determining the small solutions to s unit equations in this paper we generalize the method of wildanger for finding small solutions to unit equations to the case of s unit equations the method uses a minor generalization of the lll based techniques used to reduce the bounds derived from transcendence theory followed by an enumeration strategy based on the fincke pohst algorithm the method used reduces the computing time needed from mips years down to minutes

faster recursions in sphere decoding most of the calculations in standard sphere decoders are redundant in the sense that they either calculate quantities that are never used or calculate some quantities more than once a new method which is applicable to lattices as well as finite constellations is proposed to avoid these redundant calculations while still returning the same result pseudocode is given to facilitate immediate implementation simulations show that the speed gain with the proposed method increases linearly with the lattice dimension at dimension 60 the new algorithms avoid about 75 of all floating point operations

a projection method for model reduction of bilinear dynamical systems a krylov subspace based projection method is presented for model reduction of large scale bilinear systems a reduced bilinear system is constructed in such a way that it matches a desired number of moments of multivariable transfer functions corresponding to the kernels of volterra series representation of the original system applications to the simulation of dynamical responses of a nonlinear circuit and a micromachined device are presented to illustrate the efficiency of the new method and compare with an approach recently proposed by phillips

a randomized balanced proper orthogonal decomposition technique abstract in this paper we consider the model reduction problem of large scale linear systems such as systems obtained through the discretization of partial differential equations we propose a randomized proper orthogonal decomposition rpod technique to obtain the reduced order model by perturbing the primal and adjoint system using gaussian white noise we show that computations required by rpod algorithm is orders of magnitude lower while its performance is much better than other state of the art algorithms we also relate the rpod algorithm to krylov subspace methods and show that it constitutes a randomized approach to computational linear algebra problems that utilize krylov subspace methods

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

cayley differential unitary space time codes one method for communicating with multiple antennas is to encode the transmitted data differentially using unitary matrices at the transmitter and to decode differentially without knowing the channel coefficients at the receiver since channel knowledge is not required at the receiver differential schemes are ideal for use on wireless links where channel tracking is undesirable or infeasible either because of rapid changes in the channel characteristics or because of limited system resources although this basic principle is well understood it is not known how to generate good performing constellations of unitary matrices for any number of transmit and receive antennas and for any rate this is especially true at high rates where the constellations must be rapidly encoded and decoded we propose a class of cayley codes that works with any number of antennas and has efficient encoding and decoding at any rate the codes are named for their use of the cayley transform which maps the highly nonlinear stiefel manifold of unitary matrices to the linear space of skew hermitian matrices this transformation leads to a simple linear constellation structure in the cayley transform domain and to an information theoretic design criterion based on emulating a cauchy random matrix moreover the resulting cayley codes allow polynomial time near maximum likelihood ml decoding based on either successive nulling canceling or sphere decoding simulations show that the cayley codes allow efficient and effective high rate data transmission in multiantenna communication systems without knowing the channel

l_ 2 l_ infty model reduction for switched lpv systems with average dwell time in this note the model reduction problem for a class of discrete time switched linear parameter varying systems under average dwell time switching is investigated a parameterized reduced model is constructed and the corresponding existence conditions of such models are derived via strict lmi formulation the minimal average dwell time among all the subsystems and the desired reduced system are obtained such that the resulting model error system is exponentially stable and has a guaranteed l 2 l infin error performance a numerical example is given to demonstrate the potential and effectiveness of the developed theoretical results

multiuser detection with an unknown number of users this correspondence studies the problem of separating a signal of interest from co channel interference for the situation when the number of co channel users and their channels are unknown we devise a novel approach to this problem based on a trained statistical mixture model numerical results illustrate that the new method can outperform conventional training based multiuser detection

model approximation for switched genetic regulatory networks the model approximation problem is studied in this paper for switched genetic regulatory networks grns with time varying delays we focus on constructing a reduced order model to approximate the high order grns considered under the switching signal subject to certain constraints such that the approximation error system between the original and reduced order systems is exponentially stable with a disturbance attenuation performance the stability conditions and the disturbance attenuation performance are established by utilizing two integral inequality bounding techniques and the average dwell time method for the approximation error system then the solvability conditions for the reduced order models for the grns are also established using the projection method furthermore the model approximation problem can be transferred into a sequential minimization problem that is subject to linear matrix inequality constraints by using the cone complementarity algorithm finally several examples are provided to illustrate the effectiveness and the advantages of the proposed methods

