universal space time coding a universal framework is developed for constructing full rate and full diversity coherent space time codes for systems with arbitrary numbers of transmit and receive antennas the proposed framework combines space time layering concepts with algebraic component codes optimized for single input single output siso channels each component code is assigned to a thread in the space time matrix allowing it thus full access to the channel spatial diversity in the absence of the other threads diophantine approximation theory is then used in order to make the different threads transparent to each other within this framework a special class of signals which uses algebraic number theoretic constellations as component codes is thoroughly investigated the lattice structure of the proposed number theoretic codes along with their minimal delay allow for polynomial complexity maximum likelihood ml decoding using algorithms from lattice theory combining the design framework with the cayley transform allows to construct full diversity differential and noncoherent space time codes the proposed framework subsumes many of the existing codes in the literature extends naturally to time selective and frequency selective channels and allows for more flexibility in the tradeoff between power efficiency bandwidth efficiency and receiver complexity simulation results that demonstrate the significant gains offered by the proposed codes are presented in certain representative scenarios

lattice coding and decoding achieve the optimal diversity multiplexing tradeoff of mimo channels this paper considers communication over coherent multiple input multiple output mimo flat fading channels where the channel is only known at the receiver for this setting we introduce the class of lattice space time last codes we show that these codes achieve the optimal diversity multiplexing tradeoff defined by zheng and tse under generalized minimum euclidean distance lattice decoding our scheme is based on a generalization of erez and zamir mod lambda scheme to the mimo case in our construction the scalar scaling of erez zamir and costa gaussian dirty paper schemes is replaced by the minimum mean square error generalized decision feedback equalizer mmse gdfe this result settles the open problem posed by zheng and tse on the construction of explicit coding and decoding schemes that achieve the optimal diversity multiplexing tradeoff moreover our results shed more light on the structure of optimal coding decoding techniques in delay limited mimo channels and hence open the door for novel approaches for space time code constructions in particular 1 we show that mmse gdfe plays a fundamental role in approaching the limits of delay limited mimo channels in the high signal to noise ratio snr regime unlike the additive white gaussian noise awgn channel case and 2 our random coding arguments represent a major departure from traditional space time code designs based on the rank and or mutual information design criteria

uniform preconditioners for a parameter dependent saddle point problem with application to generalized stokes interface equations we consider an abstract parameter dependent saddle point problem and present a general framework for analyzing robust schur complement preconditioners the abstract analysis is applied to a generalized stokes problem which yields robustness of the cahouet chabard preconditioner motivated by models for two phase incompressible flows we consider a generalized stokes interface problem application of the general theory results in a new schur complement preconditioner for this class of problems the robustness of this preconditioner with respect to several parameters is treated results of numerical experiments are given that illustrate robustness properties of the preconditioner

lattice basis reduction improved practical algorithms and solving subset sum problems we report on improved practical algorithms for lattice basis reduction we present a variant of the l3 algorithm with deep insertions and a practical algorithm for blockwise korkine zolotarev reduction a concept extending l3 reduction that has been introduced by schnorr 1987 empirical tests show that the strongest of these algorithms solves almost all subset sum problems with up to 58 random weights of arbitrary bit length within at most a few hours on a unisys 6000 70 or within a couple of minutes on a sparc 2 computer

the golden code a 2 spl times 2 full rate space time code with nonvanishing determinants in this paper the golden code for a 2 spl times 2 multiple input multiple output mimo system is presented this is a full rate 2 spl times 2 linear dispersion algebraic space time code with unprecedented performance based on the golden number 1 spl radic 5 2

shift full rank matrices and applications in space time trellis codes for relay networks with asynchronous cooperative diversity to achieve full cooperative diversity in a relay network most of the existing space time coding schemes require the synchronization between terminals a family of space time trellis codes that achieve full cooperative diversity order without the assumption of synchronization has been recently proposed the family is based on the stack construction by hammons and el gamal and its generalizations by lu and kumar it has been shown that the construction of such a family is equivalent to the construction of binary matrices that have full row rank no matter how their rows are shifted where a row corresponds to a terminal or transmit antenna and its length corresponds to the memory size of the trellis code on that terminal we call such matrices as shift full rank sfr matrices a family of sfr matrices has been also constructed but the memory sizes of the corresponding space time trellis codes the number of columns of sfr matrices grow exponentially in terms of the number of terminals the number of rows of sfr matrices which may cause a high decoding complexity when the number of terminals is not small in this paper we systematically study and construct sfr matrices of any sizes for any number of terminals furthermore we construct shortest square sfr ssfr matrices that correspond to space time trellis codes with the smallest memory sizes and asynchronous full cooperative diversity we also present some simulation results to illustrate the performances of the space time trellis codes associated with sfr matrices in asynchronous cooperative communications

delayed decision feedback sequence estimation the authors delayed decision feedback sequence estimation ddfse for uncoded pam signals is considered estimates on the performance of the algorithm are given and simulation results are provided for several examples a more general form of ddfse applicable to coded modulation systems is also presented as an example detection of trellis coded qpsk quadrature phase shift keyed signals over intersymbol interference channels is discussed

