space time block codes from orthogonal designs we introduce space time block coding a new paradigm for communication over rayleigh fading channels using multiple transmit antennas data is encoded using a space time block code and the encoded data is split into n streams which are simultaneously transmitted using n transmit antennas the received signal at each receive antenna is a linear superposition of the n transmitted signals perturbed by noise maximum likelihood decoding is achieved in a simple way through decoupling of the signals transmitted from different antennas rather than joint detection this uses the orthogonal structure of the space time block code and gives a maximum likelihood decoding algorithm which is based only on linear processing at the receiver space time block codes are designed to achieve the maximum diversity order for a given number of transmit and receive antennas subject to the constraint of having a simple decoding algorithm the classical mathematical framework of orthogonal designs is applied to construct space time block codes it is shown that space time block codes constructed in this way only exist for few sporadic values of n subsequently a generalization of orthogonal designs is shown to provide space time block codes for both real and complex constellations for any number of transmit antennas these codes achieve the maximum possible transmission rate for any number of transmit antennas using any arbitrary real constellation such as pam for an arbitrary complex constellation such as psk and qam space time block codes are designed that achieve 1 2 of the maximum possible transmission rate for any number of transmit antennas for the specific cases of two three and four transmit antennas space time block codes are designed that achieve respectively all 3 4 and 3 4 of maximum possible transmission rate using arbitrary complex constellations the best tradeoff between the decoding delay and the number of transmit antennas is also computed and it is shown that many of the codes presented here are optimal in this sense as well

two novel methods and multi mode periodic solutions for the fermi pasta ulam model we introduce two novel methods for studying periodic solutions of the fpu model both numerically and rigorously one is a variational approach based on the dual formulation of the problem and the other involves computer assisted proofs these methods are used e g to construct a new type of solutions whose energy is spread among several modes associated with closely spaced resonances

stability of low dimensional bushes of vibrational modes in the fermi pasta ulam chains bushes of normal modes represent the exact excitations in the nonlinear physical systems with discrete symmetries physica d 117 1998 43 the present paper is the continuation of our previous paper physica d 166 2002 208 where these dynamical objects of new type were discussed for the monoatomic nonlinear chains here we develop a simple crystallographic method for finding bushes in nonlinear chains and investigate stability of one and two dimensional vibrational bushes for both fpu and fpu models in particular of those revealed recently in physica d 175 2003 31

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

universal space time codes from demultiplexed trellis codes in broadcast scenarios or in the absence of accurate channel probability distribution information code design for consistent channel by channel performance rather than average performance over a channel distribution may be desirable root and varaiya s compound channel theorem for linear gaussian channels promises the existence of universal codes that operate reliably whenever the channel mutual information mi is above the transmitted rate this paper presents two dimensional trellis codes that provide such universal performance over the compound linear vector gaussian channel when demultiplexed over two three and four transmit antennas the presented trellis codes found by exhaustive search guarantee consistent performance on every matrix channel that supports the information transmission rate with an mi gap that is similar to the capacity gap of a well designed additive white gaussian noise awgn specific code on the awgn channel as a result of their channel by channel consistency the universal trellis codes presented here also deliver comparable or in some cases superior frame error rate and bit error rate performance under quasi static rayleigh fading as compared with trellis codes of similar complexity that are designed specifically for the quasi static rayleigh fading scenario

constructions of multiblock space time coding schemes that achieve the diversity multiplexing tradeoff constructions of multiblock space time coding schemes that are optimal with respect to diversity multiplexing d m tradeoff when coding is applied over any number of fading blocks are presented in this correspondence the constructions are based on a left regular representation of elements in some cyclic division algebra in particular the main construction applies to the case when the quasi static fading interval equals the number of transmit antennas hence the resulting scheme is termed a minimal delay multiblock space time coding scheme constructions corresponding to the cases of nonminimal delay are also provided as the number of coded blocks approaches infinity coding schemes derived from the proposed constructions can be used to provide a reliable multiple input multiple output mimo communication with vanishing error probability

interactions between normal modes in nonlinear dynamical systems with discrete symmetry exact results abstract we discuss in detail the concept of bush of modes introduced by us earlier for classical nonlinear systems with discrete point or space symmetry each bush comprises all modes singled out by the symmetry group of an initial excitation and may be considered as a geometrical and dynamical object we prove theorems that describe structure and some properties of bushes for hamiltonian and for a wide class of non hamiltonian systems theorems 2 a and b permit one to introduce new variables nonlinearly connected with normal modes which in a sense are independent of each other in case they are associated with different irreducible representations of the symmetry group of a system in equilibrium such independence provides a possibility of singling out specific dynamical regimes of an essentially lesser dimensionality since many different bushes are described by the same differential equations they may be classified by certain classes of universality possible physical applications of vibrational bushes are suggested