mixed problem for some semi linear wave equation with a nonhomogeneous condition on considere le probleme aux valeurs limites et initiales suivant u tt u xx u t sign u t 0 x t 0 1 0 t u x 0 t g t u 1 t 0 u x 0 u 0 x u t x 0 u 1 x avec 0 1 avec u 0 h 1 0 1 u 1 dans l 2 0 1 et g t dans l 2 0 t un theoreme d existence globale et d unicite est demontre

partial realization theory for linear switched systems a formal power series approach the paper presents partial realization theory and a realization algorithm for linear switched systems the results are similar to partial realization theory of linear and bilinear systems our main tool is the theory of rational formal power series

mimo detection for high order qam based on a gaussian tree approximation this paper proposes a new detection algorithm for mimo communication systems employing high order qam constellations the factor graph that corresponds to this problem is very loopy in fact it is a complete graph hence a straightforward application of the belief propagation bp algorithm yields very poor results our algorithm is based on an optimal tree approximation of the gaussian density of the unconstrained linear system the finite set constraint is then applied to obtain a cycle free discrete distribution simulation results show that even though the approximation is not directly applied to the exact discrete distribution applying the bp algorithm to the cycle free factor graph outperforms current methods in terms of both performance and complexity the improved performance of the proposed algorithm is demonstrated on the problem of mimo detection

model reduction by moment matching for linear and nonlinear systems the model reduction problem for single input single output linear and nonlinear systems is addressed using the notion of moment a re visitation of the linear theory allows to obtain novel results for linear systems and to develop a nonlinear enhancement of the notion of moment this in turn is used to pose and solve the model reduction problem by moment matching for nonlinear systems to develop a notion of frequency response for nonlinear systems and to solve model reduction problems in the presence of constraints on the reduced model connections between the proposed results projection methods the covariance extension problem and interpolation theory are presented finally the theory is illustrated by means of simple worked out examples and case studies

algorithms for interpolation based qr decomposition in mimo ofdm systems detection algorithms for multiple input multiple output mimo wireless systems based on orthogonal frequency division multiplexing ofdm typically require the computation of a qr decomposition for each of the data carrying ofdm tones the resulting computational complexity will in general be significant motivated by the fact that the channel matrices arising in mimo ofdm systems result from oversampling of a polynomial matrix we formulate interpolation based qr decomposition algorithms an in depth complexity analysis based on a metric relevant for very large scale integration vlsi implementations shows that the proposed algorithms for a sufficiently large number of data carrying tones and sufficiently small channel order provably exhibit significantly smaller complexity than brute force per tone qr decomposition

the icosian code and the e_8 lattice a new 4 times 4 space time code with nonvanishing determinant this paper introduces a new rate 2 full diversity space time code for four transmit antennas and one receive antenna the 4times4 codeword matrix consists of four 2times2 alamouti blocks with entries from q i radic5 and these blocks can be viewed as quaternions which in turn represent rotations in r 3 the alamouti blocks that appear in a codeword are drawn from the icosian ring consisting of all linear combinations of 120 basic rotations corresponding to symmetries of the icosahedron this algebraic structure is different from the golden code but the complex entries are taken from a common underlying field the minimum determinant is bounded below by a constant that is independent of the signal constellation and the new code admits a simple decoding scheme that makes use of a geometric correspondence between the icosian ring and the e 8 lattice

model reduction by nice selections for linear switched systems a moment matching method for model reduction of linear switched systems lsss is presented the method can be seen as a non trivial extension of the krylov subspace methods for linear time invariant lti systems the procedure is based on the so called nice selections which represent a choice of basis in the reachability or observability space of the lss the framework can also be used for exact matching of the input output behavior of an lss with a reduced order lss for a specific switching sequence conditions for applicability of the method for model reduction are stated and finally the results are illustrated on numerical examples

asymptotic stability and energy decay rates for solutions of the wave equation with memory in a star shaped domain we study the asymptotic stability and give the energy decay rates for solutions of the wave equation with boundary dissipation of the memory type