asymptotic performance of linear receivers in mimo fading channels linear receivers are an attractive low complexity alternative to optimal processing for multiple antenna multiple input multiple output mimo communications in this paper we characterize the information theoretic performance of mimo linear receivers in two different asymptotic regimes for fixed number of antennas we investigate the limit of error probability in the high signal to noise ratio snr regime in terms of the diversity multiplexing tradeoff dmt following this we characterize the error probability for fixed snr in the regime of large but finite number of antennas as far as the dmt is concerned we report a negative result we show that both linear zero forcing zf and linear minimum mean square error mmse receivers achieve the same dmt which is largely suboptimal even in the case where outer coding and deacircnot coding is performed across the antennas we also provide an apacircnot proximate quantitative analysis of the markedly different behavior of the mmse and zf receivers at finite rate and nonasymptotic snr and show that while the zf receiver achieves poor diversity at any finite rate the mmse receiver error curve slope flattens out progressively as the coding rate increases when snr is fixed and the number of antennas becomes large we show that the mutual information at the output of an mmse or zf linear receiver has fluctuations that converge in distribution to a gaussian random variable whose mean and variance can be characterized in closed form this analysis extends to the linear reacircnot ceiver case a well known result previously obtained for the optimal receiver simulations reveal that the asymptotic analysis captures accurately the outage behavior of systems even with a moderate number of antennas

a unified construction of space time codes with optimal rate diversity tradeoff the problem of constructing space time st block codes over a fixed desired signal constellation is considered in this situation there is a tradeoff between the transmission rate as measured in constellation symbols per channel use and the transmit diversity gain achieved by the code the transmit diversity is a measure of the rate of polynomial decay of pairwise error probability of the code with increase in the signal to noise ratio snr in the setting of a quasi static channel model let n sub t denote the number of transmit antennas and t the block interval for any n sub t spl les t a unified construction of n sub t spl times t st codes is provided here for a class of signal constellations that includes the familiar pulse amplitude pam quadrature amplitude qam and 2 sup k ary phase shift keying psk modulations as special cases the construction is optimal as measured by the rate diversity tradeoff and can achieve any given integer point on the rate diversity tradeoff curve an estimate of the coding gain realized is given other results presented here include i an extension of the optimal unified construction to the multiple fading block case ii a version of the optimal unified construction in which the underlying binary block codes are replaced by trellis codes iii the providing of a linear dispersion form for the underlying binary block codes iv a gray mapped version of the unified construction and v a generalization of construction of the ary case corresponding to constellations of size sup k items ii and iii are aimed at simplifying the decoding of this class of st codes

on the complexity of sphere decoding in digital communications sphere decoding has been suggested by a number of authors as an efficient algorithm to solve various detection problems in digital communications in some cases the algorithm is referred to as an algorithm of polynomial complexity without clearly specifying what assumptions are made about the problem structure another claim is that although worst case complexity is exponential the expected complexity of the algorithm is polynomial herein we study the expected complexity where the problem size is defined to be the number of symbols jointly detected and our main result is that the expected complexity is exponential for fixed signal to noise ratio snr contrary to previous claims the sphere radius which is a parameter of the algorithm must be chosen to ensure a nonvanishing probability of solving the detection problem this causes the exponential complexity since the squared radius must grow linearly with problem size the rate of linear increase is however dependent on the noise variance and thus the rate of the exponential function is strongly dependent on the snr therefore sphere decoding can be efficient for some snr and problems of moderate size even though the number of operations required by the algorithm strictly speaking always grows as an exponential function of the problem size

a penalization method to take into account obstacles in incompressible viscous flows from the navier stokes brinkman model a penalization method has been derived by several authors to compute incompressible navier stokes equations around obstacles in this paper convergence theorems and error estimates are derived for two kinds of penalization the first one corresponds to l 2 penalization inducing a darcy equation in the solid body the second one corresponds to a h 1 penalization and induces a brinkman equation in the body numerical tests are performed to confirm the efficiency and accuracy of the method

iterative techniques for time dependent stokes problems abstract in this paper we consider solving the coupled systems of discrete equations which arise from implicit time stepping procedures for the time dependent stokes equations using a mixed finite element spatial discretization at each time step a two by two block system corresponding to a perturbed stokes problem must be solved although there are a number of techniques for iteratively solving this type of block system to be effective they require a good preconditioner for the resulting pressure operator schur complement in contrast to the time independent stokes equations where the pressure operator is well conditioned the pressure operator for the perturbed system becomes more ill conditioned as the time step is reduced and or the reynolds number is increased in this paper we shall describe and analyze preconditioners for the resulting pressure systems these preconditioners give rise to iterative rates of convergence which are independent of both the mesh size h as well as the time step and reynolds number parameter k

on further reduction of complexity in tree pruning based sphere search in this letter we propose an extension of the probabilistic tree pruning sphere decoding ptp sd algorithm that provides further improvement of the computational complexity with minimal extra cost and negligible performance penalty in contrast to the ptp sd that considers the tightening of necessary conditions in the sphere search using per layer radius adjustment the proposed method focuses on the sphere radius control strategy when a candidate lattice point is found for this purpose the dynamic radius update strategy depending on the lattice point found as well as the lattice independent radius selection scheme are jointly exploited as a result while maintaining the effectiveness of the ptp sd further reduction of the computational complexity in particular for high snr regime can be achieved from simulations in multiple input and multiple output mimo channels it is shown that the proposed method provides a considerable improvement in complexity with near ml performance

full diversity high rate space time block codes from division algebras we present some general techniques for constructing full rank minimal delay rate at least one space time block codes stbcs over a variety of signal sets for arbitrary number of transmit antennas using commutative division algebras field extensions as well as using noncommutative division algebras of the rational field spl qopf embedded in matrix rings the first half of the paper deals with constructions using field extensions of spl qopf working with cyclotomic field extensions we construct several families of stbcs over a wide range of signal sets that are of full rank minimal delay and rate at least one appropriate for any number of transmit antennas we study the coding gain and capacity of these codes using transcendental extensions we construct arbitrary rate codes that are full rank for arbitrary number of antennas we also present a method of constructing stbcs using noncyclotomic field extensions in the later half of the paper we discuss two ways of embedding noncommutative division algebras into matrices left regular representation and representation over maximal cyclic subfields the 4 spl times 4 real orthogonal design is obtained by the left regular representation of quaternions alamouti s 1998 code is just a special case of the construction using representation over maximal cyclic subfields and we observe certain algebraic uniqueness characteristics of it also we discuss a general principle for constructing cyclic division algebras using the nth root of a transcendental element and study the capacity of the stbcs obtained from this construction another family of cyclic division algebras discovered by brauer 1933 is discussed and several examples of stbcs derived from each of these constructions are presented

