low precision a d conversion for maximum information rate in channels with memory analog to digital converters that maximize the information rate between the quantized channel output sequence and the channel input sequence are designed for discrete time channels with intersymbol interference additive noise and for independent and identically distributed signaling optimized scalar quantizers with regions achieve the full information rate of log2 bits per channel use with a transmit alphabet of size at infinite signal to noise ratio these quantizers however are not necessarily uniform quantizers low precision scalar and two dimensional analog to digital converters are designed at finite signal to noise ratio and an upper bound on the information rate is derived simulation results demonstrate the effectiveness of the designed quantizers over conventional quantizers the advantage of the new quantizers is further emphasized by an example of a channel for which a slicer with a single threshold at zero and a carefully optimized channel input with memory fail to achieve a rate of one bit per channel use at high signal to noise ratio in contrast to memoryless binary signaling and an optimized quantizer

noncoherent decorrelative detection for nonorthogonal multipulse modulation over the multiuser gaussian channel this paper introduces the problem of noncoherent detection for nonorthogonal multipulse modulation in the context of the synchronous multiuser gaussian channel each user sends an m ary information symbol by transmitting one of m possibly nonorthogonal waveforms furthermore the m signals of one user are allowed to be correlated with the signals of all other users a key idea proposed here is that of a noncoherent decorrelative receiver front end like its counterpart in single pulse modulation this front end eliminates multiuser interference it therefore reduces the multiuser detection problem into decoupled single user problems over equivalent noise enhanced single user channels each equivalent single user channel is rather general and can be described as one where the waveforms employed are not only correlated but are also of unequal energies several new results pertaining to the design and analysis of optimum and suboptimum noncoherent detectors for this single user channel are obtained in the multiuser channel these detectors constitute the post decorrelative processing units for each user

boundary circles for area preserving maps abstract we report on numerical observations of various properties of boundary circles for area preserving maps we find that the continued fraction expansion of their rotation number generally has a special form we describe how their rotation number changes as parameters are varied we observe a statistically self similar structure in the neighbourhood of boundary circles which is probably relevant to the long time tails of the decay of correlations in the irregular components

a general framework for transmission with transceiver distortion and some applications a general theoretical framework is presented for analyzing information transmission over gaussian channels with memoryless transceiver distortion which encompasses various nonlinear distortion models including transmit side clipping receive side analog to digital conversion and others the framework is based on the so called generalized mutual information gmi and the analysis in particular benefits from the setup of gaussian codebook ensemble and nearest neighbor decoding for which it is established that the gmi takes a general form analogous to the channel capacity of undistorted gaussian channels with a reduced effective signal to noise ratio snr that depends on the nominal snr and the distortion model when applied to specific distortion models an array of results of engineering relevance is obtained for channels with transmit side distortion only it is shown that a conventional approach which treats the distorted signal as the sum of the original signal part and a uncorrelated distortion part achieves the gmi for channels with output quantization closed form expressions are obtained for the effective snr and the gmi and related optimization problems are formulated and solved for quantizer design finally super nyquist sampling is analyzed within the general framework and it is shown that sampling beyond the nyquist rate increases the gmi for all snr values for example with binary symmetric output quantization information rates exceeding one bit per channel use are achievable by sampling the output at four times the nyquist rate

bit error rate of binary and quaternary dpsk signals with multiple differential feedback detection a differentially coherent detection scheme with improved bit error rate ber performance is presented for differentially encoded binary and quaternary phase shift keying psk modulation the improvement is based on using l symbol detectors with delays of 1 2 l symbol periods and on feeding back detected psk symbols exact formulas for the bit error probability are derived for the case that correct symbols are fed back the effect of symbol errors in the feedback path on the ber is determined by computer simulations

phase quantized block noncoherent communication analog to digital conversion adc is a key bottleneck in scaling dsp centric receiver architectures to multigigabit s speeds recent information theoretic results obtained under ideal channel conditions perfect synchronization no dispersion indicate that low precision adc 1 4 bits could be a suitable choice for designing such high speed systems in this work we study the impact of employing low precision adc in a carrier asynchronous system specifically we consider transmission over the block noncoherent additive white gaussian noise channel and investigate the achievable performance under low precision output quantization we focus attention on an architecture in which the receiver quantizes only the phase of the received signal this has the advantage of being implementable without automatic gain control using multiple 1 bit adcs preceded by analog multipliers for standard uniform phase shift keying psk modulation we study the structure of the transition density of the phase quantized block noncoherent channel several results based on the symmetry inherent in the channel model are provided to characterize this transition density low complexity procedures for computing the channel information rate and for block demodulation are obtained using these results numerical computations are performed to compare the performance of quantized and unquantized systems for different quantization precisions and different block lengths with qpsk modulation it is observed for example that for snr larger than 2 3 db 8 bin phase quantization of the received signal recovers about 80 85 of the mutual information attained with unquantized observations while 12 bin phase quantization recovers more than 90 of the unquantized mutual information dithering the constellation is shown to improve the performance in the face of drastic quantization

joint noncoherent demodulation and decoding for the block fading channel a practical framework for approaching shannon capacity the paper contains a systematic investigation of practical coding strategies for noncoherent communication over fading channels guided by explicit comparisons with information theoretic benchmarks noncoherent reception is interpreted as joint data and channel estimation assuming that the channel is time varying and a priori unknown we consider iterative decoding for a serial concatenation of a standard binary outer channel code with an inner modulation code amenable to noncoherent detection for an information rate of about 1 2 bit per channel use the proposed scheme using a quaternary phase shift keying qpsk alphabet provides performance within 1 6 1 7 db of shannon capacity for the block fading channel and is about 2 5 3 db superior to standard differential demodulation in conjunction with an outer channel code we also provide capacity computations for noncoherent communication using standard phase shift keying psk and quadrature amplitude modulation qam alphabets comparing these with the capacity with unconstrained input provides guidance as to the choice of constellation as a function of the signal to noise ratio these results imply that qpsk suffices to approach the unconstrained capacity for the relatively low information and fading rates considered in our performance evaluations but that qam is superior to psk for higher information or fading rates motivating further research into efficient noncoherent coded modulation with qam alphabets