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

on existence and asymptotic stability of solutions of the degenerate wave equation with nonlinear boundary conditions abstract we study the global existence of solutions of the nonlinear degenerate wave equation 0 x y y 0 in 0 y 0 on 1 0 y y f y g y 0 on 0 0 y x 0 y 0 y x 0 y 1 x in where y denotes the derivative of y with respect to parameter t f s c0 s s and g is a nondecreasing c1 function such that k1 s 2 g s s k2 s 2 for some k1 k2 0 with 0 0 if n 1 2 the existence of solutions is proved by means of the faedo galerkin method furthermore when 0 the uniform decay is obtained by making use of the perturbed energy method

a simplex algorithm for rational cp factorization in this paper we provide an algorithm similar to the simplex algorithm which determines a rational cp factorization of a given matrix whenever the matrix allows such a factorization this algorithm can be used to show that every integral completely positive 2 times 2 matrix has an integral cp factorization

model simplification for switched hybrid systems abstract this paper is concerned with the problem of h model reduction for switched system which is an important class of hybrid systems frequently encountered in practical situations two sharply different approaches are proposed to solve this problem the first approach casts the model reduction into a convex optimization problem which is the first attempt to solve the model reduction problem by using linearization procedure the second one based on the cone complementarity linearization idea casts the model reduction problem into a sequential minimization problem subject to linear matrix inequality constraints both approaches have their own advantages and disadvantages concerning conservatism and computational complexity a numerical example illustrates the effectiveness of the proposed theories

existence and uniform decay rates of solutions to a degenerate system with memory conditions at the boundary in this article we study the degenerate system r 1 r 2 0 subject to memory conditions on the boundary given email protected 1 x u t email protected email protected u v email protected 0 r 2 x v t email protected a u v email protected 0 email protected 0 email protected 0 tg 1 t s email protected email protected s email protected 1x 0 email protected 0 email protected 0 tg 2 t s email protected email protected s email protected 1x 0 u 0 v 0 u 0 v 0 r 1u t 0 r 2v t 0 r 1u 1 r 2v 1 email protected where w is a bounded region in r n whose boundary is partitioned into disjoint sets c 0 c 1 we prove that the dissipations given by the memory terms are strong enough to guarantee exponential or polynomial decay provided the relaxation functions also decay exponentially or polynomially and with the same rate of decay

soft input soft output single tree search sphere decoding soft input soft output siso detection algorithms form the basis for iterative decoding the computational complexity of siso detection often poses significant challenges for practical receiver implementations in particular in the context of multiple input multiple output mimo wireless communication systems in this paper we present a low complexity siso sphere decoding algorithm based on the single tree search paradigm proposed originally for soft output mimo detection in studer soft output sphere decoding algorithms and vlsi implementation ieee j sel areas commun vol 26 no 2 pp 290 300 feb 2008 the new algorithm incorporates clipping of the extrinsic log likelihood ratios llrs into the tree search which results in significant complexity savings and allows to cover a large performance complexity tradeoff region by adjusting a single parameter furthermore we propose a new method for correcting approximate llrs resulting from sub optimal detectors which often significantly improves detection performance at low additional computational complexity

upper bounds in spectral test for multiple recursive random number generators with missing terms abstract one method for generating random numbers rns of long period recommended by many scholars is the multiple recursive generator mrg in that the current rn is essentially a linear combination of the k preceding ones in this paper the upper bounds for a figure of merit adopted in the spectral test are derived for the k th order mrg with p k terms as p gets smaller the bounds become smaller as well the simplest form of the k th order mrg with two terms frequently discussed in literature is found to have the worst bound

a semilinear wave equation with space time dependent coefficients and a memory boundarylike antiperiodic condition a low frequency asymptotic expansion this paper studies a low frequency asymptotic expansion for a unique strong solution to an initial boundary value problem of a semilinear wave equation this equation admits space time dependent coefficients and a memory boundarylike antiperiodic condition for some small parameters from coefficients of this semilinear wave equation and of boundary conditions we approximate a unique strong solution to this problem by a polynomial of these parameters and coefficients of this polynomial are strong solutions of a sequence of well defined linear initial boundary value problems

