dithered quantization via orthogonal transformations dithered quantization is a technique used to reduce or eliminate the statistical dependence between the signal and quantization error this is most often achieved via adding pseudo random noise prior to quantization the present work develops a different dithering method where dithering is accomplished by applying an orthogonal transformation to a vector of samples prior to quantization and applying its inverse to the output of the quantizer focusing on uniform scalar quantization it is shown that for any quantization rate the proposed architecture approaches second order independence i e asymptotically vanishing correlation as the dimension of the vector of samples processed jointly grows

an information theoretic framework for deriving canonical decision feedback receivers in gaussian channels a framework is presented that allows a number of known results relating feedback equalization linear prediction and mutual information to be easily understood a lossless additive decomposition of mutual information in a general class of gaussian channels is introduced and shown to produce an information preserving canonical decision feedback receiver the approach is applied to intersymbol interference isi channels to derive the well known minimum mean square error mmse decision feedback equalizer dfe when applied to the synchronous code division multiple access cdma channel the result is the mmse or signal to interference ratio sir maximizing decision feedback detector which is shown to achieve the channel sum capacity at the vertices of the capacity region finally in the case of the asynchronous cdma channel we are able to give new connections between information theory decision feedback receivers and structured factorizations of multivariate spectra

adaptive minimum symbol error rate equalization for quadrature amplitude modulation we propose the adaptive minimum symbol error rate algorithm which is a low complexity technique for adapting the coefficients of a linear equalizer in systems using pulse amplitude or quadrature amplitude modulation the proposed algorithm very nearly minimizes error probability in white gaussian noise and can significantly outperform the minimum mean squared error equalizer by as much as 16 db when the number of equalizer coefficients is small relative to the severity of the intersymbol interference

on the multifractal nature of fully developed turbulence and chaotic systems it is generally argued that the energy dissipation of three dimensional turbulent flow is concentrated on a set with non integer hausdorff dimension recently in order to explain experimental data it has been proposed that this set does not possess a global dilatation invariance it can be considered to be a multifractal set the authors review the concept of multifractal sets in both turbulent flows and dynamical systems using a generalisation of the beta model

a compute and forward scheme for gaussian bi directional relaying with inter symbol interference we provide inner and outer bounds on the capacity region for the gaussian bi directional relaying over inter symbol interference channels the outer bound is obtained by the conventional cut set argument for the inner bound we propose a compute and forward coding scheme based on lattice partition chains and study its achievable rate the coding scheme is a time domain coding scheme which uses a novel precoding scheme at the transmitter in combination with lattice precoding and a minimum mean squared error receiver to recover linear combinations of lattice codewords the proposed compute and forward coding scheme substantially outperforms decode and forward schemes while it is well known that for the point to point communication case both independent coding along sub channels and time domain coding can approach the capacity limit as a byproduct of the proposed scheme we show that for the bi directional relay case independent coding along sub channels is not optimal in general and joint coding across sub channels can improve the capacity for some channel realizations

optimum space time processors with dispersive interference unified analysis and required filter span we consider optimum space time equalizers with unknown dispersive interference consisting of a linear equalizer that both spatially and temporally whitens the interference and noise followed by a decision feedback equalizer or maximum likelihood sequence estimator we first present a unified analysis of the optimum space time equalizer and then show that for typical fading channels with a given signal to noise ratio snr near optimum performance can be achieved with a finite length equalizer expressions are given for the required filter span as a function of the dispersion length number of cochannel interferers number of antennas and snr which are useful in the design of practical near optimum space time equalizers

achieving the gaussian rate distortion function by prediction the ldquowater fillingrdquo solution for the quadratic rate distortion function of a stationary gaussian source is given in terms of its power spectrum this formula naturally lends itself to a frequency domain ldquotest channelrdquo realization we provide an alternative time domain realization for the rate distortion function based on linear prediction the predictive test channel has some interesting implications including the optimality at all distortion levels of pre post filtered vector quantized differential pulse code modulation dpcm and a duality relationship with decision feedback equalization dfe for intersymbol interference isi channels

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

design of block transceivers with decision feedback detection this paper presents a method for jointly designing the transmitter receiver pair in a block by block communication system that employs intrablock decision feedback detection we provide closed form expressions for transmitter receiver pairs that simultaneously minimize the arithmetic mean squared error mse at the decision point assuming perfect feedback the geometric mse and the bit error rate of a uniformly bit loaded system at moderate to high signal to noise ratios separate expressions apply for the zero forcing and minimum mse mmse decision feedback structures in the mmse case the proposed design also maximizes the gaussian mutual information and suggests that one can approach the capacity of the block transmission system using independent instances of the same gaussian code for each element of the block our simulation studies indicate that the proposed transceivers perform significantly better than standard transceivers and that they retain their performance advantages in the presence of error propagation

downlink mmse transceiver optimization for multiuser mimo systems duality and sum mse minimization we address the problem of minimum mean square error mmse transceiver design for point to multipoint transmission in multiuser multiple input multiple output mimo systems we focus on the problem of minimizing the downlink sum mse under a sum power constraint it is shown that this problem can be solved efficiently by exploiting a duality between the downlink and uplink mse feasible regions we propose two different optimization frameworks for downlink mmse transceiver design the first one solves an equivalent uplink problem then the result is transferred to the original downlink problem duality ensures that any uplink mmse scheme e g linear mmse reception or mmse decision feedback equalization dfe has a downlink counterpart we propose two globally optimum algorithms based on convex optimization the basic idea of the second framework is to perform optimization in an alternating manner by switching between the virtual uplink and downlink channels this strategy exploits that the same mse can be achieved in both links for a given choice of transmit and receive filters this iteration is proven to be convergent

substitution hamiltonians with bounded trace map orbits we investigate discrete one dimensional schrodinger operators with aperiodic potentials generated by primitive invertible substitutions on a two letter alphabet we prove that the spectrum coincides with the set of energies having a bounded trace map orbit and show that it is a cantor set of zero lebesgue measure this result confirms a suggestion arising from a study of roberts and complements results obtained by bovier and ghez as an application we present a class of models exhibiting a purely singular continuous spectrum with probability one