noncoherent coded modulation trellis coded modulation with two or multidimensional signal constellations together with coherent maximum likelihood detection is considered an attractive solution for communications over the additive white gaussian noise awgn channel in this paper a new noncoherent communication system is introduced called noncoherent coded modulation ncm as an alternative to coherent coded modulation ncm achieves almost the same power efficiency without bandwidth expansion or an extensive increase in complexity as a noncoherent system the method does not need carrier phase estimation nonetheless differential encoding is not required high performance noncoherent detection is achieved by using multiple symbol observations unlike previous approaches a sliding window for the observations is used with each observation covering several branches of the trellis such that the observations are time overlapped we define a new type of noncoherent maximum likelihood sequence estimator mlse and analyze its performance over the awgn channel by numerical calculation of the union bound we perform a computerized search and present new codes for noncoherent detection with their performance the new codes cover many useful rates and complexities and achieve higher performance than existing codes for noncoherent detection the method can also be used for multiple symbol demodulation of mdpsk with better results than existing methods

cortical surface based searchlight decoding abstract local voxel patterns of fmri signals contain specific information about cognitive processes ranging from basic sensory processing to high level decision making these patterns can be detected using multivariate pattern classification and localization of these patterns can be achieved with searchlight methods in which the information content of spherical sub volumes of the fmri signal is assessed the only assumption made by this approach is that the patterns are spatially local we present a cortical surface based searchlight approach to pattern localization voxels are grouped according to distance along the cortical surface the intrinsic metric of cortical anatomy rather than euclidean distance as in volumetric searchlights using a paradigm in which the category of visually presented objects is decoded we compare the surface based method to a standard volumetric searchlight technique group analyses of accuracy maps produced by both methods show similar distributions of informative regions the surface based method achieves a finer spatial specificity with comparable peak values of significance while the volumetric method appears to be more sensitive to small informative regions and might also capture information not located directly within the gray matter furthermore our findings show that a surface centered in the middle of the gray matter contains more information than to the white gray boundary or the pial surface

searchlight based multi voxel pattern analysis of fmri by cross validated manova abstract multi voxel pattern analysis mvpa is a fruitful and increasingly popular complement to traditional univariate methods of analyzing neuroimaging data we propose to replace the standard decoding approach to searchlight based mvpa measuring the performance of a classifier by its accuracy with a method based on the multivariate form of the general linear model following the well established methodology of multivariate analysis of variance manova we define a measure that directly characterizes the structure of multi voxel data the pattern distinctness d our measure is related to standard multivariate statistics but we apply cross validation to obtain an unbiased estimate of its population value independent of the amount of data or its partitioning into training and test sets the estimate d can therefore serve not only as a test statistic but also as an interpretable measure of multivariate effect size the pattern distinctness generalizes the mahalanobis distance to an arbitrary number of classes but also the case where there are no classes of trials because the design is described by parametric regressors it is defined for arbitrary estimable contrasts including main effects pattern differences and interactions pattern changes in this way our approach makes the full analytical power of complex factorial designs known from univariate fmri analyses available to mvpa studies moreover we show how the results of a factorial analysis can be used to obtain a measure of pattern stability the equivalent of cross decoding

survival probability for the stadium billiard abstract we consider the open stadium billiard consisting of two semicircles joined by parallel straight sides with one hole situated somewhere on one of the sides due to the hyperbolic nature of the stadium billiard the initial decay of trajectories due to loss through the hole appears exponential however some trajectories bouncing ball orbits persist and survive for long times and therefore form the main contribution to the survival probability function at long times using both numerical and analytical methods we concur with previous studies that the long time survival probability for a reasonably small hole drops like c o n s t a n t t i m e 1 here we obtain an explicit expression for the constant

poincare recurrences from the perspective of transient chaos we obtain a description of the poincare recurrences of chaotic systems in terms of the ergodic theory of transient chaos it is based on the equivalence between the recurrence time distribution and an escape time distribution obtained by leaking the system and taking a special initial ensemble this ensemble is atypical in terms of the natural measure of the leaked system the conditionally invariant measure accordingly for general initial ensembles the average recurrence and escape times are different however we show that the decay rate of these distributions is always the same our results remain valid for hamiltonian systems with mixed phase space and validate a split of the chaotic saddle in hyperbolic and nonhyperbolic components

near maximum likelihood detector and channel estimator for uplink multiuser massive mimo systems with one bit adcs in massive multiple input multiple output mimo systems it may not be power efficient to have a pair of high resolution analog to digital converters adcs for each antenna element in this paper a near maximum likelihood nml detector for uplink multiuser massive mimo systems is proposed where each antenna is connected to a pair of one bit adcs i e one for each real and imaginary component of the baseband signal the exhaustive search over all the possible transmitted vectors required in the original maximum likelihood ml detection problem is relaxed to formulate an ml estimation problem then the ml estimation problem is converted into a convex optimization problem which can be efficiently solved using the solution the base station can perform simple symbol by symbol detection for the transmitted signals from multiple users to further improve detection performance we also develop a two stage nml detector that exploits the structures of both the original ml and the proposed one stage nml detectors numerical results show that the proposed nml detectors are efficient enough to simultaneously support multiple uplink users adopting higher order constellations e g 16 quadrature amplitude modulation since our detectors exploit the channel state information as part of the detection an ml channel estimation technique with one bit adcs that shares the same structure with our proposed nml detector is also developed the proposed detectors and channel estimator provide a complete low power solution for the uplink of a massive mimo system