preconditioning heterogeneous boldsymbol h mathrm div problems by additive schur complement approximation and applications in this paper we propose and analyze a preconditioner for a system arising from a mixed finite element approximation of second order elliptic problems describing processes in highly heterogeneous media our approach uses the technique of multilevel methods see e g p vassilevski multilevel block factorization preconditioners matrix based analysis and algorithms for solving finite element equations springer new york 2008 and the recently proposed preconditioner based on additive schur complement approximation by j kraus siam j sci comput 34 2012 pp a2872 a2895 the main results are the design study and numerical justification of iterative algorithms for these problems that are robust with respect to the contrast of the media defined as the ratio between the maximum and minimum values of the coefficient of the problem numerical tests provide experimental evidence for the high quality of the preconditioner and its desired robustness with respect to the material contrast such resu

on the sphere decoding algorithm i expected complexity the problem of finding the least squares solution to a system of linear equations where the unknown vector is comprised of integers but the matrix coefficient and given vector are comprised of real numbers arises in many applications communications cryptography gps to name a few the problem is equivalent to finding the closest lattice point to a given point and is known to be np hard in communications applications however the given vector is not arbitrary but rather is an unknown lattice point that has been perturbed by an additive noise vector whose statistical properties are known therefore in this paper rather than dwell on the worst case complexity of the integer least squares problem we study its expected complexity averaged over the noise and over the lattice for the sphere decoding algorithm of fincke and pohst we find a closed form expression for the expected complexity both for the infinite and finite lattice it is demonstrated in the second part of this paper that for a wide range of signal to noise ratios snrs and numbers of antennas the expected complexity is polynomial in fact often roughly cubic since many communications systems operate at noise levels for which the expected complexity turns out to be polynomial this suggests that maximum likelihood decoding which was hitherto thought to be computationally intractable can in fact be implemented in real time a result with many practical implications

lie algebroid cohomology as a derived functor abstract we show that the hypercohomology of the chevalley eilenberg de rham complex of a lie algebroid l over a scheme with coefficients in an l module can be expressed as a derived functor we use this fact to study a hochschild serre type spectral sequence attached to an extension of lie algebroids

universal binary semidefinite relaxation for ml signal detection semidefinite relaxation sdr provides a computationally efficient polynomial time approximation of the maximum likelihood detector however most of the existing works mainly focus on particular signal constellations in this paper we propose a universal binary semidefinite relaxation scheme that can handle arbitrary signal constellations in polynomial time the proposed scheme first binarizes the original signal space to a linearly constrained binary space and then solves the detection problem through sdr colorblack a specialized dual barrier method is provided to solve the sdr more efficiently in addition we propose to apply on the fly decision feedback to further reduce the computational complexity and improve the detection performance the proposed binary sdr together with on the fly decision feedback scheme can provide comparable or better solutions compared to existing sdr methods specialized to specific constellations such as 16 qam and 8 psk in terms of computational complexity and symbol error rate furthermore the proposed scheme is universal and can solve any other constellations such as 12 qam 32 qam or m psk

robust multilevel solvers for high contrast anisotropic multiscale problems a robust multilevel method for computing the solution of a scalar elliptic equation with anisotropic highly varying tensor coefficients is presented the method which belongs to the class of nonlinear algebraic multilevel iterations amlis uses an abstract framework for general symmetric positive definite bilinear forms previously presented in another publication by the author the crucial ingredient for obtaining robustness with respect to the variations in the coefficients and the anisotropies is the design of a nested sequence of spaces based on local generalized eigenvalue problems a discussion on how to achieve large coarsening factors in this sequence of spaces which is desirable in terms of computational complexity is included particular emphasis is put on how to handle the situation when the computed generating sets of the nested spaces are not minimal i e do not constitute bases several numerical examples are provided verifying the theoretically established robustness results

on maximum likelihood detection and the search for the closest lattice point maximum likelihood ml decoding algorithms for gaussian multiple input multiple output mimo linear channels are considered linearity over the field of real numbers facilitates the design of ml decoders using number theoretic tools for searching the closest lattice point these decoders are collectively referred to as sphere decoders in the literature in this paper a fresh look at this class of decoding algorithms is taken in particular two novel algorithms are developed the first algorithm is inspired by the pohst enumeration strategy and is shown to offer a significant reduction in complexity compared to the viterbo boutros sphere decoder the connection between the proposed algorithm and the stack sequential decoding algorithm is then established this connection is utilized to construct the second algorithm which can also be viewed as an application of the schnorr euchner strategy to ml decoding aided with a detailed study of preprocessing algorithms a variant of the second algorithm is developed and shown to offer significant reductions in the computational complexity compared to all previously proposed sphere decoders with a near ml detection performance this claim is supported by intuitive arguments and simulation results in many relevant scenarios