an exhaustive analysis of two term multiple recursive random number generators with efficient multipliers this paper presents results of an exhaustive computer search for the maximum spectral value in full period two term kth order multiple recursive generators mrgs with efficient multipliers for orders k 2 3 7 we provide a table of kth order mrgs with largest spectral values these mrgs not only have the best spectral values found so far but also can be implemented efficiently by applying the approximate factoring method

an analysis of linear congruential random number generators when multiplier restrictions exist abstract this research conducts an exhaustive search for the best spectral test performance in a full period linear congruential generator lcg with the largest prime modulus smaller than 2b for bit sizes b 8 9 31 three types of restrictions on multipliers are presented and some full period lcgs are presented for use in three different spectral test dimensions according to the exhaustive searches we perform the results indicate differences exist among the numbers of possible multipliers for the three types of multiplier restrictions we demonstrate that these differences can affect the performance of spectral tests for different dimensions

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

balanced truncation for discrete time markov jump linear systems this technical note investigates the model reduction problem for mean square stable discrete time markov jump linear systems for this class of systems a balanced truncation algorithm is developed the reduced order model is suboptimal however the approximation error which is captured by means of the stochastic gain is bounded from above by twice the sum of singular numbers associated to the truncated states of each mode such a result allows rigorous simplification of the dynamics of each mode in an independent manner with respect to a metric which is relevant from a robust control point of view

lattice decoding for joint detection in direct sequence cdma systems a new joint detection method based on sphere packing lattice decoding is presented in this paper the algorithm is suitable for both synchronous and asynchronous multiple access direct sequence code division multiple access ds cdma systems and it may jointly detect up to 64 users with a reasonable complexity the detection complexity is independent of the modulation size and large m pam or m qam constellations can be used furthermore a theoretical gain analysis is performed in which the multiple access system performance is derived from the lattice parameters

efficient linear programming algorithm to generate the densest lattice sphere packings finding the densest sphere packing in d dimensional euclidean space r d is an outstanding fundamental problem with relevance in many fields including the ground states of molecular systems colloidal crystal structures coding theory discrete geometry number theory and biological systems numerically generating the densest sphere packings becomes very challenging in high dimensions due to an exponentially increasing number of possible sphere contacts and sphere configurations even for the restricted problem of finding the densest lattice sphere packings in this paper we apply the torquato jiao packing algorithm which is a method based on solving a sequence of linear programs to robustly reproduce the densest known lattice sphere packings for dimensions 2 through 19 we show that the tj algorithm is appreciably more efficient at solving these problems than previously published methods indeed in some dimensions the former procedure can be as much as three orders of magnitude faster at finding the optimal solutions than earlier ones we also study the suboptimal local density maxima solutions inherent structures or extreme lattices to gain insight about the nature of the topography of the density landscape

effective and efficient restriction on producing the multipliers for the multiple recursive random number generator abstract the most efficient and easiest way for implementing a multiple recursive random number generator is the approximate factoring af method in the literature the af method can be applied in the three types of restriction on multiplier this paper considers the effectiveness and efficiency of these restrictions from the theoretical and empirical points of view the most effective and efficient restriction is presented the number of arithmetic operations required by the af method is also discussed

technical communique h model reduction for uncertain switched linear discrete time systems in this paper the problem of h model reduction for switched linear discrete time systems with polytopic uncertainties is investigated a reduced order switched model is constructed for a given robustly stable switched system which has the same structural polytopic uncertainties as the original system such that the resulting error system is robustly asymptotically stable and an h error performance is guaranteed a sufficient condition for the existence of the desired reduced order model is derived and formulated in terms of a set of linear matrix inequalities by solving the corresponding convex optimization problem in such existence condition the vertex system of reduced order model can be obtained which also provides an h gain for the error system between the original system and the reduced order model a numerical example is given to show the effectiveness and the potential of the proposed techniques