quantization of binary input discrete memoryless channels the quantization of the output of a binary input discrete memoryless channel to a smaller number of levels is considered an algorithm which finds an optimal quantizer in the sense of maximizing mutual information between the channel input and quantizer output is given this result holds for arbitrary channels in contrast to previous results for restricted channels or a restricted number of quantizer outputs in the worst case the algorithm complexity is cubic m 3 in the number of channel outputs m optimality is proved using the theorem of burshtein della pietra kanevsky and nadas for mappings which minimize average impurity for classification and regression trees

quantized massive mu mimo ofdm uplink coarse quantization at the base station bs of a massive multi user mu multiple input multiple output mimo wireless system promises significant power and cost savings coarse quantization also enables significant reductions of the raw analog to digital converter data that must be transferred from a spatially separated antenna array to the baseband processing unit the theoretical limits as well as practical transceiver algorithms for such quantized mu mimo systems operating over frequency flat narrowband channels have been studied extensively however the practically relevant scenario where such communication systems operate over frequency selective wideband channels is less well understood this paper investigates the uplink performance of a quantized massive mu mimo system that deploys orthogonal frequency division multiplexing ofdm for wideband communication we propose new algorithms for quantized maximum a posteriori channel estimation and data detection and we study the associated performance quantization tradeoffs our results demonstrate that coarse quantization e g four to six bits depending on the ratio between the number of bs antennas and the number of users in massive mu mimo ofdm systems entails virtually no performance loss compared with the infinite precision case at no additional cost in terms of baseband processing complexity

characterization and computation of optimal distributions for channel coding this paper concerns the structure of capacity achieving input distributions for stochastic channel models and a renewed look at their computational aspects the following conclusions are obtained under general assumptions on the channel statistics i the capacity achieving input distribution is binary for low signal to noise ratio snr the proof is obtained on comparing the optimization equations that determine channel capacity with a linear program over the space of probability measures ii simple discrete approximations can nearly reach capacity even in cases where the optimal distribution is known to be absolutely continuous with respect to lebesgue measure iii a new class of algorithms is introduced based on the cutting plane method to iteratively construct discrete distributions along with upper and lower bounds on channel capacity it is shown that the bounds converge to the true channel capacity and that the distributions converge weakly to a capacity achieving distribution

a discrete queue based model for capturing memory and soft decision information in correlated fading channels a discrete binary input 2q ary output communication channel with memory is introduced to judiciously capture both the statistical memory and the soft decision information of a time correlated discrete fading channel dfc used with antipodal signaling and soft output quantization of resolution q the discrete channel which can be explicitly described via its binary input process and a 2q ary noise process is shown to be symmetric thus admitting a simple expression for its capacity when its noise is stationary ergodic it is observed that considerable capacity gains can be achieved due to the channel s memory and the use of as few as 2 bits for soft decision over interleaving the channel to render it memoryless and hard decision demodulation q 1 the 2q ary noise process is next modeled via a queue based qb ball sampling mechanism to produce a mathematically tractable stationary ergodic markovian noise source the dfc is fitted by the qb noise model via an iterative procedure that minimizes the kullback leibler divergence rate between the dfc and qb noise sources modeling results measured in terms of channel noise correlation function and capacity reveal a good agreement between the two channels for a broad range of fading conditions

least squares quantization in pcm it has long been realized that in pulse code modulation pcm with a given ensemble of signals to handle the quantum values should be spaced more closely in the voltage regions where the signal amplitude is more likely to fall it has been shown by panter and dite that in the limit as the number of quanta becomes infinite the asymptotic fractional density of quanta per unit voltage should vary as the one third power of the probability density per unit voltage of signal amplitudes in this paper the corresponding result for any finite number of quanta is derived that is necessary conditions are found that the quanta and associated quantization intervals of an optimum finite quantization scheme must satisfy the optimization criterion used is that the average quantization noise power be a minimum it is shown that the result obtained here goes over into the panter and dite result as the number of quanta become large the optimum quautization schemes for 2 b quanta b 1 2 cdots 7 are given numerically for gaussian and for laplacian distribution of signal amplitudes

noncoherent demodulation techniques for trellis coded m dpsk signals considers noncoherent decoding of trellis coded m dpsk transmission and attempts to unify and contrast the approaches to this problem which have been previously reported in the second part of the paper the maximum likelihood block decoders for the awgn channel are outlined first assuming that the decoder has no knowledge of the state of the encoder at the beginning of the block and then assuming that it knows the state because these exhaustive decoders suffer from an exponential growth in complexity with block length two simplified decoders are proposed that approach the performance of the exhaustive decoders with a much more manageable complexity through a union bound analysis and computer simulations it is shown that it is possible to achieve large gains over uncoded systems with a very reasonable decoder complexity

