameter dependent problems at a reduced computational cost by constructing a reduced order representation of the solution on a coarse grid the main idea of the method consists of 1 the construction of snapshot space 2 the construction of the offline space and 3 the construction of the online space the latter for parameter dependent problems in 13 it was shown that the gmsfem provides a flexible tool to solve multiscale problems with a complex input space by generating appropriate snapshot offline and online spaces in this paper we study an adaptive enrichment procedure and derive an a posteriori error indicator which gives an estimate of the local error over coarse grid regions we consider two kinds of error indicators where one is based on the l 2 norm of the local residual and the other is based on the weighted h 1 norm of the local residual where the weight is related to the coefficient of the elliptic equation we show that the use of weighted h 1 norm residual gives a more robust error indicator which works well for cases with high contrast media the convergence analysis of the method is given in our analysis we do not consider the error due to the fine grid discretization of local problems and only study the errors due to the enrichment numerical results are presented that demonstrate the robustness of the proposed error indicators

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

multigrid with rough coefficients and multiresolution operator decomposition from hierarchical information games we introduce a near linear complexity geometric and meshless algebraic multigrid multiresolution method for pdes with rough l infty coefficients with rigorous a priori accuracy and performance estimates the method is discovered through a decision game theory formulation of the problems of 1 identifying restriction and interpolation operators 2 recovering a signal from incomplete measurements based on norm constraints on its image under a linear operator and 3 gambling on the value of the solution of the pde based on a hierarchy of nested measurements of its solution or source term the resulting elementary gambles form a hierarchy of deterministic basis functions of h 1 0 omega gamblets that 1 are orthogonal across subscales subbands with respect to the scalar product induced by the energy norm of the pde 2 enable sparse compression of the solution space in h 1 0 omega and 3 induce an orthogonal multiresolution operator decomposition the operating diagram of the multig

combining beamforming and space time coding using noisy quantized feedback the goal of combining beamforming and spacetime coding is to obtain full diversity order and to provide additional received power array gain compared to conventional space time codes in this work a class of code constellations is proposed called generalized partly orthogonal designs pods and both high rate and low rate feedback information is incorporated with possible feedback errors a binary symmetric channel bsc model characterizes feedback errors two cases are studied first when the bsc bit error probability is known a priori to the transmission ends and second when it is not known exactly based on a minimum pairwise error probability pep design criterion we design a channel optimized vector quantizer covq for feedback information and a precoder matrix codebook to adjust the transmission codewords the attractive property of our combining scheme is that it converges to conventional space time coding with low rate and erroneous feedback and to directional beamforming with high rate and error free feedback this scheme also shows desirable robustness against feedback channel modeling mismatch

convergence of a multiscale finite element method for elliptic problems with rapidly oscillating coefficients we propose a multiscale finite element method for solving second order elliptic equations with rapidly oscillating coefficients the main purpose is to design a numerical method which is capable of correctly capturing the large scale components of the solution on a coarse grid without accurately resolving all the small scale features in the solution this is accomplished by incorporating the local microstructures of the differential operator into the finite element base functions as a consequence the base functions are adapted to the local properties of the differential operator in this paper we provide a detailed convergence analysis of our method under the assumption that the oscillating coefficient is of two scales and is periodic in the fast scale while such a simplifying assumption is not required by our method it allows us to use homogenization theory to obtain a useful asymptotic solution structure the issue of boundary conditions for the base functions will be discussed our numerical experiments demonstrate convincingly that our multiscale method indeed converges to the correct solution independently of the small scale in the homogenization limit application of our method to problems with continuous scales is also considered

the variational multiscale method a paradigm for computational mechanics abstract we present a general treatment of the variational multiscale method in the context of an abstract dirichlet problem we show how the exact theory represents a paradigm for subgrid scale models and a posteriori error estimation we examine hierarchical p methods and bubbles in order to understand and ultimately approximate the fine scale green s function which appears in the theory we review relationships between residual free bubbles element green s functions and stabilized methods these suggest the applicability of the methodology to physically interesting problems in fluid mechanics acoustics and electromagnetics