minimum ber linear transceivers for mimo channels via primal decomposition this paper considers the employment of linear transceivers for communication through multiple input multiple output mimo channels with channel state information csi at both sides of the link the design of linear mimo transceivers has been studied since the 1970s by optimizing simple measures of the quality of the system such as the trace of the mean square error matrix subject to a power constraint recent results showed how to solve the problem in an optimal way for the family of schur concave and schur convex cost functions in particular when the constellations used on the different transmit dimensions are equal the bit error rate ber averaged over these dimensions happens to be a schur convex function and therefore it can be optimally solved in a more general case however when different constellations are used the average ber is not a schur convex function and the optimal design in terms of minimum ber is an open problem this paper solves the minimum ber problem with arbitrary constellations by first reformulating the problem in convex form and then proposing two solutions one is a heuristic and suboptimal solution which performs remarkably well in practice the other one is the optimal solution obtained by decomposing the convex problem into several subproblems controlled by a master problem a technique borrowed from optimization theory for which extremely simple algorithms exist thus the minimum ber problem can be optimally solved in practice with very simple algorithms

dynamic nulling and canceling for efficient near ml decoding of mimo systems it is known that conventional nulling and canceling nc detection for multiple input multiple output mimo systems cannot exploit all of the available diversity and thus its performance is significantly inferior to that of maximum likelihood ml detection conventional nc employs the layerwise postequalization signal to noise ratios snrs as reliability measures for layer sorting these snrs are average quantities that do not depend on the received vector in this paper we propose the novel dynamic nulling and canceling dnc technique that uses approximate a posteriori probabilities as measures of layer reliability the dnc technique is a minimum mean square error mmse nulling scheme combined with an improved dynamic layer sorting rule that exploits the information contained in the current received vector we calculate the error probability of dnc for a simple special case and show that it is upper bounded by the error probability of conventional nc simulation results are presented for spatial multiplexing systems and for systems using linear dispersion codes it is demonstrated that the dnc technique can yield near ml performance for a wide range of system sizes and channel snrs at a fraction of the computational complexity of the sphere decoding algorithm for ml detection

block transmission over dispersive channels transmit filter optimization and realization and mmse dfe receiver performance optimal transmit filters for packet based data transmission on dispersive gaussian noise linear time invariant channels are derived by maximizing the mutual information subject to a fixed input power budget a quasi stationary approximation to the optimal nonstationary input covariance process is derived and shown to exhibit negligible mutual information loss from the optimal case for situations of most practical interest moreover this quasi stationary approximation results in efficiently computed lattice or pole zero implementations of the transmit filter by considering the popular finite impulse response minimum mean square error decision feedback equalizer fir mmse dfe as a receiver structure we show that transmitter optimization results in an appreciable improvement in the decision point signal to noise ratio finally we show that as the output blocklength becomes infinite the optimum finite dimensional nonstationary input covariance process converges to a stationary process whose power spectrum obeys the well known water pouring distribution

lattice based linear precoding for mimo channels with transmitter csi herein the design of linear dispersion codes for multiple input multiple output communication systems is investigated the receiver as well as the transmitter are assumed to have perfect knowledge of the channel and the receiver is assumed to employ maximum likelihood detection we propose to use linear precoding and lattice invariant operations to transform the channel matrix into a lattice generator matrix with large minimum distance separation with appropriate approximations it is shown that this corresponds to selecting lattices with good sphere packing properties lattice invariant transformations are then used to minimize the power consumption an algorithm for this power minimization is presented along with a lower bound on the optimization numerical results indicate significant gains by using the proposed method compared to channel diagonalization with adaptive bit loading

capacity penalty due to ideal zero forcing decision feedback equalization we consider the capacity c of a continuous time channel with frequency response h f and additive white gaussian noise if h f sup 2 behaves like a polynomial of order spl rho at high frequencies we show that the per symbol capacity approaches spl rho 2 nats per channel use at high signal powers if the receiver uses an ideal zero forcing decision feedback equalizer dfe consisting of a sampled whitened matched filter followed by a zero forcing tail canceler that is free of error propagation the overall system is free of intersymbol interference and has a well defined capacity c sub zf by comparing this capacity with the capacity c of the underlying channel we quantify the loss of information inherent in the tail canceling operation that typifies zero forcing dfe and zero forcing precoding systems for strictly bandlimited channels we find that the capacity penalty approaches zero in the limit of large signal power on the other hand for nonstrictly bandlimited channels the asymptotic penalty is nonzero however with bandwidth optimization the asymptotic penalty is at most 0 59 db and the asymptotic ratio c sub zf c is at least 93 6 depending on the asymptotic order spl rho of the channel response

lattice reduction aided mmse decision feedback equalizers the lll algorithm developed by lenstra lenstra and lovasz has been widely studied to improve the conditioning of linear systems of equations that arise in multi input multi output mimo antenna systems in the first part of this correspondence we show how a certain class of matrices can be transformed so that the lll algorithm can be carried out efficiently without compromising its performance then the proposed transformation is applied to the matrix with block lower triangular toeplitz matrices that arises in the decision feedback equalizer dfe to improve the bit error rate ber performance with a slight computational overhead

easily computed lower bounds on the information rate of intersymbol interference channels provable lower bounds are presented for the information rate i x x s n where x is the symbol drawn independently and uniformly from a finite size alphabet s is a discrete valued random variable rv and n is a gaussian rv it is well known that with s representing the precursor intersymbol interference isi at the decision feedback equalizer dfe output i x x s n serves as a tight lower bound for the symmetric information rate sir as well as capacity of the isi channel corrupted by gaussian noise when evaluated on a number of well known finite isi channels these new bounds provide a very similar level of tightness against the sir to the conjectured lower bound by shamai and laroia at all signal to noise ratio snr ranges while being actually tighter when viewed closed up at high snrs the new lower bounds are obtained in two steps first a mismatched mutual information function is introduced which can be proved as a lower bound to i x x s n secondly this function is further bounded from below by an expression that can be computed easily via a few single dimensional integrations with a small computational load

downlink mmse transceiver optimization for multiuser mimo systems mmse balancing we study the problem of mean square error mse transceiver design for point to multipoint transmission in multiuser multiple input multiple output mimo systems we focus on four optimization problems minimizing the maximum weighted layer wise or user wise mse under a total power constraint minimizing the total transmit power subject to a set of layer wise or user wise mse requirements the non convexity of these problems makes the derivation of globally optimal algorithms very difficult for transceiver design new optimal power allocation strategies are derived for the problems considered here based on the power allocation we study how this can be used for iterative transceiver optimization we propose iterative algorithms and prove the monotonic convergence of the algorithms the major advantages of the proposed algorithms are their low complexity and fast convergence behavior during the first few iterations the proposed algorithms are suitable not only for downlink transmission but also for uplink transmission with a total power constraint