capacity achieving distributions in gaussian multiple access channel with peak power constraints this paper addresses a two user gaussian multiple access channel mac under peak power constraints at the transmitters it is shown that generating the code books of both users according to discrete distributions with a finite number of mass points achieves the largest weighted sum rate in the network this verifies that any point on the boundary of the capacity region of a two user mac under peak power constraints at both transmitters is achieved by discrete distributions with a finite number of mass points although the capacity achieving distributions are not necessarily unique it is verified that only discrete distributions with a finite number of mass points can achieve a point on the boundary of the capacity region it is shown that there exist an infinite number of sum rate optimal points on the boundary of the capacity region in contrast to the gaussian mac with average power constraints we verify that time division td cannot achieve any of the sum rate optimal points in the gaussian mac with peak power constraints using the so called i mmse identity of guo et al the largest achievable sum rate by orthogonal code division ocd is characterized where it is shown that walsh hadamard spreading codes of length 2 are optimal in the symmetric case where the peak power constraints at both transmitters are identical we verify that ocd can achieve a sum rate that is strictly larger than the highest sum rate achieved by td finally it is demonstrated that there are values for the maximum peak power at the transmitters such that ocd can not achieve any of the sum rate optimal points on the boundary of the capacity region

the performance of trellis coded mdpsk with multiple symbol detection the idea of using a multiple more than two symbol observation interval to improve error probability performance is applied to differential detection of trellis coded multiple phase shift keying mpsk over an additive white gaussian noise awgn channels an equivalent euclidean distance measure per trellis branch is determined for this detection scheme this is used to define an augmented larger multiplicity trellis code whose distance measure is the conventional squared euclidean distance typical of conventional trellis coded modulation on the awgn such an augmented multiple trellis code is a convenient mathematical tool for simplifying the analysis results are obtained by a combination of analysis and computer simulation it is shown that only a slight increase e g one symbol in the length of the observation interval will provide a significant improvement in bit error probability performance

simulation based computation of information rates for channels with memory the information rate of finite state source channel models can be accurately estimated by sampling both a long channel input sequence and the corresponding channel output sequence followed by a forward sum product recursion on the joint source channel trellis this method is extended to compute upper and lower bounds on the information rate of very general channels with memory by means of finite state approximations further upper and lower bounds can be computed by reduced state methods

statistical inference and multiple testing correction in classification based multi voxel pattern analysis mvpa random permutations and cluster size control an ever increasing number of functional magnetic resonance imaging fmri studies are now using information based multi voxel pattern analysis mvpa techniques to decode mental states in doing so they achieve a significantly greater sensitivity compared to when they use univariate frameworks however the new brain decoding methods have also posed new challenges for analysis and statistical inference on the group level we discuss why the usual procedure of performing t tests on accuracy maps across subjects in order to produce a group statistic is inappropriate we propose a solution to this problem for local mvpa approaches which achieves higher sensitivity than other procedures our method uses random permutation tests on the single subject level and then combines the results on the group level with a bootstrap method to preserve the spatial dependency induced by local mvpa methods we generate a random permutation set and keep it fixed across all locations this enables us to later apply a cluster size control for the multiple testing problem more specifically we explicitly compute the distribution of cluster sizes and use this to determine the p values for each cluster using a volumetric searchlight decoding procedure we demonstrate the validity and sensitivity of our approach using both simulated and real fmri data sets in comparison to the standard t test procedure implemented in spm8 our results showed a higher sensitivity we discuss the theoretical applicability and the practical advantages of our approach and outline its generalization to other local mvpa methods such as surface decoding techniques

unitary space time modulation for multiple antenna communications in rayleigh flat fading motivated by information theoretic considerations we propose a signaling scheme unitary space time modulation for multiple antenna communication links this modulation is ideally suited for rayleigh fast fading environments since it does not require the receiver to know or learn the propagation coefficients unitary space time modulation uses constellations of t spl times m space time signals spl phi sub i l 1 l where t represents the coherence interval during which the fading is approximately constant and m t is the number of transmitter antennas the columns of each spl phi sub i are orthonormal when the receiver does not know the propagation coefficients which between pairs of transmitter and receiver antennas are modeled as statistically independent this modulation performs very well either when the signal to noise ratio snr is high or when t spl gt m we design some multiple antenna signal constellations and simulate their effectiveness as measured by bit error probability with maximum likelihood decoding we demonstrate that two antennas have a 6 db diversity gain over one antenna at 15 db snr

what s in a pattern examining the type of signal multivariate analysis uncovers at the group level abstract multivoxel pattern analysis mvpa has gained enormous popularity in the neuroimaging community over the past few years at the group level most mvpa studies adopt an information based approach in which the sign of the effect of individual subjects is discarded and a non directional summary statistic is carried over to the second level this is in contrast to a directional activation based approach typical in univariate group level analysis in which both signal magnitude and sign are taken into account the transition from examining effects in one voxel at a time vs several voxels univariate vs multivariate has thus tacitly entailed a transition from directional to non directional signal definition at the group level while a directional group level mvpa approach implies that individuals have similar multivariate spatial patterns of activity in a non directional approach each individual may have a distinct spatial pattern using an experimental dataset we show that directional and non directional group level mvpa approaches uncover distinct brain regions with only partial overlap we propose a method to quantify the degree of spatial similarity in activation patterns over subjects applied to an auditory task we find higher values in auditory regions compared to control regions

variational bayesian mixed effects inference for classification studies multivariate classification algorithms are powerful tools for predicting cognitive or pathophysiological states from neuroimaging data assessing the utility of a classifier in application domains such as cognitive neuroscience brain computer interfaces or clinical diagnostics necessitates inference on classification performance at more than one level i e both in individual subjects and in the population from which these subjects were sampled such inference requires models that explicitly account for both fixed effects within subjects and random effects between subjects variance components while models of this sort are standard in mass univariate analyses of fmri data they have not yet received much attention in multivariate classification studies of neuroimaging data presumably because of the high computational costs they entail this paper extends a recently developed hierarchical model for mixed effects inference in multivariate classification studies and introduces an efficient variational bayes approach to inference using both synthetic and empirical fmri data we show that this approach is equally simple to use as yet more powerful than a conventional t test on subject specific sample accuracies and computationally much more efficient than previous sampling algorithms and permutation tests our approach is independent of the type of underlying classifier and thus widely applicable the present framework may help establish mixed effects inference as a future standard for classification group analyses