on the spectrum of distances of a multilevel code decoded by a multistage decoder in this correspondence we are concerned with the error rates contributed by component codes in a multilevel code decoded by a multistage decoder these error rates are required for estimating the performance of the structure but more importantly they can serve as a design tool for achieving high coding gain the latter objective can be reached by approaching a balance among these error rates for evaluating the error rate contributed by a component code it is essential to calculate the corresponding spectrum of euclidean distances a method for computing this spectrum is developed in this correspondence the method is general and applicable to any signal constellation and convolutional as well as block component codes the error coefficient available in the literature for some multilevel codes with an infinite size signal constellation is shown to be significantly different from that of a practical finite constellation note that the complete spectrum is essential when codewords of a component code with hamming distance beyond the minimum distance affect the error rate see e g turbo codes

soft decoding techniques for codes and lattices including the golay code and the leech lattice two kinds of algorithms are considered 1 if is a binary code of length n a soft decision decoding algorithm for changes an arbitrary point of r n into a nearest codeword nearest in euclidean distance 2 similarly a decoding algorithm for a lattice lambda in r n changes an arbitrary point of r n into a closest lattice point some general methods are given for constructing such algorithms ami are used to obtain new and faster decoding algorithms for the gosset lattice e 8 the golay code the leech lattice

a recursive approach to low complexity codes a method is described for constructing long error correcting codes from one or more shorter error correcting codes referred to as subcodes and a bipartite graph a graph is shown which specifies carefully chosen subsets of the digits of the new codes that must be codewords in one of the shorter subcodes lower bounds to the rate and the minimum distance of the new code are derived in terms of the parameters of the graph and the subeodes both the encoders and decoders proposed are shown to take advantage of the code s explicit decomposition into subcodes to decompose and simplify the associated computational processes bounds on the performance of two specific decoding algorithms are established and the asymptotic growth of the complexity of decoding for two types of codes and decoders is analyzed the proposed decoders are able to make effective use of probabilistic information supplied by the channel receiver e g reliability information without greatly increasing the number of computations required it is shown that choosing a transmission order for the digits that is appropriate for the graph and the subcodes can give the code excellent burst error correction abilities the construction principles

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

diversity embedded space time codes rate and diversity impose a fundamental tradeoff in wireless communication high rate space time codes come at a cost of lower reliability diversity and high reliability diversity implies a lower rate however wireless networks need to support applications with very different quality of service qos requirements and it is natural to ask what characteristics should be built into the physical layer link in order to accommodate them in this paper we design high rate space time codes that have a high diversity code embedded within them this allows a form of communication where the high rate code opportunistically takes advantage of good channel realizations while the embedded high diversity code provides guarantees that at least part of the information is received reliably we provide constructions of linear and nonlinear codes for a fixed transmit alphabet constraint the nonlinear constructions are a natural generalization to wireless channels of multilevel codes developed for the additive white gaussian noise awgn channel that are matched to binary partitions of quadrature amplitude modulation qam and phase shift keying psk constellations the importance of set partitioning to code design for the wireless channel is that it provides a mechanism for translating constraints in the binary domain into lower bounds on diversity protection in the complex domain we investigate the systems implications of embedded diversity codes by examining value to unequal error protection rate opportunism and packet delay optimization these applications demonstrate that diversity embedded codes have the potential to outperform traditional single layer codes in moderate signal to noise snr regimes

multilevel trellis coded modulations for the rayleigh fading channel the authors present coded 8 phase shift keyed 8 psk modulations for the rayleigh fading channel the schemes are based on multilevel trellis coded modulation constructions and utilize maximum free hamming distance binary convolutional codes as building blocks a suboptimal multistage decoder that utilizes interstage interleaving and iterative decoding is proposed and evaluated examples are constructed to show that the proposed schemes outperform the best modified codes of the ungerboeck type due to significantly higher implicit time diversity yielding seven branches of built in time diversity whereas the ungerboeck code yields four branches of time diversity for a 64 state system the transmission delay is higher however the new schemes can provide three levels of unequal error protection when 8 psk or 8 differential phase shift keying 8 dpsk modulations are used they provide 10 14 db channel signal to noise ratio gain over uncoded 4 dpsk at a bit error rate of 10 sup 3 for a modest decoding complexity