sumis near optimal soft in soft out mimo detection with low and fixed complexity the fundamental problem of interest here is soft input soft output multiple input multiple output mimo detection we propose a method referred to as subspace marginalization with interference suppression sumis that yields unprecedented performance at low and fixed deterministic complexity our method provides a well defined tradeoff between computational complexity and performance apart from an initial sorting step consisting of selecting channel matrix columns the algorithm involves no searching nor algorithmic branching hence the algorithm has a completely predictable run time and allows for a highly parallel implementation we numerically assess the performance of sumis in different practical settings full partial channel state information sequential iterative decoding and low high rate outer codes we also comment on how the sumis method performs in systems with a large number of transmit antennas

a unified framework for tree search decoding rediscovering the sequential decoder we consider receiver design for coded transmission over linear gaussian channels we restrict ourselves to the class of lattice codes and formulate the joint detection and decoding problem as a closest lattice point search clps here a tree search framework for solving the clps is adopted in our framework the clps algorithm is decomposed into the preprocessing and tree search stages the role of the preprocessing stage is to expose the tree structure in a form matched to the search stage we argue that the forward and feedback matrix filters of the minimum mean square error decision feedback equalizer mmse dfe are instrumental for solving the joint detection and decoding problem in a single search stage it is further shown that mmse dfe filtering allows for solving underdetermined linear systems and using lattice reduction methods to diminish complexity at the expense of a marginal performance loss for the search stage we present a generic method based on the branch and bound bb algorithm and show that it encompasses all existing sphere decoders as special cases the proposed generic algorithm further allows for an interesting classification of tree search decoders sheds more light on the structural properties of all known sphere decoders and inspires the design of more efficient decoders in particular an efficient decoding algorithm that resembles the well known fano sequential decoder is identified the excellent performance complexity tradeoff achieved by the proposed mmse dfe fano decoder is established via simulation results and analytical arguments in several multiple input multiple output mimo and intersymbol interference isi scenarios

robust multilevel methods for general symmetric positive definite operators a general robust multilevel method for solving symmetric positive definite systems resulting from discretizing elliptic partial differential equations is developed the term robust refers to the convergence rate of the method being independent of discretization parameters i e the problem size and problem parameters important instances of such problem parameters are in particular highly varying coefficients the method belongs to the class of nonlinear algebraic multilevel iterations the crucial ingredient for obtaining robustness is the construction of a nested sequence of spaces based on local generalized eigenvalue problems the method is analyzed in a rather general setting applying to the scalar elliptic equation the equations of linear elasticity and equations arising in the solution of maxwell s equations numerical results for the scalar elliptic equation are presented showing its robust convergence behavior

homogenization of the navier stokes equations in open sets perforated with tiny holes i abstract framework a volume distribution of holes this paper treats the homogenization of the stokes or navier stokes equations with a dirichlet boundary condition in a domain containing many tiny solid obstacles periodically distributed in each direction of the axes for example in the three dimensional case the obstacles have a size of e3 and are located at the nodes of a regular mesh of size e a suitable extension of the pressure is used to prove the convergence of the homogenization process to a brinkman type law in which a linear zero order term for the velocity is added to a stokes or navier stokes equation

geometric multigrid for darcy and brinkman models of flows in highly heterogeneous porous media we apply geometric multigrid methods for the finite element approximation of flow problems governed by darcy and brinkman systems used in modeling highly heterogeneous porous media the method is based on divergence conforming discontinuous galerkin methods and overlapping patch based domain decomposition smoothers we show in benchmark experiments that the method is robust with respect to mesh size and contrast of permeability for highly heterogeneous media

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

the error probability of the fixed complexity sphere decoder the fixed complexity sphere decoder fsd has been previously proposed for multiple input multiple output mimo detection in order to overcome the two main drawbacks of the sphere decoder sd namely its variable complexity and its sequential structure although the fsd has shown remarkable quasi maximum likelihood ml performance and has resulted in a highly optimized real time implementation no analytical study of its performance existed for an arbitrary mimo system herein the error probability of the fsd is analyzed proving that it achieves the same diversity as the maximum likelihood detector mld independent of the constellation used in addition it can also asymptotically yield ml performance in the high signal to noise ratio snr regime those two results together with its fixed complexity make the fsd a very promising algorithm for uncoded mimo detection

perfect space time codes for any number of antennas in a recent paper perfect n times n space time codes were introduced as the class of linear dispersion space time st codes having full rate nonvanishing determinant a signal constellation isomorphic to either the rectangular or hexagonal lattices in 2n 2 dimensions and uniform average transmitted energy per antenna consequence of these conditions include optimality of perfect codes with respect to the zheng tse diversity multiplexing gain tradeoff dmt as well as excellent low signal to noise ratio snr performance yet perfect space time codes have been constructed only for two three four and six transmit antennas in this paper we construct perfect codes for all channel dimensions present some additional attributes of this class of st codes and extend the notion of a perfect code to the rectangular case

lie algebroid cohomology and lie algebroid extensions abstract we consider the extension problem for lie algebroids over schemes over a field given a locally free lie algebroid q over a scheme x and a coherent sheaf of lie o x algebras l we determine the obstruction to the existence of extensions 0 l e q 0 and classify the extensions in terms of a suitable lie algebroid hypercohomology group in the preliminary sections we study free lie algebroids and recall some basic facts about lie algebroid hypercohomology

on low complexity space time coding for quasi static channels we propose a new space time coding scheme for the quasi static multiple antenna channel with perfect channel state information at the receiver and no channel state information at the transmitter in our scheme codewords produced by a trellis encoder are formatted into space time codeword arrays such that decoding can be implemented efficiently by minimum mean square error mmse decision feedback interference mitigation coupled with viterbi decoding through the use of per survivor processing we discuss the code design for the new scheme and show that finding codes with optimal diversity is much easier than for conventional trellis space time codes stcs we provide an upper bound on the word error rate wer of our scheme which is both accurate and easy to evaluate then we find upper and lower bounds on the information outage probability with discrete independent and identically distributed i i d inputs as opposed to gaussian inputs as in most previous works and we show that the mmse front end yields a large advantage over the whitened matched filter i e zero forcing front end finally we provide a comprehensive performance complexity comparison of our scheme with coded vertical bell labs layered space time v blast architecture and with the recently proposed threaded space time codes we also discuss the concatenation of our scheme with block space time precoders such as the linear dispersion codes