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

calculation of diffusion coefficients for chaotic maps abstract a new numerical method for the calculation of diffusion coefficients of maps showing chaotic behaviour is given based on the comparison of the dynamical process described by the map and a model diffusion process the method presents advantages over previously used methods in that it can be used on maps with bounded chaotic regions in phase space it can be used to model map having diffusion coefficients varying in phase space and in that it is fast and efficient the method is tested on three well known maps the standard map the web map and the fermi map each one of which exhibits features specially chosen to make full use of the advantages of the proposed method

on binary quantizer for maximizing mutual information we consider a channel with a binary input x being corrupted by a continuous valued noise that results in a continuous valued output y an optimal binary quantizer is used to quantize the continuous valued output y to the final binary output z to maximize the mutual information i x z we show that when the ratio of the channel conditional density r y frac p y y x 0 p y y x 1 is a strictly increasing or decreasing function of y then a quantizer having a single threshold can maximize mutual information furthermore we show that an optimal quantizer possibly with multiple thresholds is the one with the thresholding vector whose elements are all the solutions of r y r for some constant r 0 in addition we also characterize necessary conditions using fixed point theorem for the optimality and uniqueness of a quantizer based on these conditions we propose an efficient procedure for determining all locally optimal quantizers and thus a globally optimal quantizer can be found our results also confirm some previous results using alternative elementary proofs

escape exponent for transient chaos and chaotic scattering in non hyperbolic hamiltonian systems it is shown that in non hyperbolic hamiltonian systems where correlations decay as a power law transient chaos and chaotic scattering demonstrate different power laws numerical evidence of this effect for the stadium billiard is presented

emergence of continual directed flow in hamiltonian systems we propose a minimal model for the emergence of a directed flow in autonomous hamiltonian systems it is shown that internal breaking of the spatio temporal symmetries via localised initial conditions that are unbiased with respect to the transporting degree of freedom and transient chaos conspire to form the physical mechanism for the occurrence of a current most importantly after passage through the transient chaos trajectories perform solely regular transporting motion so that the resulting current is of continual ballistic nature this has to be distinguished from the features of transport reported previously for driven hamiltonian systems with mixed phase space where transport is determined by intermittent behaviour exhibiting power law decay statistics of the duration of regular ballistic periods

multivariate signal parameter estimation under dependent noise from 1 bit dithered quantized data motivated by applications in sensor networks and communications we consider multivariate signal parameter estimation when only dithered 1 bit quantized samples are available the observation noise is taken to be a stationary strongly mixing process which covers a wide range of processes including autoregressive moving average arma models the noise is allowed to be gaussian or to have a heavy tail with possibly infinite variance an estimate of the signal parameters is proposed and is shown to be weakly consistent joint asymptotic normality of the parameters estimate is also established and the asymptotic mean and covariance matrices are identified

soft decision demodulation design for covq over white colored and isi gaussian channels in this work the design of a q bit scalar and vector soft decision demodulator for gaussian channels with binary phase shift keying modulation is investigated the demodulator is used in conjunction with a soft decision channel optimized vector quantization covq system the covq is constructed for an expanded q 1 discrete channel consisting of the concatenation of the modulator the gaussian channel and the demodulator it is found that as the demodulator resolution q increases the capacity of the expanded channel increases resulting in an improvement of the covq performance consequently the soft decision demodulator is designed to maximize the capacity of the expanded channel three gaussian channel models are considered as follows 1 additive white gaussian noise channels 2 additive colored gaussian noise channels and 3 gaussian channels with intersymbol interference comparisons are made with a hard decision covq systems b covq systems which utilize interleaving and c an unquantized q spl infin soft decision decoder proposed by skoglund and hedelin 1999 it is shown that substantial improvements can be achieved over covq systems which utilize hard decision demodulation and or channel interleaving the performance of the proposed covq system is comparable with the system by skoglund and hedelin though its computational complexity is substantially less

multiple symbol differentially detected multilevel codes for the rayleigh fading channel conventional differential detection is known to perform poorly on the fast fading rayleigh fading channel due to the rapid variation of the channel state the technique of multiple symbol differential detection msdd improves the error performance by detecting over a sequence of symbols and exploiting the inherent correlation of the fading process to further reduce the error rate we need to introduce some form of coding successful coding for the rayleigh fading channel requires interleaving to decorrelate the channel a conflicting requirement to msdd we propose a solution consisting of interleaving blocks of l m ary phase shift keying mpsk symbols that are multiple symbol differentially detected the blocks are treated as elements of an m sup l symbol alphabet over which a multilevel code based on geometrically uniform partitions is defined

validating cluster size inference random field and permutation methods cluster size tests used in analyses of brain images can have more sensitivity compared to intensity based tests the random field rf theory has been widely used in implementation of such tests however the behavior of such tests is not well understood especially when the rf assumptions are in doubt in this paper we carried out a simulation study of cluster size tests under varying smoothness thresholds and degrees of freedom comparing rf performance to that of the permutation test which is known to be exact for gaussian images we find that the rf methods are generally conservative especially for low smoothness and low threshold for t images the rf tests are found to be conservative at lower thresholds and do not perform well unless the threshold is high and images are sufficiently smooth the permutation test performs well for any settings though the discreteness in cluster size must be accounted for we make specific recommendations on when permutation tests are to be preferred to rf tests