combining beamforming and orthogonal space time block coding multiple transmit and receive antennas can be used in wireless systems to achieve high data rate communication efficient space time codes have been developed that utilize a large portion of the available capacity these codes are designed under the assumption that the transmitter has no knowledge about the channel in this work on the other hand we consider the case when the transmitter has partial but not perfect knowledge about the channel and how to improve a predetermined code so that this fact is taken into account a performance criterion is derived for a frequency nonselective fading channel and then utilized to optimize a linear transformation of the predetermined code the resulting optimization problem turns out to be convex and can thus be efficiently solved using standard methods in addition a particularly efficient solution method is developed for the special case of independently fading channel coefficients the proposed transmission scheme combines the benefits of conventional beamforming with those given by orthogonal space time block coding simulation results for a narrow band system with multiple transmit antennas and one or more receive antennas demonstrate significant gains over conventional methods in a scenario with nonperfect channel knowledge

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

upscaling method for problems in perforated domains with non homogeneous boundary conditions on perforations using non local multi continuum method nlmc abstract in this paper we present an upscaling method for problems in perforated domains with non homogeneous boundary conditions on perforations our methodology is based on the recently developed non local multicontinuum method nlmc the main ingredient of the method is the construction of suitable local basis functions with the capability of capturing multiscale features and non local effects we will construct multiscale basis functions for the coarse regions and additional multiscale basis functions for perforations with the aim of handling non homogeneous boundary conditions on perforations we start with describing our method for the laplace equation and then extending the framework for the elasticity problem and parabolic equations the resulting upscaled model has minimal size and the solution has physical meaning on the coarse grid we will present numerical results 1 for steady and unsteady problems 2 for laplace and elastic operators and 3 for neumann and robin non homogeneous boundary conditions on perforations numerical results show that the proposed method can provide good accuracy and provide significant reduction on the degrees of freedoms

on trellis codes with a delay processor and a signal mapper it is already known that a trellis code t which is constructed by using the encoder of a convolutional code c with short constraint length followed by a delay processor and a signal mapper is equivalent to a trellis code with large constraint length in this paper we derive a new lower bound on the free distance of t which in some cases is better than the previously derived bound moreover instead of the decoding used in earlier publications we apply iterative decoding on both tailbiting and zero tail representations of t to take advantage of the new lower bound and in the meantime to decrease the associated error coefficient caused by the decoding used in earlier publications comparisons among various designs of such a trellis code and some well known coding methods are also provided

multilevel coded modulation for unequal error protection and multistage decoding ii asymmetric constellations in this paper theoretical upper bounds and computer simulation results on the error performance of multilevel block coded modulations for unequal error protection uep and multistage decoding are presented it is shown that nonstandard signal set partitionings and multistage decoding provide excellent uep capabilities beyond those achievable with conventional coded modulation the coding scheme is designed in such a way that the most important information bits have a lower error rate than other information bits the large effective error coefficients normally associated with standard mapping by set partitioning are reduced by considering nonstandard partitionings of the underlying signal set the bits to signal mappings induced by these partitionings allow the use of soft decision decoding of binary block codes moreover parallel operation of some of the staged decoders is possible to achieve high data rate transmission so that there is no error propagation between these decoders hybrid partitionings are also considered that trade off increased intraset distances in the last partition levels with larger effective error coefficients in the middle partition levels the error performance of specific examples of multilevel codes over 8 psk and 64 qam signal sets are simulated and compared with theoretical upper bounds on the error performance