preconditioning in h div and applications we consider the solution of the system of linear algebraic equations which arises from the finite element discretization of boundary value problems associated to the differential operator i grad div the natural setting for such problems is in the hilbert space h div and the variational formulation is based on the inner product in h div we show how to construct preconditioners for these equations using both domain decomposition and multigrid techniques these preconditioners are shown to be spectrally equivalent to the inverse of the operator as a consequence they may be used to precondition iterative methods so that any given error reduction may be achieved in a finite number of iterations with the number independent of the mesh discretization we describe applications of these results to the efficient solution of mixed and least squares finite element approximations of elliptic boundary value problems

new algebraic constructions of rotated z sup n lattice constellations for the rayleigh fading channel in this correspondence we present various families of full diversity rotated z sup n lattice constellations based on algebraic number theory constructions we are able to give closed form expressions of their minimum product distance using the corresponding algebraic properties

lattice reduction aided conditional detection for mimo systems we introduce a low complexity detector with near optimal performance for transmission over multi antenna systems by using lattice basis reduction for generating almost orthogonal channel submatrices we enhance the conditional optimization technique to implement a fast yet efficient detector the lattice reduction aided lra conditional method is presented as a general detection technique over fading channels to yield significant saving in computational complexity while achieving close to maximum likelihood ml error performance by employing the orthogonality defect factor as a universal measure to select a near orthogonal channel submatrix for conditional detection we implement efficient detectors for mimo systems in particular an almost optimal decoder with linear complexity for the golden code is presented over quasi static channels

factoring polynomials with rational coefficients in this paper we present a polynomial time algorithm to solve the following problem given a non zero polynomial fe q x in one variable with rational coefficients find the decomposition of f into irreducible factors in q x it is well known that this is equivalent to factoring primitive polynomials fez x into irreducible factors in z x here we call f z x primitive if the greatest common divisor of its coefficients the content of f is 1 our algorithm performs well in practice cf 8 its running time measured in bit operations is o nl2 n9 log fd3

space time codes from structured lattices we present constructions of space time st codes based on lattice coset coding first we focus on st code constructions for the short block length case i e when the block length is equal to or slightly larger than the number of transmit antennas we present constructions based on dense lattice packings and nested lattice voronoi shaping our codes achieve the optimal diversity multiplexing tradeoff dmt of quasi static multiple input multiple output mimo fading channels for any fading statistics and perform very well also at practical moderate values of signal to noise ratios snr then we extend the construction to the case of large block lengths by using trellis coset coding we provide constructions of trellis coded modulation tcm schemes that are endowed with good packing and shaping properties both short block and trellis constructions allow for a reduced complexity decoding algorithm based on minimum mean squared error generalized decision feedback equalizer mmse gdfe lattice decoding and a combination of this with a viterbi tcm decoder for the tcm case beyond the interesting algebraic structure we exhibit codes whose performance is among the state of the art considering codes with similar encoding decoding complexity

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

coding and decoding for the dynamic decode and forward relay protocol we study the dynamic decode and forward ddf protocol for a single half duplex relay single antenna channel with quasi static fading the ddf protocol is well known and has been analyzed in terms of the diversity multiplexing tradeoff dmt in the infinite block length limit we characterize the finite block length dmt and give new explicit code constructions the finite block length analysis illuminates a few key aspects that have been neglected in the previous literature 1 we show that one dominating cause of degradation with respect to the infinite block length regime is the event of decoding error at the relay 2 we explicitly take into account the fact that the destination does not generally know a priori the relay decision time at which the relay switches from listening to transmit mode both of the above problems can be tackled by a careful design of the decoding algorithm in particular we introduce a decision rejection criterion at the relay based on forney s decision rule a variant of the neyman pearson rule such that the relay triggers transmission only when its decision is reliable also we show that a receiver based on the generalized likelihood ratio test glrt rule that jointly decodes the relay decision time and the information message achieves the optimal dmt our results show that no cyclic redundancy check crc for error detection or additional protocol overhead to communicate the decision time are needed for ddf finally we investigate the use of minimum mean squared error generalized decision feedback equalizer mmse gdfe lattice decoding at both the relay and the destination and show that it provides near optimal performance at moderate complexity

on fast decodable space time block codes we focus on full rate fast decodable space time block codes stbcs for 2 times 2 and 4times2 multiple input multiple output mimo transmission we first derive conditions and design criteria for reduced complexity maximum likelihood ml decodable 2times2 stbcs and we apply them to two families of codes that were recently discovered next we derive a novel reduced complexity 4times2 stbc and show that it outperforms all previously known codes with certain constellations

closest point search in lattices in this semitutorial paper a comprehensive survey of closest point search methods for lattices without a regular structure is presented the existing search strategies are described in a unified framework and differences between them are elucidated an efficient closest point search algorithm based on the schnorr euchner 1995 variation of the pohst 1981 method is implemented given an arbitrary point x spl isin spl ropf sup m and a generator matrix for a lattice spl lambda the algorithm computes the point of spl lambda that is closest to x the algorithm is shown to be substantially faster than other known methods by means of a theoretical comparison with the kannan 1983 1987 algorithm and an experimental comparison with the pohst 1981 algorithm and its variants such as the viterbo boutros see ibid vol 45 p 1639 42 1999 decoder modifications of the algorithm are developed to solve a number of related search problems for lattices such as finding a shortest vector determining the kissing number computing the voronoi 1908 relevant vectors and finding a korkine zolotareff 1873 reduced basis