improvements in closest point search based on dual hkz bases in this paper we review the technique to solve the cvp based on dual hkz bases by j blomer 4 the technique is based on the transference theorems given by banaszczyk 3 which imply some necessary conditions on the coefficients of the closest vectors with respect to a basis whose dual is hkz reduced recursively starting with the last coefficient intervals of length i can be derived for the i th coefficient of any closest vector this leads to n candidates for closest vectors in this paper we refine the necessary conditions derived from the transference theorems giving an exponential reduction of the number of candidates the improvement is due to the fact that the lengths of the intervals are not independent in the original algorithm the candidates for a coefficient pair v i v i 1 correspond to the integer points in a rectangle of volume email protected i 1 in our analysis we show that the candidates for v i v i 1 in fact lie in an ellipse with transverse and conjugate diameter i 1 respectively i this reduces the expected number of points to be enumerated by an exponential factor of about 0 886 n we further show how a choice of the coefficients v n v i 1 influences the interval from which v i can be chosen numerical computations show that these considerations allow to bound the expected number of points to be enumerated by n 0 7 5 n for 10

on the approximate solution of a mathematical model of a viscoelastic bar abstract the mathematical model expressing the shock between a solid body and a linear viscoelastic bar is considered within the framework of the mikusinski calculus the existence of the solution of the corresponding problem in the field of mikusinski operators is proved moreover an approximate solution of the corresponding problem is constructed and the error of approximation is estimated

global existence and stability for wave equation of kirchhoff type with memory condition at the boundary abstract we consider a nonlinear wave equation of kirchhoff type with memory condition at the boundary and we study the asymptotic behavior of the corresponding solutions we proved that the energy decay with the same rate of decay of the relaxation function that is the energy decays exponentially when the relaxation function decay exponentially and polynomially when the relaxation function decay polynomially

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

on a shock problem involving a linear viscoelastic bar abstract the paper deals with the initial boundary value problem for the linear wave equation 1 u tt t u xx ku u t f x t 0 x 1 0 t t u 0 t 0 t u x 1 t q t u x 0 u 0 x u t x 0 u 1 x where k are given constants and u 0 u 1 f are given functions the unknown function u x t and the unknown boundary value q t satisfy the following linear integral equation 2 q t k 1 t u 1 t 1 t u t 1 t g t 0 t k t s u 1 s d s where g k k 1 1 are given functions the paper consists of four parts in part 1 we prove a theorem of global existence and uniqueness of a weak solution u q of problem 1 2 the proof is based on a galerkin type approximation associated to various energy estimates type bounds weak convergence and compactness arguments in part 2 it is devoted to the study of the regularity of the solution u q with respect to the functions 1 f g k k 1 in part 3 we prove that the solution u q of this problem is stable with respect to the data k 1 f g k k 1 finally in part 4 we obtain an asymptotic expansion of the solution u q of this problem up to order n 1 in k for k sufficiently small

an iterative svd krylov based method for model reduction of large scale dynamical systems abstract in this paper we propose a model reduction algorithm for approximation of large scale linear time invariant dynamical systems the method is a two sided projection combining features of the singular value decomposition svd based and the krylov based model reduction techniques while the svd side of the projection depends on the observability gramian the krylov side is obtained via iterative rational krylov steps the reduced model is asymptotically stable matches certain moments and solves a restricted h 2 minimization problem we present modifications to the proposed approach for employing low rank gramians in the reduction step and also for reducing discrete time systems several numerical examples from various disciplines verify the effectiveness of the proposed approach it performs significantly better than the q cover a yousouff r e skelton covariance equivalent realizations with applications to model reduction of large scale systems in c t leondes ed control and dynamic systems vol 22 academic press 1985 pp 273 348 a yousouff d a wagie r e skelton linear system approximation via covariance equivalent realizations journal of math anal and appl 196 1985 91 115 and the least squares s gugercin a c antoulas model reduction of large scale systems by least squares linear algebra appl 415 2 3 2006 290 321 methods that have a similar projection structure to the proposed method also in terms of both the h 2 and h error measures its performance is comparable to or sometimes better than that of balanced truncation moreover the method proves to be robust with respect to the perturbations due to usage of approximate gramians

performance of sphere decoding of block codes a sphere decoder searches for the closest lattice point within a certain search radius the search radius provides a tradeoff between performance and complexity we focus on analyzing the performance of sphere decoding of linear block codes we analyze the performance of soft decision sphere decoding on awgn channels and a variety of modulation schemes a hard decision sphere decoder is a bounded distance decoder with the corresponding decoding radius we analyze the performance of hard decision sphere decoding on binary and q ary symmetric channels an upper bound on the performance of maximum likelihood decoding of linear codes defined over fq e g reed solomon codes and transmitted over q ary symmetric channels is derived and used in the analysis we then discuss sphere decoding of general block codes or lattices with arbitrary modulation schemes the tradeoff between the performance and complexity of a sphere decoder is then discussed