an error event sensitive tradeoff between rate and coding gain in mimo mac this paper investigates the design of codes for multiple input multiple output mimo multiple access channel mac if a joint maximum likelihood decoding is to be performed at the receiver then every mimo mac code can be regarded as a single user code where the minimum determinant criterion proposed by tarokh et al is useful for designing such codes and for upper bounding the maximum pairwise error probability pep whenever the codes are of finite rate and operate in finite signal to noise ratio range unlike the case of single user codes where the minimum determinant can be lower bounded by a fixed constant as code rate grows it was proved by lahtonen et al that the minimum determinant of mimo mac codes decays as a function of the rates this decay phenomenon is further investigated in this paper and upper bounds for the decays of minimum determinant corresponding to each error event are provided lower bounds for the optimal decay are established and are based on an explicit construction of codes using algebraic number theory and diophantine approximation for some error profiles the constructed codes are shown to meet the aforementioned upper bounds hence they are optimal finite rate codes in terms of peps associated with such error events an asymptotic diversity multiplexing gain tradeoff dmt analysis of the proposed codes is also given it is shown that these codes are dmt optimal when the values of multiplexing gains are small

remarks on space time codes including a new lower bound and an improved code this article presents a new asymptotically exact lower bound on pairwise error probability of a space time code as well as an example code that outperforms the comparable orthogonal design based space time odst code also contained in the article are an exact expression for pairwise error probability pep signal design guidelines and some observations relating to the reception of odst codes

on the densest mimo lattices from cyclic division algebras it is shown why the discriminant of a maximal order within a cyclic division algebra must be minimized in order to get the densest possible matrix lattices with a prescribed nonvanishing minimum determinant using results from class field theory a lower bound to the minimum discriminant of a maximal order with a given center and index the number of tx rx antennas is derived also numerous examples of division algebras achieving the bound are given for example a matrix lattice with quadrature amplitude modulation qam coefficients that has 2 5 times as many codewords as the celebrated golden code of the same minimum determinant is constructed also a general algorithm due to ivanyos and ronyai for finding maximal orders within a cyclic division algebra is described and enhancements to this algorithm are discussed also some general methods for finding cyclic division algebras of a prescribed index achieving the lower bound are proposed

bushes of vibrational modes for fermi pasta ulam chains abstract some exact solutions and multimode invariant submanifolds were found for the fermi pasta ulam fpu model by poggi and ruffo physica d 103 1997 251 in the present paper we demonstrate how results of such a type can be obtained for an arbitrary n particle chain with periodic boundary conditions with the aid of our group theoretical approach physica d 117 1998 43 based on the concept of bushes of normal modes in mechanical systems with discrete symmetry the integro differential equation describing the fpu dynamics in the modal space is derived the loss of stability of the bushes of modes for the fpu model in particular for the limiting case n for the dynamical regime with displacement pattern having period twice the lattice spacing mode is studied our results for the fpu chain are compared with those by poggi and ruffo for the fpu chain

nonlinear constructive interference in electrical lattices we analyze the constructive interference of input signals in nonlinear discrete two dimensional media the media consist of inductor capacitor lattices with saturating voltage dependent capacitors we find that nonlinearity significantly boosts the ability of such media to generate large amplitude output signals from small amplitude inputs to understand this boosting we develop a general perturbative method suitable for finding the steady state solution of a damped n ifmmode times else texttimes fi n nonlinear lattice that is driven at a single frequency we verify our theory using extensive numerical simulations

higher order averaging periodic solutions linear systems and an application existence and stability of periodic solutions by using second order averaging when the vector field by first order averaging vanishes will be studied in this paper as well as its generalization to higher order a special averaging algorithm for the computation of higher approximations of the fundamental matrix of linear equations with periodic coefficients is given as an application the existence and stability of periodic solutions of an inhomogeneous second order equation with time dependent damping coefficient are studied