construction of new delay tolerant space time codes perfect space time codes stc are optimal codes in their original construction for multiple input multiple output mimo systems based on cyclic division algebras cda they are full rate full diversity codes have non vanishing determinants nvd and hence achieve diversity multiplexing tradeoff dmt in addition these codes have led to optimal distributed space time codes when applied in cooperative networks under the assumption of perfect synchronization between relays however they lose their diversity when delays are introduced and thus are not delay tolerant in this paper using the cyclic division algebras of perfect codes we construct new codes that maintain the same properties as perfect codes in the synchronous case moreover these codes preserve their full diversity in asynchronous transmission

on space time coding with pulse position and amplitude modulations for time hopping ultra wideband systems in this work we propose novel families of space time st block codes that can be associated with impulse radio ultra wideband ir uwb communication systems the carrier less nature of this nonconventional totally real transmission technique necessitates the construction of new suitable coding schemes in fact the last generation of complex valued st codes namely the perfect codes cannot be associated with ir uwb systems where the phase reconstitution at the receiver side is practically infeasible on the other hand while the perfect codes were considered mainly with quadrature amplitude modulation qam and hexagonal hex constellations ir uwb systems are often associated with pulse position modulation ppm and hybrid ppm pam pulse amplitude modulation constellations in this paper instead of adopting the classical approach of constructing st codes over infinite fields or for the perfect codes we study the possibility of constructing modulation specific codes that are exclusive to ppm and ppm pam the proposed full rate codes are totally real information lossless and have a uniform average energy per transmit antenna they permit to achieve a full diversity order with any number of transmit antennas in some situations the proposed schemes have an optimal nonvanishing coding gain and satisfy all the construction constraints of the perfect codes in addition to the constraint of being totally real simulations performed over realistic indoor uwb channels showed that the proposed schemes outperform the best known codes constructed from cyclic division algebras

a note on the uniform inf sup condition for the brinkman problem in highly heterogeneous media abstract in this short note we study the interpolation spaces based uniform inf sup condition for brinkman equation in highly heterogeneous domains the result is known to hold in the case of a uniform constant permeability our numerical construction and experiments show that it is not true for the taylor hood and the mini elements applied to problems with highly heterogeneous coefficients

an a posteriori error analysis of a velocity pseudostress formulation of the generalized stokes problem abstract we consider a stabilized mixed finite element method introduced recently for the generalized stokes problem the method is obtained by adding suitable least squares terms to the dual mixed variational formulation of the problem in terms of the velocity and the pseudostress we obtain a new a posteriori error estimator of residual type and prove that it is reliable and locally efficient specifically we develop an a posteriori error analysis based on the quasi helmholtz decomposition which allows us to prove the so called local efficiency of the estimator with a non homogeneous boundary condition finally we present some numerical examples that confirm the theoretical properties of our approach

sphere decoding algorithms with improved radius search we start by identifying a relatively efficient version of sphere decoding algorithm sda that performs exact maximum likelihood ml decoding we develop novel algorithms based on an improved increasing radius search iirs which offer error performance and decoding complexity between two extremes the ml receiver and the nulling canceling nc receiver with detection ordering with appropriate choices of parameters our iirs offers the flexibility to trade error performance for complexity we provide design intuitions and guidelines analytical parameter specifications and a semianalytical error performance analysis simulations illustrate that iirs achieves considerable complexity reduction while maintaining performance close to ml

improved methods for calculating vectors of short length in a lattice including a complexity analysis the standard methods for calculating vectors of short length in a lattice use a reduction procedure followed by enumerating all vectors of z in a suitable box however it suffices to consider those x e z which lie in a suitable ellipsoid having a much smaller volume than the box we show in this paper that searching through that ellipsoid is in many cases much more efficient if combined with an appropriate reduction procedure our method allows to do computations in lattices of much higher dimensions several randomly constructed numerical examples illustrate the superiority of our new method over the known ones

information lossless space time block codes from crossed product algebras it is known that the alamouti code is the only complex orthogonal design cod which achieves capacity and that too for the case of two transmit and one receive antenna only damen proposed a design for two transmit antennas which achieves capacity for any number of receive antennas calling the resulting space time block code stbc when used with a signal set an information lossless stbc in this paper using crossed product central simple algebras we construct stbcs for arbitrary number of transmit antennas over an a priori specified signal set alamouti code and quasi orthogonal designs are the simplest special cases of our constructions we obtain a condition under which these stbcs from crossed product algebras are information lossless we give some classes of crossed product algebras from which the stbcs obtained are information lossless and also of full rank we present some simulation results for two three and four transmit antennas to show that our stbcs perform better than some of the best known stbcs and also that these stbcs are approximately 1 db away from the capacity of the channel with quadrature amplitude modulation qam symbols as input

an algebraic coding scheme for wireless relay networks with multiple antenna nodes we consider the problem of coding over a half duplex wireless relay network where both the transmitter and the receiver have respectively several transmit and receive antennas whereas each relay is a small device with only a single antenna since in this scenario requiring the relays to decode results in severe rate hits we propose a full rate strategy where the relays do a simple operation before forwarding the signal based on the idea of distributed space time coding our scheme relies on division algebras an algebraic object which allows the design of fully diverse matrices the code construction is applicable to systems with any number of transmit receive antennas and relays and has better performance than random code constructions with much less encoding complexity finally the robustness of the proposed distributed space time codes to node failures is considered