spectrally efficient noncoherent communication this paper considers noncoherent communication over a frequency nonselective channel in which the time varying channel gain is unknown a priori but is approximately constant over a coherence interval unless the coherence interval is large coherent communication which requires explicit channel estimation and tracking prior to detection incurs training overhead which may be excessive especially for multiple antenna communication in contrast noncoherent detection may be viewed as a generalized likelihood ratio test glrt which jointly estimates the channel and the data and hence does not require separate training the main results in this paper are as follows 1 we develop a signal space criterion for signal and code design for noncoherent communication in terms of the distances of signal points from the decision boundaries 2 the noncoherent metric thus obtained is used to guide the design of signals for noncoherent communication that are based on amplitude phase constellations these are significantly more efficient than conventional differential phase shift keying psk especially at high signal to noise ratio snr also known results on the high snr performance of multiple symbol demodulation of differential psk are easily inferred from the noncoherent metric 3 the glrt interpretation is used to obtain near optimal low complexity implementations of noncoherent block demodulation in particular this gives an implementation of multiple symbol demodulation of differential psk which is of linear complexity in the block length and whose degradation from the exact exponential complexity implementation can be made as small as desired

single bit oversampled a d conversion with exponential accuracy in the bit rate a scheme for simple oversampled analog to digital a d conversion using single bit quantization is presented the scheme is based on recording positions of zero crossings of the input signal added to a deterministic dither function this information can be represented in a manner such that the bit rate increases only logarithmically with the oversampling factor r the input band limited signal can be reconstructed from this information locally with o 1 r pointwise error resulting in an exponentially decaying distortion rate characteristic in the course of studying the accuracy of the proposed a d conversion scheme some new results are established about reconstruction of band limited signals from irregular samples using linear combination of functions with fast decay schemes for local interpolation of band limited signals from quantized irregular samples are also proposed

on the capacity of binary and gaussian channels with run length limited inputs bounds on the capacity of binary symmetric channels and additive gaussian channels with run length limited two level binary bipolar inputs are presented and their tightness is demonstrated for some cases stationary input sequences which do not degrade capacity are considered when deriving the bounds lower bounds on the magnetic recording density for a simple continuous time recording model incorporating a minimal intertransition constraint are evaluated for soft and hard decisions a superiority of about 1 5 db in signal to noise ratio is observed for the soft decision scheme

valid population inference for information based imaging from the second level t test to prevalence inference in multivariate pattern analysis of neuroimaging data second level inference is often performed by entering classification accuracies into a t test vs chance level across subjects we argue that while the random effects analysis implemented by the t test does provide population inference if applied to activation differences it fails to do so in the case of classification accuracy or other information like measures because the true value of such measures can never be below chance level this constraint changes the meaning of the population level null hypothesis being tested which becomes equivalent to the global null hypothesis that there is no effect in any subject in the population consequently rejecting it only allows to infer that there are some subjects in which there is an information effect but not that it generalizes rendering it effectively equivalent to fixed effects analysis this statement is supported by theoretical arguments as well as simulations we review possible alternative approaches to population inference for information based imaging converging on the idea that it should not target the mean but the prevalence of the effect in the population one method to do so permutation based information prevalence inference using the minimum statistic is described in detail and applied to empirical data

effective dynamics in hamiltonian systems with mixed phase space an adequate characterization of the dynamics of hamiltonian systems at physically relevant scales has been largely lacking here we investigate this fundamental problem and we show that the finite scale hamiltonian dynamics is governed by effective dynamical invariants which are significantly different from the dynamical invariants that describe the asymptotic hamiltonian dynamics the effective invariants depend both on the scale of resolution and the region of the phase space under consideration and they are naturally interpreted within a framework in which the nonhyperbolic dynamics of the hamiltonian system is modeled as a chain of hyperbolic systems

poincare recurrences and transient chaos in systems with leaks in order to simulate observational and experimental situations we consider a leak in the phase space of a chaotic dynamical system we obtain an expression for the escape rate of the survival probability by applying the theory of transient chaos this expression improves previous estimates based on the properties of the closed system and explains dependencies on the position and size of the leak and on the initial ensemble with a subtle choice of the initial ensemble we obtain an equivalence to the classical problem of poincare recurrences in closed systems which is treated in the same framework finally we show how our results apply to weakly chaotic systems and justify a split of the invariant saddle into hyperbolic and nonhyperbolic components related respectively to the intermediate exponential and asymptotic power law decays of the survival probability

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

bit error probability for noncoherent orthogonal signals in fading with optimum combining for correlated branch diversity due to the interest in wireless personal communications there has been a lot of research on the performance of receivers with diversity most analyses assume the diversity branches are independent this paper presents an analysis of the bit error probability for receivers in which the diversity branches are correlated noncoherent orthogonal digital modulation ncodm with rician and rayleigh slow nonselective fading models are assumed through the use of the diagonalization of quadratic forms most of the calculations of the bit error probability can be reduced to a two dimensional numerical integration for some cases for dual diversity a closed form expression for the error probability is given a number of diversity combining laws including square law and maximum likelihood are considered we find that rician fading can be worse than rayleigh fading in correlated diversity environments a situation quite different from the independent diversity case also for the rayleigh fading model with correlated branch diversity we find that an equal weight square law combiner usually has the same error performance as the more complex maximum likelihood combiner however this is not the case for a rician fading model with the same correlation environment simple diagonalization methods that compensate for the lossy effect of correlation are specified and found to be effective when the dominant noise and interference have almost the same correlation distribution as the fading signals