symmetric invariant manifolds in the fermi pasta ulam lattice abstract the fermi pasta ulam fpu lattice with periodic boundary conditions and n particles admits a large group of discrete symmetries the fixed point sets of these symmetries naturally form invariant symplectic manifolds that are investigated in this short note for each k dividing n we find k degree of freedom invariant manifolds they represent short wavelength solutions composed of k fourier modes and can be interpreted as embedded lattices with periodic boundary conditions and only k particles inside these invariant manifolds other invariant structures and exact solutions are found which represent for instance periodic and quasi periodic solutions and standing and travelling waves some of these results have been found previously by other authors via a study of mode coupling coefficients and recently also by investigating bushes of normal modes the method of this paper is similar to the latter method and much more systematic than the former we arrive at previously unknown results without any difficult computations it is shown moreover that similar invariant manifolds exist also in the klein gordon kg lattice and in the thermodynamic and continuum limits

q breathers in fermi pasta ulam chains existence localization and stability the fermi pasta ulam fpu problem consists of the nonequipartition of energy among normal modes of a weakly anharmonic atomic chain model in the harmonic limit each normal mode corresponds to a periodic orbit in phase space and is characterized by its wave number q we continue normal modes from the harmonic limit into the fpu parameter regime and obtain persistence of these periodic orbits termed here q breathers qb they are characterized by time periodicity exponential localization in the q space of normal modes and linear stability up to a size dependent threshold amplitude trajectories computed in the original fpu setting are perturbations around these exact qb solutions the qb concept is applicable to other nonlinear lattices as well

selection and rate adaptation schemes for mimo multiple access channels with low rate channel feedback in this paper two selection schemes are proposed for coded transmission over multiple input multiple output mimo multiple access channels mac to yield a much higher diversity multiplexing gain tradeoff dmt performance these schemes require a channel feedback but at an extremely low rate the first scheme is based on user selection and can be easily implemented in the existing mimo mac systems upper bounds on the minimal computational complexity required by sphere decoders to decode dmt optimal codes for this scheme as well as for mimo mac without feedback are given it is shown that this scheme can offer both a much larger dmt and an exponential reduction on decoding complexity compared with the latter the second scheme selects jointly the users and their transmit antennas it requires an additional design of rate assignments for performance optimization a very general framework on the design of optimal rate assignments is thus provided it is shown that this scheme can yield dmt performances far superior to the optimal mimo mac dmt without channel feedback the simulation results confirm that in some cases this scheme can provide an astonishing snr gain of 14 64 db at outage probability 10 6 compared with the optimal mimo mac coding schemes without feedback

on the autocorrelation of finite length sequences lt is well known that all autocorrelation sequences are positive semi definite the correlation sequence is further constrained when as is often the case it is obtained from correlating a finite length data sequence with itself in this paper we study the effect of the data sequence length on the attainable correlations we derive a formula for the sequence length needed to match an autocorrelation value at a given lag the formula indicates that inordinately long sequences are needed to obtain a normalized autocorrelation coefficient near unity we conclude that all zero moving average models may be ill suited for highly correlated signals the formula for the single lag case is then used to obtain a bound on the sequence length needed to match a set of autocorrelations simultaneously

diversity multiplexing tradeoff and outage performance for rician mimo channels in this paper we analyze the diversity multiplexing tradeoff dmt originally introduced by zheng and tse and outage performance for rician multiple input multiple output mimo channels the dmt characteristics of rayleigh and rician channels are shown to be identical in a high signal to noise ratio snr regime the log log plot of outage probability versus snr curve for a rician channel is a shifted version of that for the corresponding rayleigh channel the snr gap between the outage curves of the rayleigh and rician channels is derived the dmt and outage performance are also analyzed for rician multiple input single output miso single input multiple output simo channels over a finite snr regime a closed form expression for the outage probability is derived and the finite snr dmt characteristic is analyzed it is observed that the maximum diversity gain can be achieved at some finite snr the maximum gain tends to increase linearly with the rician factor the finite snr diversity gain is shown to be a linear function of the finite snr multiplexing gain the consistency between the dmts for finite and infinite snrs is also shown

stability of linear predictors and numerical range of a linear operator corresp the zeros of a predictor polynomial are shown to belong to the numerical range of a linear operator associated with the particular prediction problem considered application of this result to the autocorrelation and postwindowed cases shows that the predictor polynomials enjoy a well defined stability margin which depends in particular on the length of the data sequence the generalization of these results to the multichannel case is also discussed