unified stabilized finite element formulations for the stokes and the darcy problems in this paper we propose stabilized finite element methods for both stokes and darcy s problems that accommodate any interpolation of velocities and pressures apart from the interest of this fact the important issue is that we are able to deal with both problems at the same time in a completely unified manner in spite of the fact that the functional setting is different concerning the stabilization formulation we discuss the effect of the choice of the length scale appearing in the expression of the stabilization parameters both in what refers to stability and to accuracy this choice is shown to be crucial in the case of darcy s problem as an additional feature of this work we treat two types of stabilized formulations showing that they have a very similar behavior

mmse decision feedback equalizers and coding i equalization results the minimum mean squared error decision feedback equalizer mmse dfe has properties that suggest that it is a canonical equalization structure for systems that combine equalization with coded modulation the structure and performance of the mmse dfe are succinctly derived using linear estimation theoretic principles in this first part of this two part paper the front end of the mmse dfe called the mean square whitened matched filter ms wmf is preferable in some ways to a matched filter or a whitened matched filter as a canonical receiver front end in a coded system the feedback filter of the mmse dfe may be implemented in the transmitter using precoding the mmse dfe can perform significantly better than a zero forcing decision feedback equalizer particularly at moderate to low snr s and on severe isi channels the mmse dfe is biased the optimum unbiased mmse dfe is the mmse dfe with the bias removed removing bias improves error probability but reduces the snr to snr sub mmse dfe u snr sub mmse dfe 1 it is shown that this snr relationship is a particular case of a very general result and that snr sub mmse dfe u gives a more realistic estimate of snr the results are extended to partial response equalization and to equalization with correlated inputs in an appendix

a robust finite element method for darcy stokes flow finite element methods for a family of systems of singular perturbation problems of a saddle point structure are discussed the system is approximately a linear stokes problem when the perturbation parameter is large while it degenerates to a mixed formulation of poisson s equation as the perturbation parameter tends to zero it is established basically by numerical experiments that most of the proposed finite element methods for stokes problem or the mixed poisson s system are not well behaved uniformly in the perturbation parameter this is used as the motivation for introducing a new robust finite element which exhibits this property

perfect space time block codes in this paper we introduce the notion of perfect space time block codes stbcs these codes have full rate full diversity nonvanishing constant minimum determinant for increasing spectral efficiency uniform average transmitted energy per antenna and good shaping we present algebraic constructions of perfect stbcs for 2 3 4 and 6 antennas

achieving 1 2 log 1 snr on the awgn channel with lattice encoding and decoding we address an open question regarding whether a lattice code with lattice decoding as opposed to maximum likelihood ml decoding can achieve the additive white gaussian noise awgn channel capacity we first demonstrate how minimum mean square error mmse scaling along with dithering lattice randomization techniques can transform the power constrained awgn channel into a modulo lattice additive noise channel whose effective noise is reduced by a factor of spl radic 1 snr snr for the resulting channel a uniform input maximizes mutual information which in the limit of large lattice dimension becomes 1 2 log 1 snr i e the full capacity of the original power constrained awgn channel we then show that capacity may also be achieved using nested lattice codes the coarse lattice serving for shaping via the modulo lattice transformation the fine lattice for channel coding we show that such pairs exist for any desired nesting ratio i e for any signal to noise ratio snr furthermore for the modulo lattice additive noise channel lattice decoding is optimal finally we show that the error exponent of the proposed scheme is lower bounded by the poltyrev exponent

a simple construction of a fortin operator for the two dimensional taylor hood element abstract a fortin operator is constructed to verify the discrete inf sup condition for the lowest order taylor hood element and its variant in two dimensions the approach is closely related to the recent work by mardal et al 2013 that is based on the isomorphism of the tangential edge bubble function space to a subspace of the lowest order edge element space a more precise characterization of this subspace and a numerical quadrature are introduced to simplify the analysis and remove the mesh restriction the constructed fortin operator is stable in both h 1 and l 2 norm for general shape regular triangulations

on lattice sequential decoding for the unconstrained awgn channel in this paper the performance limits and the computational complexity of the lattice sequential decoder are analyzed for the unconstrained additive white gaussian noise channel the performance analysis available in the literature for such a channel has been studied only under the use of the minimum euclidean distance decoder that is commonly referred to as the lattice decoder lattice decoders based on solutions to the np hard closest vector problem are very complex to implement and the search for low complexity receivers for the detection of lattice codes is considered a challenging problem however the low computational complexity advantage that sequential decoding promises makes it an alternative solution to the lattice decoder in this work we characterize the performance and complexity tradeoff via the error exponent and the decoding complexity respectively of such a decoder as a function of the decoding parameter the bias term for the above channel we derive the cut off volume to noise ratio that is required to achieve a good error performance with low decoding complexity

delay tolerant distributed tast codes for cooperative diversity in cooperative networks using a decode and forward strategy the multiple relays effectively transmit a distributed space time code the performance of which can be severely degraded when timing synchronization among the relays is not assured e g in cases of broadcast to dispersed recipients or in networks without a shared high quality timing reference recent work by xia and hammons have investigated the design of distributed space time codes that are delay tolerant in the sense that full spatial diversity is achieved regardless of timing offsets in general the previously known space time block codes belonging to the class of c linear codes however which are important because they achieve full spatial diversity and admit near optimal lattice decoding algorithms are not delay tolerant in this paper we present a new family of such codes that are fully delay tolerant the new codes generalize the threaded algebraic space time tast codes introduced by el gamal and damen like their brethren the new distributed tast codes are effective and flexible enabling use of different signaling constellations transmission rates numbers of transmit and receive antennas and decoders of varying levels of complexity