geometric programming duals of channel capacity and rate distortion we show that the lagrange dual problems of the channel capacity problem with input cost and the rate distortion problem are simple geometric programs upper bounds on channel capacity and lower bounds on rate distortion can be efficiently generated from their duals for channel capacity the geometric programming dual characterization is shown to be equivalent to the minmax kullback leibler kl characterization in csiszar et al 1981 for rate distortion the geometric programming dual is extended to rate distortion with two sided state information a duality by mapping is then given between the lagrange dual problems of channel capacity with input cost and rate distortion which resolves several apparent asymmetries between their primal problems in the familiar form of mutual information optimization problems both the primal and dual problems can be interpreted in a common framework of free energy optimization from statistical physics

multiple phase codes for detection without carrier phase reference we consider the construction and analysis of linear block codes for m ary phase shift keying that can be decoded without carrier phase synchronization under these circumstances the function that has a significant impact on performance is the noncoherent distance analogous to the euclidean distance for the coherent case the major difficulty in constructing and analyzing such codes lies in the fact that the noncoherent distance is not a true metric for this reason prior work mainly relies on numerical approaches to search for good codes and to determine the corresponding minimum noncoherent distance we first present a theorem that links the noncoherent distance with the euclidean and lee 1958 distances this theorem allows us to construct good codes and determine their minimum noncoherent distances analytically based on this theorem we classify the codes whose duals consist of a cyclic group these codes are of minimum redundancy we further investigate codes with the flavor of hamming and shortened hamming codes many of these new codes provide significantly larger coding gains than previously known codes linear codes derived from code division multiple access cdma sequences are considered as well these codes in general provide rather large coding gains finally an algorithm is introduced that can be appended to any suboptimal decoding technique to enhance the performance

sparse regularization techniques provide novel insights into outcome integration processes abstract by exploiting information that is contained in the spatial arrangement of neural activations multivariate pattern analysis mvpa can detect distributed brain activations which are not accessible by standard univariate analysis recent methodological advances in mvpa regularization techniques have made it feasible to produce sparse discriminative whole brain maps with highly specific patterns furthermore the most recent refinement the graph net explicitly takes the 3d structure of fmri data into account here these advanced classification methods were applied to a large fmri sample n 70 in order to gain novel insights into the functional localization of outcome integration processes while the beneficial effect of differential outcomes is well studied in trial and error learning outcome integration in the context of instruction based learning has remained largely unexplored in order to examine neural processes associated with outcome integration in the context of instruction based learning two groups of subjects underwent functional imaging while being presented with either differential or ambiguous outcomes following the execution of varying stimulus response instructions while no significant univariate group differences were found in the resulting fmri dataset l1 regularized sparse classifiers performed significantly above chance and also clearly outperformed the standard l2 regularized dense support vector machine on this whole brain between subject classification task moreover additional l2 regularization via the elastic net and spatial regularization by the graph net improved interpretability of discriminative weight maps but were accompanied by reduced classification accuracies most importantly classification based on sparse regularization facilitated the identification of highly specific regions differentially engaged under ambiguous and differential outcome conditions comprising several prefrontal regions previously associated with probabilistic learning rule integration and reward processing additionally a detailed post hoc analysis of these regions revealed that distinct activation dynamics underlay the processing of ambiguous relative to differential outcomes together these results show that l1 regularization can improve classification performance while simultaneously providing highly specific and interpretable discriminative activation patterns

capacity analysis for continuous alphabet channels with side information part i a general framework capacity analysis for channels with side information at the receiver has been an active area of interest this problem is well investigated for the case of finite alphabet channels however the results are not easily generalizable to the case of continuous alphabet channels due to analytical difficulties inherent with continuous alphabets in the first part of this two part paper we address an analytical framework for capacity analysis of continuous alphabet channels with side information at the receiver for this purpose we establish novel necessary and sufficient conditions for weak continuity and strict concavity of the mutual information these conditions are used in investigating the existence and uniqueness of the capacity achieving measures furthermore we derive necessary and sufficient conditions that characterize the capacity value and the capacity achieving measure for continuous alphabet channels with side information at the receiver

slow relaxation in weakly open rational polygons the interplay between the regular piecewise linear and irregular vertex angle boundary effects in nonintegrable rational polygonal billiards of m equal sides is discussed decay dynamics in polygons of perimeter p m and small opening delta is analyzed through the late time survival probability s m approximately equal t delta two distinct slow relaxation channels are established the primary universal channel exhibits relaxation of regular sliding orbits with delta 1 the secondary channel is given by delta 1 and becomes open when m p m delta it originates from vertex order disorder dual effects and is due to relaxation of chaoticlike excitations

multiple symbol differential detection of mpsk a differential detection technique for mpsk multiple phase shift keying which uses a multiple symbol observation interval is presented and its performance is analyzed and simulated the technique makes use of maximum likelihood sequence estimation of the transmitted phases rather than symbol by symbol detection as in the conventional differential detection thus the performance of this multiple symbol detection scheme fills the gap between conventional two symbol observation differentially coherent detection of mpsk and ideal coherent of mpsk with differential encoding the amount of improvement gained over conventional differential detection depends on the number of phases m and the number of additional symbol intervals added to the observation what is particularly interesting is that substantial performance improvement can be obtained for only one or two additional symbol intervals of observation the analysis and simulation results presented are for uncoded mpsk