a new class of iterative equalizers for space time bicm over mimo block fading multipath awgn channel this paper addresses the issue of advanced equalization methods for space time communications over multiple input multiple output block fading channel with intersymbol interference instead of resorting to conventional multiuser detection techniques based on the straightforward analogy between antennas and users we adopt a different point of view and separate time equalization from space equalization thus introducing a higher degree of freedom in the overall space time equalizer design time domain equalization relies on minimum mean square error criterion and operates on multidimensional modulation symbols whose individual components can be detected in accordance with another criterion in particular when the optimum maximum a posteriori criterion is chosen substantial performance gains over conventional space time turbo equalization have been observed for different transmission scenarios at the price of an increased albeit manageable computational complexity

adaptive noncoherent dfe for mdpsk signals transmitted over isi channels a novel noncoherent decision feedback equalization ndfe scheme for m ary differential phase shift keying signals transmitted over intersymbol interference channels is presented a suboptimum version with lower computational complexity and a noncoherent linear equalizer nle are derived from the original ndfe scheme furthermore the relation of the novel nle to a previously proposed nle is investigated in contrast to known ndfe schemes the novel scheme can approach the performance of coherent minimum mean squared error decision feedback equalization for adaptation of the feedforward and feedback filters efficient novel modified least mean square and recursive least squares algorithms are presented finally it is shown that the proposed adaptive ndfe scheme is robust against frequency offset

mmse decision feedback equalizers and coding ii coding results for pt i see ibid vol 43 no 10 p 2582 1995 the minimum mean squared error decision feedback equalizer mmse dfe has properties that suggest that it is a canonical equalization structure in systems that combine equalization with coded modulation with a given symbol rate 1 t and transmit spectrum the output signal to noise ratio snr sub mmse dfe u of a mmse dfe with an unbiased decision rule is a single parameter that characterizes the channel for coding purposes indeed the transmit spectrum that maximizes snr sub mmse dfe u is the capacity achieving water pouring spectrum and the capacity c t in bits per two dimensions is given by c t log sub 2 1 snr sub mmse dfe u regardless of the channel characteristics the performance of a coded system with a mmse dfe equalization structure may be accurately estimated using the gain of the coding scheme at a given pr e this performance is shown to be approximately the same as that of a multicarrier system using the same transmit spectrum and similar coding such systems are known to be able to approach capacity arbitrarily closely 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 simulation results indicate that performance of the mmse dfe is surprisingly insensitive to transmit spectral shaping as long as the transmit spectrum exceeds the capacity achieving band but that there is an optimal symbol rate that should approximately be used

interior point least squares estimation transient convergence analysis and application to mmse decision feedback equalization in many communication systems training sequences are used to help the receiver identify and or equalize the channel the amount of training data required depends on the convergence properties of the adaptive filtering algorithms used for equalization in this paper we propose the use of a new adaptive filtering method called interior point least squares ipls for adaptive equalization first we show that ipls converges exponentially fast in the transient phase then we use the ipls algorithm to update the weight vector for a minimum mean square error decision feedback equalizer mmse dfe in a cdma downlink scenario numerical simulations show that when training sequences are short ipls consistently outperforms rls in terms of system bit error rate and packet error rate as the training sequence gets longer ipls matches the performance of the rls algorithm

reversing symmetry group of and matrices with connections to cat maps and trace maps dynamical systems can have both symmetries and time reversing symmetries together these two types of symmetries form a group called the reversing symmetry group with the symmetries forming a normal subgroup of we give a complete characterization of and hence in the dynamical systems associated with the groups of integral matrices and to do this we use well known methods of number theory such as dirichlet s unit theorem for quadratic fields and gaus results on the equivalence of integer quadratic forms and employ the algebraic structure of the modular group as a free product we show how some recently discussed generalizations of the reversing symmetry group are also nicely illustrated when we consider affine extensions of these matrix groups our results are applicable to hyperbolic toral automorphisms anosov or cat maps pseudo anosov maps and the group of three dimensional 3d trace maps that preserve the fricke vogt invariant

intermittency in chaotic systems and renyi entropies the authors show that the renyi entropies characterise the temporal intermittency in chaotic systems and are linked to a set of generalized lyapounov exponents related to the time fluctuations of the responses to slight perturbations on the trajectory it is also briefly indicated how a simple extension of a numerical algorithm proposed by grassberger and procaccia 1983 allows one to compute these entropies from a signal

generalized geometric mean decomposition and dfe transceiver design part ii performance analysis in a companion paper the generalized geometric mean decomposition ggmd was proposed and used to design ggmd decision feedback equalizer dfe transceivers for arbitrary multiple input multiple output mimo channels without zero forcing constraint for the application to cyclic prefix cp systems the ggmd dfe transceiver has the most advantage over the gmd dfe mmse transceiver in terms of design and implementation complexity this paper presents the performance analysis for the ggmd dfe transceiver implementation proposed in part i the arithmetic mean square error mse symbol error rate ser and gaussian mutual information of the proposed system are investigated the performance advantages of ggmd dfe transceiver over popular orthogonal frequency division multiplexing ofdm and single carrier cp mmse systems are shown analytically and verified by numerical simulations

nested linear lattice codes for structured multiterminal binning network information theory promises high gains over simple point to point communication techniques at the cost of higher complexity however lack of structured coding schemes limited the practical application of these concepts so far one of the basic elements of a network code is the binning scheme wyner 1974 1978 and other researchers proposed various forms of coset codes for efficient binning yet these schemes were applicable only for lossless source or noiseless channel network coding to extend the algebraic binning approach to lossy source or noisy channel network coding previous work proposed the idea of nested codes or more specifically nested parity check codes for the binary case and nested lattices in the continuous case these ideas connect network information theory with the rich areas of linear codes and lattice codes and have strong potential for practical applications we review these developments and explore their tight relation to concepts such as combined shaping and precoding coding for memories with defects and digital watermarking we also propose a few novel applications adhering to a unified approach

robust design of adaptive equalizers although equalizers promise to improve the signal to noise energy ratio zero forcing equalizers are derived classically in a deterministic setting minimizing intersymbol interference while minimum mean square error mmse equalizer solutions are derived in a stochastic context based on quadratic wiener cost functions in this paper we show that it is possible and in our opinion even simpler to derive the classical results in a purely deterministic setup interpreting both equalizer types as least squares solutions this in turn allows the introduction of a simple linear reference model for equalizers which supports the exact derivation of a family of iterative and recursive algorithms with robust behavior the framework applies equally to multiuser transmissions and multiple input multiple output mimo channels a major contribution is that due to the reference approach the adaptive equalizer problem can equivalently be treated as an adaptive system identification problem for which very precise statements are possible with respect to convergence robustness and l2 stability robust adaptive equalizers are much more desirable as they guarantee a much stronger form of stability than conventional in the mean square sense convergence even some blind channel estimation schemes can now be included in the form of recursive algorithms and treated under this general framework