μ dependent model reduction for uncertain discrete time switched linear systems with average dwell time in this article the model reduction problem for a class of discrete time polytopic uncertain switched linear systems with average dwell time switching is investigated the stability criterion for general discrete time switched systems is first explored and a dependent approach is then introduced for the considered systems to the model reduction solution a reduced order model is constructed and its corresponding existence conditions are derived via lmi formulation the admissible switching signals and the desired reduced model matrices are accordingly obtained from such conditions such that the resulting model error system is robustly exponentially stable and has an exponential h performance a numerical example is presented to demonstrate the potential and effectiveness of the developed theoretical results

soft quasi maximum likelihood detection for multiple antenna wireless channels the paper addresses soft maximum likelihood ml detection for multiple antenna wireless communication channels we propose a soft quasi ml detector that maximizes the log likelihood function by deploying a semi definite relaxation sdr given perfect channel state information at the receiver the quasi ml sdr detector closely approximates the performance of the optimal ml detector in both coded and uncoded multiple input multiple output mimo channels with quadrature phase shift keying qpsk modulation and frequency flat rayleigh fading the complexity of the quasi ml sdr detector is much less than that of the optimal ml detector thus offering more favorable performance complexity characteristics in contrast to the existing sphere decoder the new quasi ml detector enjoys guaranteed polynomial worst case complexity the two detectors exhibit quite comparable performance in a variety of ergodic qpsk mimo channels but the complexity of the quasi ml detector scales better with increasing number of transmit and receive antennas especially in the region of low signal to noise ratio snr

balanced truncation for a class of stochastic jump linear systems and model reduction for hidden markov models this paper develops a generalization of the balanced truncation algorithm applicable to a class of discrete time stochastic jump linear systems the approximation error which is captured by means of the stochastic l 2 gain is bounded from above by twice the sum of singular numbers associated to the truncated states similar to the case of linear time invariant systems a two step model reduction algorithm for hidden markov models is also developed the first step relies on the aforementioned balanced truncation algorithm due to a topological equivalence established between hidden markov models and a subclass of stochastic jump linear systems in a second step the positivity constraints which reflect the hidden markov model structure are enforced by solving a low dimensional optimization problem

sphere constrained ml detection for frequency selective channels the maximum likelihood ml sequence detection problem for channels with memory is investigated the viterbi algorithm va provides an exact solution its computational complexity is linear in the length of the transmitted sequence but exponential in the channel memory length on the other hand the sphere decoding sd algorithm also solves the ml detection problem exactly and has expected complexity which is a low degree polynomial often cubic in the length of the transmitted sequence over a wide range of signal to noise ratios we combine the sphere constrained search strategy of sd with the dynamic programming principles of the va the resulting algorithm has the worst case complexity determined by the va but often significantly lower expected complexity

leveraging coherent space time codes for noncoherent communication via training training codes are introduced for the multiple antenna noncoherent multiple block rayleigh fading channel in which the fading coefficients which are constant over a fixed number of dimensions coherence interval for each block and then change independently to a new realization are known neither at the transmitter nor at the receiver each codeword of a training code consists of a part known to the receiver used to form a minimum mean squared error mmse estimate of the channel and a part that contains codeword s of a space time block or trellis code designed for the coherent channel in which the receiver has perfect knowledge of the channel the channel estimate is used as if it were error free for decoding the information bearing part of the training codeword training codes are hence easily designed to have high rate and low decoding complexity by choosing the underlying coherent code to have high rate and to be efficiently decodable conditions for which the estimator detector e d receiver is equivalent to the optimal noncoherent receiver are established a key performance analysis result of this paper is that the training codes when decoded with the e d receiver achieve a diversity order of the error probability that is equal to the diversity order of the underlying coherent code in some cases the performance of training codes can be measured relative to coherent reception via training efficiency which is then optimized over the energy allocation between the training and data phases in the limit of increasing block lengths training codes always achieve the performance of coherent reception the examples of training codes provided in this work have polynomial complexity in rate but an error rate comparable to the best performing unitary designs available even though the latter require exponential decoding complexity