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

can a finite element method perform arbitrarily badly in this paper we construct elliptic boundary value problems whose standard finite element approximations converge arbitrarily slowly in the energy norm and show that adaptive procedures cannot improve this slow convergence we also show that the l 2 norm and the nodal point errors converge arbitrarily slowly with the l 2 norm two cases need to be distinguished and the usual duality principle does not characterize the error completely the constructed elliptic problems are one dimensional

special finite element methods for a class of second order elliptic problems with rough coefficients in this paper the approximate solution of a class of second order elliptic equations with rough coefficients is considered problems of the type considered arise in the analysis of unidirectional composites where the coefficients represent the properties of the material several methods for this class of problems are presented and it is shown that they have the same accuracy as usual methods have for problems with smooth coefficients the methods are referred to as special finite element methods because they are of finite element type but employ special shape functions chosen to accurately model the unknown solution

space time trellis codes over rapid rayleigh fading channels with channel estimation part ii performance analysis and code design for non identical channels we consider the maximum likelihood ml receiver design performance analysis and code design for space time trellis codes sttc over non identical rapid fading channels with imperfect channel state information csi the exact pairwise error probability pep and pep bounds for the ml receiver are obtained a new code design criterion exploiting the statistical information of the channel estimates is proposed which can minimize the performance loss caused by channel estimation error new codes are obtained via an iterative search algorithm with reduced complexity under actual channel estimation conditions our codes perform better than the existing codes in the literature which are designed on the assumption of identical channels and perfect csi at the receiver more performance gain can be achieved by our codes when the degree of imbalance among the links is higher

generalized finite element methods their performance and their relation to mixed methods the notion of a generalized finite element method is introduced this class of methods is analyzed and their relation to mixed methods is discussed the class of generalized finite element methods offers a wide variety of computational procedures from which particular procedures can be selected for particular problems a particular generalized finite element method which is very effective for problems with rough coefficients is discussed in detail

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

recursive space time trellis codes using differential encoding differential space time modulation dstm has been recently proposed by hughes and hochwald and sweldens when the channel information is not known at the receiver where the demodulation is in fact the same as the coherent demodulation of space time block coding by replacing the channel matrix with the previously received signal matrix on the other hand the dstm also needs a recursive memory of a matrix block at the encoder and therefore provides a trellis structure when the channel information is known at the receiver which is the interest of this paper this recursive structure of the dstm has been adopted lately by schlegel and grant in joint with a conventional binary code and joint iterative decoding demodulation with a superior performance the number of states of the trellis from the recursive structure depends on both the memory size which is fixed in this case and the unitary space time code ustc when a ustc for the dstm forms a group the number of states is the same as the size of the ustc otherwise the number of the states is the size of the semi group generated by the ustc from all the multiplications of the matrices in the ustc it is well known in the conventional convolutional coding cc or the trellis coded modulation tcm the free hamming or euclidean distance or the performance increases when the number of states increases by adding more memory with a properly designed cc or tcm in this paper we systematically study and design the ustc dstm for the recursive space time trellis modulation and show that the diversity product increases when the number of states increases which is not because of the memory size but because of the different ustc designs that generate different sizes of semi groups we propose a new ustc design criterion to ensure that the trellis structure improves the diversity product over the ustc as a block code based on the new criterion we propose a new class of ustc design for an arbitrary number of transmit antennas that has an analytical diversity product formula for two transmit antennas we then follow schlegel and grant s approach for joint encoding and iterative decoding of a binary coded dstm turbo space time coding and numerically show that our new ustc designs for the recursive space time trellis modulation outperforms the group ustc used by schlegel and grant