a computationally efficient multilevel coding scheme for isi channels this paper proposes a multilevel coding scheme with linear mapping for intersymbol interference isi channels and derives a low complexity receiver structure that can achieve the isi channel capacity the transmitter superimposes many layers of independent binary antipodal streams to generate a quadrature amplitude modulation qam or gaussian like channel input the receiver performs multistage decoding with decision feedback and interference cancellation within each stage is a linear minimum mean square error mmse equalizer followed by an error correcting decoder the complexity scales linearly with the channel length and the number of layers and the process is shown to be asymptotically information lossless if a fixed input power is properly distributed over a sufficiently large number of layers this framework is then extended to achieve the capacity of the isi channel using a transmitter side spectral shaping filter that converts a gaussian input sequence with a white spectrum to one with a water filling spectrum

low complexity block turbo equalization for ofdm systems in time varying channels we propose low complexity block turbo equalizers for orthogonal frequency division multiplexing ofdm systems in time varying channels the presented work is based on a soft minimum mean squared error mmse block linear equalizer ble that exploits the banded structure of the frequency domain channel matrix as well as a receiver window that enforces this banded structure this equalization approach allows us to implement the proposed designs with a complexity that is only linear in the number of subcarriers three block turbo equalizers are discussed two are based on a biased mmse criterion while the third is based on the unbiased mmse criterion simulation results show that the proposed iterative mmse ble achieves a better bit error rate ber performance than a previously proposed iterative mmse serial linear equalizer sle the proposed equalization algorithms are also tested in the presence of channel estimation errors

iterative symbol timing recovery for short burst transmission schemes this paper presents a novel iterative symbol timing recovery str scheme for short burst transmission formats a paradigm commonly found in modern wireless systems like for instance time division multiple access tdma schemes and future wireless packet data networks both data aided da and decision directed dd solutions are considered and performance is pursued by means of an iterative burst by burst scheme which exploits the farrow structure for the polynomial interpolation filter the convergence of the algorithm is discussed according to the expectation maximization em framework performance is evaluated by simulating 4 qam and 16 qam transceivers and simulations results are compared under different modulation orders and channel conditions for both the decision directed and data aided cases

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

receivers with widely linear processing for frequency selective channels we propose several equalization schemes based on widely linear processing wlp the received signal and its complex conjugate are separately filtered and the results are linearly combined it is shown that wlp yields a gain in performance if the noiseless received signal can be interpreted as the convolution of a real valued data sequence and an equivalent complex valued intersymbol interference channel impulse response such a model applies to e g amplitude shift keying offset quadrature amplitude modulation and binary minimum shift keying type modulation we consider receivers without and with decision feedback finite impulse response filters are derived for these structures which are optimum with respect to the zero forcing and minimum mean squared error mmse criteria respectively in the mmse case adaptive algorithms for filter adjustment are given infinite filter orders are investigated in order to obtain analytical performance results furthermore suboptimum trellis based detection with widely linear preprocessing is briefly discussed it is demonstrated analytically and by numerical examples that widely linear schemes may outperform conventional schemes significantly depending on the considered application

relationships between the constant modulus and wiener receivers the godard 1980 or the constant modulus algorithm cma is an effective technique for blind receiver design in communications however due to the complexity of the constant modulus cm cost function the performance of the cm receivers has primarily been evaluated using simulations theoretical analysis is typically based on either the noiseless case or approximations of the cost function the following question while resolvable numerically for a specific example remains unanswered in a generic manner in the presence of channel noise where are the cm local minima and what are their mean squared errors mse in this paper a geometrical approach is presented that relates the cm to wiener or minimum mse receivers given the mse and the intersymbol user interference of a wiener receiver a sufficient condition is given for the existence of a cm local minimum in the neighborhood of the wiener receiver the mse bounds on cm receiver performance are derived and shown to be tight in simulations the analysis shows that while in some cases the cm receiver performs almost as well as the nonblind wiener receiver it is also possible that due to its blind nature the cm receiver may perform considerably worse than a nonblind wiener receiver

on the capacity loss due to separation of detection and decoding the performance loss due to separation of detection and decoding on the binary input additive white gaussian noise awgn channel is quantified in terms of mutual information results are reported for both the code division multiple access cdma channel in the large system limit and the intersymbol interference isi channel the results for cdma rely on the replica method developed in statistical mechanics it is shown that a previous result of shamai and verdu found for gaussian input alphabet holds also for binary input alphabets for the isi channel the performance loss is calculated via the bahl cocke jelinek raviv bcjr algorithm comparisons are made to the capacity of separate detection and decoding using suboptimum detectors such as a decision feedback equalizer

intermittency as multifractality in history space temporal intermittency in a chaotic dynamical system can be regarded as a manifestation of the multifractal properties of the set of histories the renyi entropies kq which generalize the kolmogorov entropy k1 play a role analogous to the exponents tau q characterising the scaling properties of the moments of the mass distribution the authors introduce the topological entropy h lambda of the subset of histories with the same local expansion parameter they show that kq and h lambda are related to each other by means of a legendre transformation

trace maps as 3d reversible dynamical systems with an invariant one link between the theory of quasicrystals and the theory of nonlinear dynamics is provided by the study of so called trace maps a subclass of them are mappings on a one parameter family of 2d surfaces that foliate 3 and also 3 they are derived from transfer matrix approaches to properties of 1d quasicrystals in this article we consider various dynamical properties of trace maps we first discuss the fibonacci trace map and give new results concerning boundedness of orbits on certain subfamilies of its invariant 2d surfaces we highlight a particular surface where the motion is integrable and semiconjugate to an anosov system i e the mapping acts as a pseudo anosov map we identify properties of symmetry and reversibility time reversal symmetry in the fibonacci trace map dynamics and discuss the consequences for the structure of periodic orbits we show that a conservative period boubling sequence can be identified when moving through the one parameter family of 2d surfaces by using generator trace maps in terms of which all trace maps obtained from invertible two letter substitution rules can be expressed we show that many features of the fibonacci trace map hold in general the role of the fricke character hat i x y z x 2 y 2 z 2 2xyz 1 its symmetry group and reversibility for the nielsen trace maps are described algebraically finally we outline possible higher dimensional generalizations