cryptanalytic attacks on the multiplicative knapsack cryptosystem and on shamir s fast signature scheme the basic merkle hellman additive trapdoor knapsack public key cryptosystem was recently shown to be insecure and attacks have also been developed on stronger variants of it such as the graham shamir system and the iterated knapsack cryptosystem it is shown that some simple variants of another merkle hellman system the multiplicative knapsack cryptosystem are insecure it is also shown that the shamir fast signature scheme can be broken quickly similar attacks can also be used to break the schobi massey authentication scheme these attacks have not been rigorously proved to succeed but heuristic arguments and empirical evidence indicate that they work on systems of practical size

reachability and observability reduction for linear switched systems with constrained switching we present an algorithm for reducing the number of continuous states of a discrete time linear switched system such that the reduced system has the same input output behavior as the original system for a subset of switching sequences the procedure can be interpreted as reachability and observability reduction for a linear switched system with constrained switching the proposed method is expected to be useful for abstraction based control synthesis methods for hybrid systems

a simultaneous balanced truncation approach to model reduction of switched linear systems this paper deals with model reduction by balanced truncation of switched linear systems sls we consider switched linear systems whose dynamics depending on the switching signal switches between finitely many linear systems with a common state space these linear systems are called the modes of the sls the idea is to seek for conditions under which there exists a single state space transformation that brings all modes of the sls in balanced coordinates as a measure of reachability and observability of the state components of the sls we take the average of the diagonal gramians we then perform balanced truncation by discarding the state components corresponding to the smallest diagonal elements of this average balanced gramian in order to carry out this program we derive necessary and sufficient conditions under which a finite collection of linear systems with common state space can be balanced by a single state space transformation among other things we derive sufficient conditions under which global uniform exponential stability of the sls is preserved under simultaneous balanced truncation likewise we derive conditions for preservation of positive realness or bounded realness of the sls finally in case that the conditions for simultaneous balancing do not hold or we simply do not want to check these conditions we propose to compute a suitable state space transformation on the basis of minimization of an overall cost function associated with the modes of the sls we show that in case our conditions do hold this transformation is in fact simultaneously balancing bringing us back to the original method described in this paper

a semilinear wave equation with space time dependent coefficients and a memory boundarylike antiperiodic condition regularity and stability this paper deals with regularity and stability of solutions to an initial boundary value problem of a semilinear wave equation this equation admits space time dependent coefficients and a memory boundarylike antiperiodic condition for regularity or existence of a unique strong solution the faedo galerkin method and the energy method associated with the maximal solution of a nonlinear volterra integral equation are applied then as an application of the regularity result stability of this unique strong solution is obtained by the energy method

reduced and fixed complexity variants of the lll algorithm for communications the lenstra lenstra lovasz lll algorithm is a popular lattice reduction algorithm in communications in this paper variants of the lll algorithm with either reduced or fixed complexity are proposed and analyzed specifically the use of effective lll reduction for lattice decoding is presented where size reduction is only performed for pairs of consecutive basis vectors its average complexity measured by the number of floating point operations and averaged over i i d standard normal lattice bases is shown to be o n 3 log n where n is the lattice dimension this average complexity is an order lower than previously thought to address the issue of variable complexity of the lll algorithm two fixed complexity approximations are proposed one is fixed complexity effective lll for which the first vector of the basis is proven to be bounded in length the other is fixed complexity lll with deep insertion which is shown to be closely related to the well known v blast algorithm such fixed complexity structures are much desirable in hardware implementation since they allow straightforward constant throughput implementation