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

nonlocal multicontinua upscaling for multicontinua flow problems in fractured porous media abstract our goal of this paper is to develop a new upscaling method for multicontinua flow problems in fractured porous media we consider a system of equations that describes flow phenomena with multiple flow variables defined on both matrix and fractures to construct our upscaled model we will apply the nonlocal multicontinua nlmc upscaling technique the upscaled coefficients are obtained by using some multiscale basis functions which are solutions of local problems defined on oversampled regions for each continuum within a target coarse element we will solve a local problem defined on an oversampling region obtained by extending the target element by few coarse grid layers with a set of constraints which enforce the local solution to have mean value one on the chosen continuum and zero mean otherwise the resulting multiscale basis functions have been shown to have good approximation properties to illustrate the idea of our approach we will consider a dual continua background model consisting of discrete fractures in two space dimensions that is we consider a system with three continua we will present several numerical examples and they show that our method is able to capture the interaction between matrix continua and discrete fractures on the coarse grid efficiently

h optimal feedback controllers for linear multivariable systems this paper treats the problem of designing for a linear multivariable plant a feedback controller which minimizes the h infty norm of a weighted sensitivity matrix there exists a family of optimal improper feedbacks this family is determined by application of a theory of ball and helton a method for computing optimal feedbacks is described in detail and a numerical example is included it is shown that an optimal improper feedback can be approximated by a proper one under certain conditions on the weighting matrices

statistical analysis of the product high order ambiguity function the high order ambiguity function haf was introduced for the estimation of polynomial phase signals pps embedded in noise since the haf is a nonlinear operator it suffers from noise masking effects and from the appearance of undesired cross terms and possibly spurious harmonics in the presence of multicomponent mc signals the product haf phaf was then proposed as a way to improve the performance of the haf in the presence of noise and to solve the ambiguity problem in this correspondence we derive a statistical analysis of the phaf in the presence of additive white gaussian noise awgn valid for high signal to noise ratio snr and a finite number of data samples the analysis is carried out in detail for single component pps but the multicomponent case is also discussed error propagation phenomena implicit in the recursive structure of the phaf based estimator are explicitly taken into account the analysis is validated by simulation results for both single and multicomponent ppss

metric based upscaling we consider divergence form elliptic operators in dimension n ge 2 with l coefficients although solutions of these operators are only holder continuous we show that they are differentiable c1 with respect to harmonic coordinates it follows that numerical homogenization can be extended to situations where the medium has no ergodicity at small scales and is characterized by a continuum of scales this new numerical homogenization method is based on the transfer of a new metric in addition to traditional averaged homogenized quantities from subgrid scales into computational scales error bounds can be given and this method can also be used as a compression tool for differential operators 2006 wiley periodicals inc

on the performance evaluation of trellis codes generating function techniques for analyzing the error event and the bit error probabilities for trellis codes are considered the conventional state diagram approach for linear codes where the number of states is equal to the number of trellis states cannot be applied directly to arbitrary trellis codes and instead a state diagram where the number of states is equal to the square of the number of trellis states must be used it is shown that for an interesting class of trellis codes a modified generating function can be defined for which the number of states em is equal to the number of trellis states the class of codes considered includes trellis codes of rate r n 1 n based upon set partitioning whenever the first partition breaks the signal constellation into two subsets which have the same configuration matrix i e the same ordered set of mutual distances the complexity of calculating this modified generating function is the same as for the ordinary generating function of a convolutional code with the same number of trellis states bounds on the performance of some interesting codes are given based upon this method

coded phase frequency modulation channel coding combined with expanded signal sets has been shown 1 to improve error performance over uncoded modulation without expanding the bandwidth of the transmitted signals in this paper new coded modulation formats defined over an expanded set of signals varying both in phase and frequency are presented the new schemes combine fsk and psk modulation and make use of trellis coding and viterbi decoding to improve error performance over uncoded modulation the free euclidean distance is calculated for several classes of codes and upper bounds and simulation results are also presented for some simple codes the spectral characteristics of the proposed coded modulation formats are evaluated and compared to conventional two dimensional modulation formats differential encoding and various extensions of the basic scheme are also discussed