new approach for error compensation in coded v blast ofdm systems in this paper we investigate coded layered space time architectures for frequency selective fading multiple input multiple output orthogonal frequency division multiplexing ofdm channels by computing outage capacity formulas we will show that the capacity of the vertical bell labs layered space time v blast architecture can closely approach the shannon capacity in the frequency selective ofdm environment motivated by the capacity analysis we propose pragmatic approaches which preserve the optimality of the layered space time concept we present methods to prevent the error propagation from catastrophically affecting the signal detection in subsequent layers first we start with a comprehensive signal modeling which includes error propagation we derive an improved signal detector and describe the optimal soft bit log likelihood ratio value computation method by taking decision errors into account for soft input channel decoding then to further enhance the v blast performance we show that cancellation using decoded decisions from previous layers makes the decision errors almost completely disappear so that the layered space time architecture can approach the attainable channel capacity finally simulations confirm that the proposed schemes show a significant performance improvement over the conventional methods

looking at the equilibrium measures in dynamical systems the authors discuss how finite time fluctuations of the chaoticity degree permit one to observe a family of equilibrium measures defined in the thermodynamical formalism for expanding one dimensional maps and for axion a systems by means of generalised lyapunov exponents one can thus calculate the kolmogorov entropies the lyapunov exponents and the hausdorff dimensions for this set of measures they perform such a calculation for the lozi map an almost everywhere hyperbolic diffeomorphism of the plane they stress the heuristic power of their approach which can be extended to more generic non hyperbolic systems in this case they suggest that phase transition phenomena might appear as a consequence of the existence of laminar like regular periods during chaotic evolutions

analog matching of colored sources to colored channels analog uncoded transmission provides a simple and robust scheme for communicating a gaussian source over a gaussian channel under the mean squared error mse distortion measure unfortunately its performance is usually inferior to the all digital separation based source channel coding solution which requires exact knowledge of the channel at the encoder the loss comes from the fact that except for very special cases e g white source and channel of matching bandwidth bw it is impossible to achieve perfect matching of source to channel and channel to source by linear means we show that by combining prediction and modulo lattice operations it is possible to match any colored gaussian source to any colored gaussian noise channel of possibly different bw hence achieve shannon s optimum attainable performance r d c furthermore when the source and channel bws are equal but otherwise their spectra are arbitrary this scheme is asymptotically robust in the sense that for high signal to noise ratio snr a single encoder independent of the noise variance achieves the optimum performance the derivation is based upon a recent modulo lattice modulation scheme for transmitting a wyner ziv source over a dirty paper channel

sorted spectral factorization of matrix polynomials in mimo communications sorted spectral factorization of matrix polynomials is studied such type of factoring hermitian matrix polynomials is the key step in calculating the optimum receive filter matrices in spatial temporal decision feedback equalization as well as the optimum transmit filter matrices in spatial temporal tomlinson harashima type precoding schemes contrary to other approaches we inherently consider asymptotic rather than finite length results for transmission over mimo channels with intersymbol interference it is shown how the different types of factorizations can be transformed onto a prototype factorization task which in turn can be solved by first performing an unsorted factorization and then determining the optimal processing order an easy to use iterative algorithm for unsorted spectral factorization and the adjustment of the optimized order in dfe and precoding are explained numerical simulations cover the impact of sorted and unsorted spectral factorization on the performance of dfe and precoding schemes

convergence properties of adaptive equalizer algorithms in this paper we provide a thorough stability analysis of two well known adaptive algorithms for equalization based on a novel least squares reference model that allows to treat the equalizer problem equivalently as system identification problem while not surprising the adaptive minimum mean square error mmse equalizer algorithm behaves l2 stable for a wide range of step sizes the even older zero forcing zf algorithm however behaves very differently we prove that the zf algorithm generally does not belong to the class of robust algorithms but can be convergent in the mean square sense we furthermore provide conditions on the upper step size bound to guarantee such mean squares convergence we specifically show how noise variance of added channel noise and the channel impulse response influences this bound simulation examples validate our findings

about the asymptotic performance of mmse mimo dfe for filter bank based multicarrier transmission we investigate the asymptotic performance of a multi input multi output decision feedback df equalizer used to detect a multicarrier mc signal based on a filter bank and transmitted over a linear dispersive channel we derive the optimum df structure for a minimum mean square error criterion we basically show that with infinite length forward and feedback filters and at high signal to noise ratio the geometrical mean of prediction errors does not depend on the paraunitary filter bank used in the transmitter hence it appears that uncoded filter bank based mc transmission and single carrier transmission both used over the same channel and with optimum df lead to the same achievable bit rate

error rates of the maximum likelihood detector for arbitrary constellations convex concave behavior and applications motivated by a recent surge of interest in convex optimization techniques convexity concavity properties of error rates of the maximum likelihood detector operating in the awgn channel are studied and extended to frequency flat slow fading channels generic conditions are identified under which the symbol error rate ser is convex concave for arbitrary multidimensional constellations in particular the ser is convex in snr for any one and two dimensional constellation and also in higher dimensions at high snr pairwise error probability and bit error rate are shown to be convex at high snr for arbitrary constellations and bit mapping universal bounds for the ser first and second derivatives are obtained which hold for arbitrary constellations and are tight for some of them applications of the results are discussed which include optimum power allocation in spatial multiplexing systems optimum power time sharing to decrease or increase jamming problem error rate an implication for fading channels fading is never good in low dimensions and optimization of a unitary precoded ofdm system for example the error rate bounds of a unitary precoded ofdm system with qpsk modulation which reveal the best and worst precoding are extended to arbitrary constellations which may also include coding the reported results also apply to the interference channel under gaussian approximation to the bit error rate when it can be expressed or approximated as a nonnegative linear combination of individual symbol error rates and to coded systems

the intersymbol interference channel lower bounds on capacity and channel precoding loss the discrete time additive gaussian intersymbol interference isi channel with i i d not necessarily gaussian input signals is considered several new and old lower bounds on the capacity are derived in a unified manner by assuming different front end receiver filters in particular the sampled whitened matched filter swmf and the minimum mean squared error decision feedback equalizer mmse dfe filter the features of the bounds are demonstrated and compared in several examples with binary and quaternary input signals it is also shown that the effect of an ideal post cursor or tail cancellation in an information preserving context depends primarily on the front end filter while as is well known ideal post cursor cancellation at the output of the swmf decreases the information the opposite trend is seen when an mmse dfe front filter is considered this observation reflects the basic theoretical obstacles in precoding i e ideal post cursor cancellation in the presence of a pre cursor it is used to assess the inherent loss in terms of information rates as compared to the rates achievable with the hypothetical ideal post cursor cancellation associated with any post cursor cancellation technique such as precoding dfe or other variants when operating in synergy with the mmse dfe front end filter the effect of the front end filter on an ideally interleaved precoded coded modulation system is also addressed