factorization properties of lattices over the integers abstract let a be a nonsingular n n matrix over the integers l l a denotes the lattice whose elements are combinations with integer coefficients of the rows of a l is cyclic if it can be defined in the modular form l x x i a i x i 0 mod d where the a i s and d are integers and 0 a i d let l l 1 l 2 b be lattices over the integers l l 1 l 2 is a factorization of l if every element of l is a combination of the rows of b such that the vector of combination coefficients is in l 1 and b is a nonsingular n n matrix the following results are proved every lattice can be expressed as a product of cyclic factors in polynomial time every cyclic lattice can be factored into simple term explained in the text factors in polynomial time every simple lattice can be factored into prime factors in polynomial time if a prime factorization of the determinant of its basis is given in addition we provide polynomial algorithms for the following problems transform a cyclic lattice given by a basis into a modular form and vice versa find a basis of a finite modular lattice given in modular form

on the diversity multiplexing tradeoff under groupwise successive interference cancelation in this paper we study the diversity multiplexing tradeoff assuming groupwise successive interference cancelation gsic gsic with layered codes in multiple input multiple output mimo can vary from the plain sic to the maximum likelihood ml decoding according to the group sizes thus is flexible in both complexity and performance the maximum group size is a dominating factor for the computation complexity of gsic when the processing complexity is polynomially dependent on the group size with a high order in this paper we show the tradeoff among the maximum group size diversity gain and multiplexing gain gdmt under the gsic and under the gsic combined with antenna selection gsicas for a given group size bound c we show that the number of groups achieving the optimal dmt under the gsic with selected transmit antennas is equal to c and a larger group should have a higher priority in decoding order the optimal grouping is obtained in a systematic way based on these results we find a limited set of groupings that contains the grouping achieving the optimal gdmt under gsic and under gsicas the optimal multiplexing gain allocation for the optimal grouping is then found systematically and efficiently within the limited set

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

applications of convex optimization in signal processing and digital communication in the last two decades the mathematical programming community has witnessed some spectacular advances in interior point methods and robust optimization these advances have recently started to significantly impact various fields of applied sciences and engineering where computational efficiency is essential this paper focuses on two such fields digital signal processing and communication in the past the widely used optimization methods in both fields had been the gradient descent or least squares methods both of which are known to suffer from the usual headaches of stepsize selection algorithm initialization and local minima with the recent advances in conic and robust optimization the opportunity is ripe to use the newly developed interior point optimization techniques and highly efficient software tools to help advance the fields of signal processing and digital communication this paper surveys recent successes of applying interior point and robust optimization to solve some core problems in these two fields the successful applications considered in this paper include adaptive filtering robust beamforming design and analysis of multi user communication system channel equalization decoding and detection throughout our emphasis is on how to exploit the hidden convexity convex reformulation of semi infinite constraints analysis of convergence complexity and performance as well as efficient practical implementation

maximum likelihood sequence estimation from the lattice viewpoint considers the problem of data detection in multilevel lattice type modulation systems in the presence of intersymbol interference and additive white gaussian noise the conventional maximum likelihood sequence estimator using the viterbi algorithm has a time complexity of o m sup spl nu 1 operations per symbol and a space complexity of o spl delta m sup spl nu storage elements where m is the size of input alphabet spl nu is the length of channel memory and spl delta is the truncation depth by revising the truncation scheme and viewing the channel as a linear transform the authors identify the problem of maximum likelihood sequence estimation with that of finding the nearest lattice point from this lattice viewpoint the lattice sequence estimator for pam systems is developed which has the following desired properties 1 its expected time complexity grows as spl delta sup 2 as snr spl rarr spl infin 2 its space complexity grow as spl delta and 3 its error performance is effectively optimal for sufficiently large m a tight upper bound on the symbol error probability of the new estimator is derived and is confirmed by the simulation results of an example channel it turns out that the estimator is effectively optimal for m spl ges 4 and the loss in signal to noise ratio is less than 0 5 db even for m 2 finally limitations of the proposed estimator are also discussed

lower bounds in spectral tests for vectors of nonsuccessive values produced by multiple recursive generator with some zero multipliers l ecuyer develops lower bounds for the maximum distance of the parallel hyperplanes generated by the vectors of nonsuccessive random numbers rns obtained from multiple recursive generators mrgs in this paper a stronger bound twice that obtained by l ecuyer is derived for kth order mrgs with fewer than k terms in the recursive relationship much stronger bounds are found large distance implies bad lattice structure in designing rn generators this factor should be taken into consideration