explicit space time codes achieving the diversity multiplexing gain tradeoff a recent result of zheng and tse states that over a quasi static channel there exists a fundamental tradeoff referred to as the diversity multiplexing gain d mg tradeoff between the spatial multiplexing gain and the diversity gain that can be simultaneously achieved by a space time st code this tradeoff is precisely known in the case of independent and identically distributed i i d rayleigh fading for tgesnt nr 1 where t is the number of time slots over which coding takes place and nt nr are the number of transmit and receive antennas respectively for t nt case we present two general techniques for building d mg optimal rectangular st codes from their square counterparts a byproduct of our results establishes that the d mg tradeoff for all tgesnt is the same as that previously known to hold for tgesnt n r 1

linear threaded algebraic space time constellations space time st constellations that are linear over the field of complex numbers are considered relevant design criteria for these constellations are summarized and some fundamental limits to their achievable performances are established the fundamental tradeoff between rate and diversity is investigated under different constraints on the peak power receiver complexity and rate scaling with the signal to noise ratio snr a new family of constellations that achieve optimal or near optimal performance with respect to the different criteria is presented the proposed constellations belong to the threaded algebraic st tast signaling framework and achieve the optimal minimum squared euclidean distance and the optimal delay for systems with one receive antenna these constellations also achieve the optimal peak to average power ratio for quadrature amplitude modulation qam and phase shift keying psk input constellations as well as optimal coding gains in certain scenarios the framework is general for any number of transmit and receive antennas and allows for realizing the optimal tradeoff between rate and diversity under different constraints simulation results demonstrate the performance gains offered by the proposed designs in average power and peak power limited systems

a universal lattice code decoder for fading channels we present a maximum likelihood decoding algorithm for an arbitrary lattice code when used over an independent fading channel with perfect channel state information at the receiver the decoder is based on a bounded distance search among the lattice points falling inside a sphere centered at the received point by judicious choice of the decoding radius we show that this decoder can be practically used to decode lattice codes of dimension up to 32 in a fading environment

low complexity decoding via reduced dimension maximum likelihood search in this paper we consider a low complexity detection technique referred to as a reduced dimension maximum likelihood search rd mls rd mls is based on a partitioned search which approximates the maximum likelihood ml estimate of symbols by searching a partitioned symbol vector space rather than that spanned by the whole symbol vector the inevitable performance loss due to a reduction in the search space is compensated by 1 the use of a list tree search which is an extension of a single best searching algorithm called sphere decoding and 2 the recomputation of a set of weak symbols i e those ignored in the reduced dimension search for each strong symbol candidate found during the list tree search through simulations on m quadrature amplitude modulation qam transmission in frequency nonselective multi input multioutput mimo channels we demonstrate that the rd mls algorithm shows near constant complexity over a wide range of bit error rate ber 10 1 10 4 while limiting performance loss to within 1 db from ml detection

on the theory of space time codes for psk modulation the design of space time codes to achieve full spatial diversity over fading channels has largely been addressed by handcrafting example codes using computer search methods and only for small numbers of antennas the lack of more general designs is in part due to the fact that the diversity advantage of a code is the minimum rank among the complex baseband differences between modulated codewords which is difficult to relate to traditional code designs over finite fields and rings we present general binary design criteria for psk modulated space time codes for linear bpsk qpsk codes the rank of binary projections of the unmodulated codewords as binary matrices over the binary field is a sufficient design criterion full binary rank guarantees full spatial diversity this criterion accounts for much of what is currently known about psk modulated space time codes we develop new fundamental code constructions for both quasi static and time varying channels these are perhaps the first general constructions other than delay diversity schemes that guarantee full spatial diversity for an arbitrary number of transmit antennas

a uniformly stable fortin operator for the taylor hood element we construct a new fortin operator for the lowest order taylor hood element which is uniformly stable both in l 2 and h 1 the construction which is restricted to two space dimensions is based on a tight connection between a subspace of the taylor hood velocity space and the lowest order nedelec edge element general shape regular triangulations are allowed for the h 1 stability while some mesh restrictions are imposed to obtain the l 2 stability as a consequence of this construction a uniform inf sup condition associated the corresponding discretizations of a parameter dependent stokes problem is obtained and we are able to verify uniform bounds for a family of preconditioners for such problems without relying on any extra regularity ensured by convexity of the domain

uniform preconditioners for the time dependent stokes problem implicit time stepping procedures for the time dependent stokes problem lead to stationary singular perturbation problems at each time step these singular perturbation problems are systems of saddle point type which formally approach a mixed formulation of the poisson equation as the time step tends to zero preconditioners for discrete analogous of these systems are discussed the preconditioners uses standard positive definite elliptic preconditioners as building blocks and lead to condition numbers which are bounded uniformly with respect to the time step and the spatial discretization the construction of the discrete preconditioners is related to the mapping properties of the corresponding continuous system

fast optimal and suboptimal any time algorithms for cdma multiuser detection based on branch and bound a fast optimal algorithm based on the branch and bound bbd method is proposed for the joint detection of binary symbols of k users in a synchronous code division multiple access channel with gaussian noise relationships between the proposed algorithms depth first bbd and fast bbd and both the decorrelating decision feedback df detector and sphere decoding algorithm are clearly drawn it turns out that decorrelating df detector corresponds to a one pass depth first bbd sphere decoding is in fact a type of depth first bbd but one that can be improved considerably via tight upper bounds and user ordering as in the fast bbd a fast any time suboptimal algorithm is also available by simply picking the current best solution in the bbd method theoretical results are given on the computational complexity and the performance of the current best suboptimal solution