mimo decision feedback equalization from an h sup spl infin perspective we approach the multiple input multiple output mimo decision feedback equalization dfe problem in digital communications from an h sup spl infin estimation point of view using the standard and simplifying assumption that all previous decisions are correct we obtain an explicit parameterization of all h sup spl infin optimal dfes in particular we show that under the above assumption minimum mean square error mmse dfes are h sup spl infin optimal the h sup spl infin approach also suggests a method for dealing with errors in previous decisions

reversing symmetries in dynamical systems dynamical systems may possess in addition to symmetries that leave the equations of motion invariant reversing symmetries that invert the equations of motion such dynamical systems are called weakly reversible some consequences of the existence of reversing symmetries for dynamical systems with discrete time mappings are discussed a reversing symmetry group is introduced and it is shown that every weakly reversible mapping l can be decomposed into two mappings k0 and k1 of the same order 2l limit l to infinity included such that k02 k12 i some applications are discussed briefly

arithmetical properties of strongly chaotic motions abstract the orbits of the generalized arnold sinai cat maps or hyperbolic automorphisms of the two dimensional torus typify purely chaotic anosov motion we transform the dynamics of the periodic orbits of these maps into modular arithmetic in suitable domains of quadratic integers classify all periodic orbits and show how to determine their periods and initial conditions the methods are based on ideal theory in quadratic fields which is reviewed it is shown that the structure of orbits rests upon some basic arithmetical notions such as unique factorization into prime ideals

on the duality of mimo transceiver designs with bit allocation bit rate and power are two commonly used optimality criteria for mimo transceiver design in the literature bit rate maximization and power minimization problems are viewed as different problems and solved independently in this paper we derive the duality between these two problems for both the cases with and without integer constraint on bit allocation we will show that if a transceiver is optimal for the power minimizing problem it is also optimal for the rate maximizing problem and the converse is true such a duality has not been stated and proved in the literature to the best of our knowledge the derivation does not involve any existing optimal solution and we can establish duality result even for the rate maximization problem with integer bit constraint which the optimal solution is not known the duality also allows us to develop an algorithm for finding the rate maximizing transceiver with integer bit allocation using the solution of power minimizing system we will also consider some possible generalizations of the problem for example when there is a constraint on the maximal constellation size and when the subchannel bit error rates bers are constrained for each of these cases we will see that the duality between the two problems continued to hold in the simulations we will compute the optimal solutions for these two problems and demonstrate the duality between these two

realizable linear and decision feedback equalizers properties and connections recently there has been renewed interest in the use of infinite impulse response iir linear equalizers les for digital communication channels as a means for both improving performance and blindly initializing decision feedback structures dfes theoretical justification for such an approach is usually given assuming unconstrained filters which are not causal and therefore not implementable in practice we present an analysis of realizable i e causal stable and of finite degree minimum mean square error mmse equalizers for single input multiple output channels both in the le and dfe cases focusing on their structures and filter orders as well as the connections between them the dfe resulting from rearranging the mmse le within a decision feedback loop is given special attention it is shown that although this dfe does not in general coincide with the mmse dfe it still enjoys certain optimality conditions the main tools employed are the wiener theory of minimum variance estimation and kalman filtering theory which show interesting properties of the mmse equalizers not revealed by previous polynomial approaches

escaping orbits in trace maps abstract we study the finitely generated group a of invertible polynomial mappings from c 3 to itself or r 3 to itself which preserve the fricke vogt invariant i x y z x2 y2 z2 2xyz 1 using properties of suitably chosen generators we give a necessary condition and sufficient conditions for infinite order elements of a to have an unbounded orbit escaping to infinity in forward or backward time our main motivation for this study is that a includes the so called trace maps derived from transfer matrix approaches to various physical processes displaying non periodicity in space or time as shown previously characterising escaping orbits leads to various conclusions for the physical model and vice versa e g electronic properties of id quasicrystals our results generalize in a simple constructive way those previously proved for fibonacci type trace maps

sum capacity of gaussian vector broadcast channels this paper characterizes the sum capacity of a class of potentially nondegraded gaussian vector broadcast channels where a single transmitter with multiple transmit terminals sends independent information to multiple receivers coordination is allowed among the transmit terminals but not among the receive terminals the sum capacity is shown to be a saddle point of a gaussian mutual information game where a signal player chooses a transmit covariance matrix to maximize the mutual information and a fictitious noise player chooses a noise correlation to minimize the mutual information the sum capacity is achieved using a precoding strategy for gaussian channels with additive side information noncausally known at the transmitter the optimal precoding structure is shown to correspond to a decision feedback equalizer that decomposes the broadcast channel into a series of single user channels with interference pre subtracted at the transmitter

stochastic unbiased minimum mean error rate algorithm for decision feedback equalizers capitalizing on a well known minimum mean square error mmse property for decision feedback equalization dfe along with the use of stochastic gradient approach we formulate an adaptive minimum error rate mer algorithm for dfe over m ary pam channels to be named as stochastic unbiased minimum mean error rate summer comparisons are made between our algorithm and existing mer algorithms in the literature also by invoking the central limit theorem we present an analytical proof that an unbiased mmse equalizer will approach an mer equalizer when the equalizer length approaches infinity thereby we obtain a lower bound expression for mer

throughput maximizing fir transmit filters for linear dispersive channels optimum finite impulse response transmit filters for symbol by symbol transmission on linear dispersive additive gaussian noise channels are derived by maximizing the channel throughput subject to a fixed average input energy constraint this maximized throughput is compared to that achievable with water pour and flat transmit filters the effect of transmit filter optimization on the receiver performance is investigated by considering the popular minimum mean square error decision feedback equalizer receiver structure