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

locations of zeros of predictor polynomials this work shows that the zeros of the predictor polynomial determined by a finite data least squares linear prediction problem lie inside an irregular polygon contained in the unit circle of the complex plane the polygon is independent of the data only depending on the length of the data and the order of the predictor the results are an analytic statement of the resolution limitations of spectral estimates based on finite data least squares linear predictors

remarks on diversity multiplexing tradeoffs for multiple access and point to point mimo channels in this paper we answer several open questions related to diversity multiplexing tradeoffs dmts for point to point and multiple access mac mimo channels by analyzing the dmt performance of a simple code we show that the optimal mac dmt holds even when the channel remains fixed for less than knt nr 1 channel uses where k is the number of users nt is the number of transmit antennas of each user and nr is the number of receive antennas at receiver we also prove that the simple code is mac dmt optimal a general code design criterion for constructing mac dmt optimal codes that is much more relaxed than the previously known design criterion is provided finally by changing some design parameters the simple code is modified for use in point to point mimo channels we show the modified code achieves the same dmt performance as the gaussian random code

trellis codes for periodic erasures this paper describes techniques for the design and analysis of trellis codes that provide reliable communication over every channel in a specified set of possible channels where each channel is characterized by additive white gaussian noise with a distinct periodic variation in signal to noise ratio an important practical application for such trellis codes is the periodic erasure channel produced by partial band interference dispersed by a block interleaver we present trellis codes that provide reliable communication over all periodic erasure patterns of a given period for which the number of unerased coded bits per period is at least equal to the number of information bits per period

stbc schemes with nonvanishing determinant for certain number of transmit antennas a space time block code scheme stbc scheme is a family of stbcs c snr indexed by the signal to noise ratio snr such that the rate of each stbc scales with snr an stbc scheme is said to have a nonvanishing determinant if the coding gain of every stbc in the scheme is lower bounded by a fixed nonzero value the nonvanishing determinant property is important from the perspective of the diversity multiplexing gain dm g tradeoff a concept that characterizes the maximum diversity gain achievable by any stbc scheme transmitting at a particular rate this correspondence presents a systematic technique for constructing stbc schemes with nonvanishing determinant based on cyclic division algebras prior constructions of stbc schemes from cyclic division algebra have either used transcendental elements in which case the scheme may have vanishing determinant or is available with nonvanishing determinant only for two three four and six transmit antennas in this correspondence we construct stbc schemes with nonvanishing determinant for the number of transmit antennas of the form 2 sup k 3 spl middot 2 sup k 2 spl middot 3 sup k and q sup k q 1 2 where q is any prime of the form 4s 3 for cyclic division algebra based stbc schemes in a recent work by elia et al the nonvanishing determinant property has been shown to be sufficient for achieving dm g tradeoff in particular it has been shown that the class of stbc schemes constructed in this correspondence achieve the optimal dm g tradeoff moreover the results presented in this correspondence have been used for constructing optimal stbc schemes for arbitrary number of transmit antennas by elia et al

universal space time trellis codes this article gives practical examples of space time trellis codes performing as predicted by root and varaiya s 1968 compound channel theorem specifically 32 state and 64 state 2 spl times 2 space time trellis codes are presented that provide a bit error rate ber of 10 sup 5 on all 2 spl times 2 matrix channels with an excess mutual information mi within 8 of the excess mi required by standard trellis codes of the same complexity operating only in additive white gaussian noise awgn not surprisingly the universal space time trellis coded modulations st tcms provide average bit and frame error rates in quasi static rayleigh fading qrf that are comparable to those achieved by st tcms designed specifically for qrf as well as standard tcms followed by the alamouti 1998 space time block code however all of these other schemes require more excess mi in the worst case and some have a significantly wider variation in the required excess mi the article also compares the universal and quasi static rayleigh fading design approaches analytically and bounds the worst case distance of a trellis code on a 2 spl times 2 channel using the distances of the code on singular and unitary channels this bound is extended to the more general n sub t spl times n sub r scenario

zero location of lacunary prediction polynomials this correspondence discusses the stability of some lacunary prediction polynomials and rederives in passing known upper bounds for the normalized autocorrelation coefficients

numerical analysis of the one mode solutions in the fermi pasta ulam system the stability of the one mode nonlinear solutions of the fermi pasta ulam ensuremath beta system is numerically investigated no external perturbation is considered for the one mode exact analytical solutions the only perturbation being that introduced by computational errors in the numerical integration of motion equations the threshold energy for the excitation of the other normal modes and the dynamics of this excitation are studied as a function of the parameter ensuremath mu characterizing the nonlinearity the energy density ensuremath epsilon and the number n of particles of the system the results achieved confirm in part previous ones obtained with a linear analysis of the problem of the stability and clarify the dynamics by which a one mode exchanges energy with the other modes with increasing energy density in a range of energy density near the threshold value and for various values of the number of particles n the nonlinear one mode exchanges energy with the other linear modes for a very short time immediately recovering all its initial energy this sort of recurrence is very similar to fermi recurrences even if in the fermi recurrences the energy of the initially excited mode changes continuously and only periodically recovers its initial value a tentative explanation for this intermittent behavior in terms of floquet s theorem is proposed preliminary results are also presented for the fermi pasta ulam ensuremath alpha system which show that there is a stability threshold for large n independent of n