localization of elliptic multiscale problems this paper constructs a local generalized finite element basis for elliptic problems with heterogeneous and highly varying coefficients the basis functions are solutions of local problems on vertex patches the error of the corresponding generalized finite element method decays exponentially with respect to the number of layers of elements in the patches hence on a uniform mesh of size h patches of diameter h log 1 h are sufficient to preserve a linear rate of convergence in h without pre asymptotic or resonance effects the analysis does not rely on regularity of the solution or scale separation in the coefficient this result motivates new and justifies old classes of variational multiscale methods see more at http www ams org journals mcom 2014 83 290 s0025 5718 2014 02868 8 sthash z2ccfxig dpuf

fraction representations of non linear systems a simplified approach abstract a non linear system has a right fraction representation if it can be represented as pq 1 where p and q are stable systems and it has a left fraction representation if it can be represented as g 1 t where g and t are stable systems we develop here a theory of right and of left fraction representations for discrete time non linear systems with bounded input sequences we indicate the connection between fraction representations and the stabilization problem for non linear systems

two level coding based on trellis coded modulation and reed solomon codes a number of two level codes based on trellis coded modulation tcm schemes and their matched single or double error correcting reed solomon codes using qam constellations are presented and evaluated compared to the well known 4d 16 state tcm scheme with a comparable bandwidth efficiency these two level codes provide greater immunity from both gaussian and impulse noise at the cost of a reasonably higher complexity and a longer decoding delay on the order of a few hundred symbols the authors also show how to cope with phase ambiguities of the constellation in these two level codes both rotationally invariant coding and rotation detecting techniques are considered

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

a novel weighted multilevel space time trellis coding scheme it has been shown that when perfect or partial channel state information csi is available at the transmitter the performance and capacity of a space time coded system can be further improved multilevel space time trellis codes mlsttc s are capable of simultaneously providing bandwidth efficiency diversity improvement and coding gain with significantly reduced decoding complexity especially for larger constellations and higher throughputs in this paper we present a design of combined multilevel space time trellis codes and beam forming based on feedback from receiver henceforth referred to as weighted multilevel space time trellis codes wmlsttcs the channel profile is used to provide a beam forming scheme that achieves the better performance by properly weighting transmitted signals weights are selected that matches best with a channel profile feedback from the receiver indicative of long term characteristics of the wireless channel wmlsttcs provide improvement in performance of mlsttcs

an analysis of the nlmc upscaling method for high contrast problems abstract in this paper we propose simple multiscale basis functions with constraint energy minimization to solve elliptic problems with high contrast medium our methodology is based on the recently developed non local multicontinuum method nlmc the main ingredient of the method is the construction of suitable local basis functions with the capability of capturing multiscale features and non local effects in our method each coarse block is decomposed into various regions according to the contrast ratio and we require that the contrast ratio should be relatively small within each region the basis functions are constructed by solving a local problem defined on the oversampling domains and they have mean value one on the chosen region and zero mean otherwise numerical analysis shows that the resulting basis functions can be localizable and have a decay property the convergence of the multiscale solution is also proved finally some numerical experiments are carried out to illustrate the performances of the proposed method they show that the proposed method can solve problem with high contrast medium efficiently in particular if the oversampling size is large enough then we can achieve the desired error

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

an approach to ungerboeck coding for rectangular signal sets corresp a method of finding good ungerboeck codes for large rectangular quadrature amplitude modulation qam signal sets is described using the concept of euclidean weights due to ungerboeck we prove that a 2 n point basic constellation may be employed to determine exactly the free distance for an ungerboeck coded rectangular 2 m point set when m n 1 bits are uncoded and the remaining bits pass through a rate n 1 n convolutionai encoder it is shown that rate 2 3 encoders may be used to achieve most of the theoretically possible coding gain in the proposed scheme where the effect of the error coefficient on the coding gain has been considered

reduced lists of error patterns for maximum likelihood soft decoding a method whereby a substantially reduced family of error patterns called survivors may be created for maximum likelihood soft decoding is introduced the family of survivor depends on the received word a decoder based on this approach first forms the survivors then scores them rather than obtaining the survivors by online elimination of error patterns the use of predetermined lists that represent all families of survivors is proposed