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 computationally efficient discrete bit loading algorithm for ofdm systems subject to spectral compatibility limits this paper considers bit loading algorithms to maximize throughput under total power and spectral mask constraints in interference free ofdm systems the contribution is twofold first we propose a simple criterion to switch between two well known algorithms from the literature the conventional greedy and greedy based bit removing with maximum allowable bit loading initialization algorithms second we present a new low complexity loading algorithm that exploits the bit vector obtained by rounding the water filling algorithm solution to the associated continuous input rate maximization problem as an efficient initial bit vector of the greedy algorithm we theoretically prove that this bit vector has two interesting properties the first one states that it is an efficient bit vector i e there is no movement of a bit from one subcarrier to another that reduces the total used power the second one states that the optimized throughput starting from this initial bit vector is achieved by adding or removing bits on each subcarrier at most once simulation results show the efficiency of the proposed algorithm i e the achievable throughput is maximized with significant reduction of computation cost as compared to many algorithms in the literature

mmse decision feedback equalizers finite length results this paper extends a number of results on the infinite length minimum mean square error decision feedback equalizer mmse dfe reported by cioffi dudevoir eyuboglu and forney see ieee trans commun 1995 to the finite length case cholesky factorization and displacement structure theory are demonstrated to be two powerful analytical tools for analyzing the finite length mmse dfe our objective throughout the paper is to establish finite length analogs of the well known infinite length mmse dfe results similarities and differences between the two cases are examined and delineated finally convergence of our derived finite length results to their well established infinite length counterparts is shown

characterisation of intermittency in chaotic systems the authors discuss the characterisation of intermittency in chaotic dynamical systems by means of the time fluctuations of the response to a slight perturbation on the trajectory a set of exponents is introduced which generalise the maximum lyapunov characteristic exponent the link with the statistical mechanics formalism is emphasised and they show that the exponents are connected to a free energy formally defined for chaotic systems they perform some analytical computations in simple cases and give a few numerical examples

the arnold cat map on prime lattices we describe the time evolution of the discrete dynamical system consisting of the iterates of the arnold cat map f x y x y mod 1 x 2y mod 1 0 x y 1 defined on prime lattices lp j p k p 0 j k p where p is prime we show that on lp for p a prime p 5 all orbits except the fixed point 0 0 have a common period the form of this common period is determined a discrete first integral constant of motion is given and used to determine the relationship between orbits as well as the orbit decomposition

performance assessment of mimo bicm demodulators based on mutual information we provide a comprehensive performance comparison of soft output and hard output demodulators in the context of non iterative multiple input multiple output bit interleaved coded modulation mimo bicm coded bit error rate ber widely used in literature for demodulator comparison has the drawback of depending strongly on the error correcting code being used this motivates us to propose the mutual information of the equivalent modulation channel comprising modulator wireless channel and demodulator as a code independent performance measure we present extensive numerical results for spatially independent identically distributed i i d ergodic and quasi static fading channels under perfect and imperfect channel state information these results reveal that the performance ranking of mimo demodulators is rate dependent and provide new insights regarding mimo bicm system design i e the choice of antenna configuration symbol constellation and demodulator for a given target rate

on the robustness of the finite length mmse dfe with respect to channel and second order statistics estimation errors the finite length minimum mean square error decision feedback equalizer mmse dfe is an efficient structure mitigating intersymbol interference isi introduced by practically all communication channels at high enough symbol rates the filters constituting the mmse dfe as well as related performance measures can be computed by assuming perfect knowledge of the channel impulse response and the input and noise second order statistics sos in practice we estimate the unknown quantities and thus inevitable estimation errors arise we model the estimation errors as small perturbations and we derive a second order approximation to the excess mse furthermore we derive second order approximations to the mean excess mse in terms of the parameter estimation error covariance matrices and simple and informative bounds revealing the factors that govern the behavior of mmse dfe under mismatch simulations confirm that the derived second order approximations provide accurate estimates of the mmse dfe performance degradation due to mismatch

time varying versus time invariant finite length mmse dfe on stationary dispersive channels a time varying structure and a time invariant structure for the finite length minimum mean square error decision feedback equalizer mmse dfe are presented and their performances are compared on a stationary channel impaired by intersymbol interference isi and additive gaussian noise the time varying structure has an innovations error sequence but incurs a throughput loss on isi channels because of its block processing nature conditions under which the time invariant structure exhibits near optimal performance are described both structures converge to the canonical mmse dfe of cioffi et al see ibid vol 43 p 2582 94 1995 and vol 43 p 2595 2604 1995 as their filters lengths become infinite

on full diversity space time block codes with partial interference cancellation group decoding in this paper we propose a partial interference cancellation pic group decoding strategy scheme for linear dispersive space time block codes stbc and a design criterion for the codes to achieve full diversity when the pic group decoding is used at the receiver a pic group decoding decodes the symbols embedded in an stbc by dividing them into several groups and decoding each group separately after a linear pic operation is implemented it can be viewed as an intermediate decoding between the maximum likelihood ml receiver that decodes all the embedded symbols together i e all the embedded symbols are in a single group and the zero forcing zf receiver that decodes all the embedded symbols separately and independently i e each group has and only has one embedded symbol after the zf operation is implemented the pic group decoding provides a framework to adjust the complexity performance tradeoff by choosing the sizes of the information symbol groups our proposed design criterion group independence for the pic group decoding to achieve full diversity is an intermediate condition between the loosest ml full rank criterion of codewords and the strongest zf linear independence condition of the column vectors in the equivalent channel matrix we also propose asymptotic optimal ao group decoding algorithm which is an intermediate decoding between the mmse decoding algorithm and the ml decoding algorithm the design criterion for the pic group decoding can be applied to the ao group decoding algorithm because of its asymptotic optimality it is well known that the symbol rate for a full rank linear stbc can be full i e nt for nt transmit antennas it has been recently shown that its rate is upper bounded by 1 if a code achieves full diversity with a linear receiver the intermediate criterion proposed in this paper provides the possibility for codes of rates between nt and 1 that achieve full diversity with the pic group decoding this therefore provides a complexity performance rate tradeoff some design examples are given

symmetries and reversing symmetries of area preserving polynomial mappings in generalised standard form abstract we determine the symmetries and reversing symmetries within g the group of real planar polynomial automorphisms of area preserving nonlinear polynomial maps l in generalised standard form l x x p 1 y y y p 2 x where p 1 and p 2 are polynomials we do this by using the amalgamated free product structure of g our results lead to normal forms for polynomial maps in generalised standard form and to a classification of the group structures of the reversing symmetry groups for such maps

adaptive linear equalization combined with noncoherent detection for mdpsk signals a novel noncoherent receiver for m ary differential phase shift keying signals transmitted over intersymbol interference channels is presented the noncoherent receiver consists of a linear equalizer and a decision feedback differential detector a significant performance gain over a previously proposed noncoherent receiver can be observed for an infinite number of feedback symbols the optimum equalizer coefficients can be calculated analytically and the performance of the proposed receiver approaches that of a coherent linear minimum mean squared error equalizer moreover a modified least mean square and a modified recursive least squares algorithm for adaptation of the equalizer coefficients are discussed

diversity analysis of symbol by symbol linear equalizers in frequency selective channels linear receivers enjoy significantly reduced complexity compared with maximum likelihood receivers at the cost of performance degradation which can be in the form of a loss of the inherent frequency diversity order or reduced coding gain this paper demonstrates that the minimum mean square error symbol by symbol linear equalizer incurs no diversity loss compared to the maximum likelihood receivers in particular for a channel with memory it achieves the full diversity order of 1 while the zero forcing symbol by symbol linear equalizer always achieves a diversity order of one