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

stability of simple periodic orbits and chaos in a fermi pasta ulam lattice we investigate the connection between local and global dynamics in the fermi pasta ulam fpu beta model from the point of view of stability of its simplest periodic orbits spo s in particular we show that there is a relatively high q mode q 2 n 1 3 of the linear lattice having one particle fixed every two oppositely moving ones called spo2 here which can be exactly continued to the nonlinear case for n 5 3m m 0 1 2 and whose first destabilization e 2u as the energy or beta increases for any fixed n practically coincides with the onset of a weak form of chaos preceding the breakdown of fpu recurrences as predicted recently in a similar study of the continuation of a very low q 3 mode of the corresponding linear chain this energy threshold per particle behaves like e 2u n alpha n 2 we also follow exactly the properties of another spo with q n 1 2 in which fixed and moving particles are interchanged called spo1 here and which destabilizes at higher energies than spo2 since e 1u n alpha n 1 we find that immediately after their first destabilization these spo s have different positive lyapunov spectra in their vicinity however as the energy increases further at fixed n these spectra converge to the same exponentially decreasing function thus providing strong evidence that the chaotic regions around spo1 and spo2 have merged and large scale chaos has spread throughout the lattice since these results hold for n arbitrarily large they suggest a direct approach by which one can use local stability analysis of spo s to estimate the energy threshold at which a transition to ergodicity occurs and thermodynamic properties such as kolmogorov sinai entropies per particle can be computed for similar one dimensional lattices

precoded integer forcing universally achieves the mimo capacity to within a constant gap an open loop single user multiple input multiple output mimo communication scheme is considered where a transmitter equipped with multiple antennas encodes the data into independent streams all taken from the same linear code the coded streams are then linearly precoded using the encoding matrix of a perfect linear dispersion space time code at the receiver side integer forcing equalization is applied followed by standard single stream decoding it is shown that this communication architecture achieves the capacity of any gaussian mimo channel up to a gap that depends only on the number of transmit antennas

the zone boundary mode in periodic nonlinear electrical lattices abstract we study the existence and linear stability of the zone boundary mode in a nonlinear electrical lattice consisting of n inductors and n voltage dependent capacitors with periodic boundary conditions the inductances are allowed to alternate while the capacitors are identical and each have a quadratic dependence on voltage by block diagonalizing a 2 n 2 n floquet problem we reduce the question of the stability of the mode to a single hill s equation that is analyzed using methods of perturbation theory and averaging we show that periodicity of the lattice inductances degrades stability and also show that the instability threshold is proportional to n 2 numerical computations validate the perturbative results

correlation matching by finite length sequences the problem of matching a finite length data sequence to a set of not necessarily uniformly spaced correlation lags is considered a characterization of the set of correlations that can be derived from sequences of a given length is presented using this characterization an algorithm called the expanding hull algorithm is presented for determining the minimum sequence length and a sequence of this length which matches a given set of correlation values is obtained this sequence has a z transform which is the lowest order correlation matching moving average model the sequence also generates the minimum length correlation extension the expanding hull algorithm also provides a method for extendibility testing of missing lag and multidimensional correlation sequences numerical examples are provided

the design of trellis coded mpsk for fading channels performance criteria it has been well established that the appropriate criterion for optimum trellis coded modulation design on the additive white gaussian noise channel is maximization of the free euclidean distance it is shown that when the trellis coded modulation is used on a rician fading channel with interleaving deinterleaving the design of the code of optimum performance is guided by other factors in particular the length of the shortest error event path and the product of branch distances possibly normalized by the euclidean distance of the path along the path although maximum free distance d sub free is still an important consideration it plays a less significant role the more severe the fading is on the channel these considerations lead to the definition of a new distance measure of optimization of trellis codes transmitted over rician fading channels if no interleaving deinterleaving is used then once again the design of the trellis code is guided by maximizing d sub free