time reversal symmetry in dynamical systems a survey abstract in this paper we survey the topic of time reversal symmetry in dynamical systems we begin with a brief discussion of the position of time reversal symmetry in physics after defining time reversal symmetry as it applies to dynamical systems we then introduce a major theme of our survey namely the relation of time reversible dynamical sytems to equivariant and hamiltonian dynamical systems we follow with a survey of the state of the art on the theory of reversible dynamical systems including results on symmetric periodic orbits local bifurcation theory homoclinic orbits and renormalization and scaling some areas of physics and mathematics in which reversible dynamical systems arise are discussed in an appendix we provide an extensive bibliography on the topic of time reversal symmetry in dynamical systems

reversing k symmetries in dynamical systems we generalize the concept of reversing symmetries of a dynamical system i e we study dynamical systems that possess symmetry properties only if considered on a proper time scale in particular considering dynamical systems with discrete time the kth iterate of a map may possess more reversing symmetries than the map itself in this way the concepts of reversing symmetries and reversing symmetry groups are generalized to reversing k symmetries and reversing k symmetry groups furthermore a method is studied for finding orbits that are k symmetric with respect to reversing k symmetries firstly an existing method for finding orbits that are symmetric with respect to one reversing symmetry is extended to the case of more than one reversing symmetry and secondly a generalization of this method to the case of reversing k symmetries is introduced some physically relevant examples of dynamical systems possessing reversing k symmetries are discussed briefly

comparison of the achievable rates in ofdm and single carrier modulation with i i d inputs we compare the maximum achievable rates in single carrier sc and orthogonal frequency division multiplexing ofdm modulation schemes under the practical assumptions of independent identically distributed finite alphabet inputs and linear intersymbol interference with additive gaussian noise we show that the shamai laroia approximation serves as a bridge between the two rates while it is well known that this approximation is often a lower bound on the sc achievable rate it is revealed to also essentially upper bound the ofdm achievable rate we apply information estimation relations in order to rigorously establish this result for both general input distributions and to sharpen it for commonly used pulse amplitude modulation pam and quadratic amplitude modulation constellations to this end novel bounds on minimum mean square error estimation of pam inputs to a scalar gaussian channel are derived which may be of general interest our results show that under reasonable assumptions optimal sc schemes may offer spectral efficiency significantly superior to that of ofdm motivating further research of such systems

generalized henon maps the cubic diffeomorphisms of the plane abstract in general a polynomial diffeomorphism of the plane can be transformed into a composition of generalized henon maps these maps exhibit some of the familiar properties of the quadratic henon map including a bounded set of bounded orbits and an anti integrable limit we investigate in particular the cubic area preserving case which reduces to two two parameter families of maps the bifurcations of low period orbits of these maps are discussed in detail

adaptive minimum symbol error rate decision feedback equalization for multilevel pulse amplitude modulation the design of decision feedback equalizers dfes is typically based on the minimum mean square error mmse principle as this leads to effective adaptive implementation in the form of the least mean square algorithm it is well known however that in certain situations the mmse solution can be distinctly inferior to the optimal minimum symbol error rate mser solution we consider the mser design for multilevel pulse amplitude modulation block data adaptive implementation of the theoretical mser dfe solution is developed based on the parzen window estimate of a probability density function furthermore a sample by sample adaptive mser algorithm called the least symbol error rate lser is derived for adaptive equalization applications the proposed lser algorithm has a complexity that increases linearly with the equalizer length computer simulation is employed to evaluate the proposed alternative mser design for equalization application with multilevel signaling schemes

reduced state sequence estimation with set partitioning and decision feedback a reduced state sequence estimator for linear intersymbol interference channels is described the estimator uses a conventional viterbi algorithm with decision feedback to search a reduced state subset trellis that is constructed using set partitioning principles the complexity of maximum likelihood sequence estimation mlse due to the length of the channel memory and the size of the signal set is systematically reduced an error probability analysis shows that a good performance complexity tradeoff can be obtained in particular the results indicate that the required complexity to achieve the performance of mlse is independent of the size of the signal set for large enough signal sets simulation results are provided for two partial response systems a simple technique for quadrature partial response signaling qprs is described that eliminates the quasicatastrophic nature of the ml trellis

iterative decoding of coded thp with quantized output this paper proposes an improved receiver for the tomlinson harashima precoder thp in this paper we demonstrate that most of the capacity loss associated with conventional thp is due to the suboptimal receiver which is a simple modulo operation we then demonstrate how this loss can can be avoided with the optimization of the receiver in the suboptimal receiver the modulo operation ignores the dependency between the implicitly added sequence of symbols removed by it we then implement a thp with quantized outputs the quantized outputs enable to implement a maximum a posteriori probability map receiver that exploits the dependency between the received symbols the map receiver is named enhanced modulo operation emod and operates as an inner decoder within an iterative scheme either with outer low density parity check ldpc code or outer turbo code simulation results show considerable gains relative to coded conventional thp and also relative to the turbo equalizer te which does not use a precoder in the transmitter

generalized dimensions entropies and liapunov exponents from the pressure function for strange sets for conformal mixing repellers such as julia sets and nonlinear one dimensional cantor sets we connect the pressure of a smooth transformation on the repeller with its generalized dimensions entropies and liapunov exponents computed with respect to a set of equilibrium gibbs measures this allows us to compute the pressure by means of simple numerical algorithms our results are then extended to axiom a attractors and to a nonhyperbolic invariant set of the line in this last case we show that a first order phase transition appears in the pressure

lower bounds and approximations for the information rate of the isi channel we consider the discrete time intersymbol interference isi channel model with additive gaussian noise and fixed independent identically distributed inputs in this setting we investigate the expression put forth by shamai and laroia as a conjectured lower bound for the input output mutual information after application of a minimum mean square error decision feedback equalizer receiver a low signal to noise ratio snr expansion is used to prove that the conjectured bound does not hold under general conditions and to characterize inputs for which it is particularly ill suited one such input is used to construct a counterexample indicating that the shamai laroia expression does not always bound even the achievable rate of the channel thus excluding a natural relaxation of the original conjectured bound however this relaxed bound is then shown to hold for any finite entropy input and isi channel when the snr is sufficiently high we derive two conditions under which the relaxed bound holds involving compound channel capacity and quasiconvexity arguments finally new simple bounds for the achievable rate are proven and compared with other known bounds information estimation relations and estimation theoretic bounds play a key role in establishing our results