open mushrooms stickiness revisited we investigate mushroom billiards a class of dynamical systems with sharply divided phase space for typical values of the control parameter of the system an infinite number of marginally unstable periodic orbits mupos exist making the system sticky in the sense that unstable orbits approach regular regions in phase space and thus exhibit quasi regular behaviour for long periods of time the problem of finding these mupos is expressed as the well known problem of finding optimal rational approximations of a real number subject to some system specific constraints by introducing a generalized mushroom and using properties of continued fractions we describe for the first time a zero measure set of control parameter values 0 1 for which all mupos are destroyed and therefore the system is less sticky leading to a different power law exponent for the poincar recurrence time distribution statistics the open mushroom billiard with a hole is then considered in order to quantify the stickiness exhibited due to mupos and exact leading order expressions for the algebraic decay of the survival probability function are calculated for mushrooms with triangular and rectangular stems numerical simulations are also performed which confirm our predictions for both sticky and less sticky mushrooms

signal parameter estimation using 1 bit dithered quantization motivated by the estimation of spatio temporal events with cheap simple sensors we consider the problem of estimation of a parameter thetas of a signal s x thetas corrupted by noise assuming that only 1 bit precision dithered quantized samples are available an estimate that does not require the knowledge of the dither signal and the noise distribution is proposed and it is analyzed in detail under variety of nonidealities the consistency and asymptotic normality of the estimate is established for deterministic and random sampling imprecise knowledge of sampling locations gaussian and non gaussian noise with possibly infinite variance a wide class of dither distributions and under erroneous transmission of the binary observations via binary symmetric channels bscs it is also shown that if approximation to the log likelihood equation in the full precision case yields a good estimate then there is a corresponding good estimate based on 1 bit dithered samples the proposed estimate requires no more computation than the maximum likelihood estimate for the full precision case and suffers only a logarithmic rate loss compared to the full precision case when uniform dithering is used it is shown that uniform dithering leads to the best rate among a broad class of dither distributions a condition under which no dithering leads to a better estimate is also given

a unified approach to the probability of error for noncoherent and differentially coherent modulations over generalized fading channels we present a unified approach to determine the exact bit error rate ber of noncoherent and differentially coherent modulations with single and multichannel reception over additive white gaussian noise and generalized fading channels the multichannel reception results assume independent fading in the channels and are applicable to systems that employ post detection equal gain combining our approach relies on an alternate form of the marcum q function and leads to expressions of the ber involving a single finite range integral which can be readily evaluated numerically aside from unifying the past results the new approach also allows for a more general solution to the problem in that it includes many situations that in the past defied a simple solution the best example of this occurs for multichannel reception where the fading on each channel need not be identically distributed nor even distributed according to the same family of distributions

efficient approximation of channel capacities we propose an iterative method for approximately computing the capacity of discrete memoryless channels possibly under additional constraints on the input distribution based on duality of convex programming we derive explicit upper and lower bounds for the capacity the presented method requires o m 2 n sqrt log n varepsilon to provide an estimate of the capacity to within varepsilon where n and m denote the input and output alphabet size a single iteration has a complexity o m n we also show how to approximately compute the capacity of memoryless channels having a bounded continuous input alphabet and a countable output alphabet under some mild assumptions on the decay rate of the channel s tail it is shown that discrete time poisson channels fall into this problem class as an example we compute sharp upper and lower bounds for the capacity of a discrete time poisson channel with a peak power input constraint

the reconstruction of analog signals from the sign of their noisy samples the reconstruction of a continuous time signal s t from the sign of its deliberately contaminated samples is considered sequential generally nonlinear estimates of s t are established and their performance is studied error bounds and convergence rates are derived the signal s t need not be band limited the convergence rates obtained here are faster than those obtained previously for nonsequential estimates the degradation in the reconstruction of the signal due to transmission over a noisy channel is also investigated and bounds on the additional error are obtained

capacity bounds via duality with applications to multiple antenna systems on flat fading channels a technique is proposed for the derivation of upper bounds on channel capacity it is based on a dual expression for channel capacity where the maximization of mutual information over distributions on the channel input alphabet is replaced with a minimization of average relative entropy over distributions on the channel output alphabet we also propose a technique for the analysis of the asymptotic capacity of cost constrained channels the technique is based on the observation that under fairly mild conditions capacity achieving input distributions escape to infinity the above techniques are applied to multiple antenna flat fading channels with memory where the realization of the fading process is unknown at the transmitter and unknown or only partially known at the receiver it is demonstrated that for high signal to noise ratio snr the capacity of such channels typically grows only double logarithmically in the snr to better understand this phenomenon and the rates at which it occurs we introduce the fading number as the second order term in the high snr asymptotic expansion of capacity and derive estimates on its value for various systems it is suggested that at rates that are significantly higher than the fading number communication becomes extremely power inefficient thus posing a practical limit on practically achievable rates upper and lower bounds on the fading number are also presented for single input single output siso systems the bounds coincide thus yielding a complete characterization of the fading number for general stationary and ergodic fading processes we also demonstrate that for memoryless multiple input single output miso channels the fading number is achievable using beam forming and we derive an expression for the optimal beam direction this direction depends on the fading law and is in general not the direction that maximizes the snr on the induced siso channel using a new closed form expression for the expectation of the logarithm of a noncentral chi square distributed random variable we provide some closed form expressions for the fading number of some systems with gaussian fading including siso systems with circularly symmetric stationary and ergodic gaussian fading the fading number of the latter is determined by the fading mean fading variance and the mean squared error in predicting the present fading from its past it is not directly related to the doppler spread for the rayleigh ricean and multiple antenna rayleigh fading channels we also present firm nonasymptotic upper and lower bounds on channel capacity these bounds are asymptotically tight in the sense that their difference from capacity approaches zero at high snr and their ratio to capacity approaches one at low snr

on the limits of communication with low precision analog to digital conversion at the receiver as communication systems scale up in speed and bandwidth the cost and power consumption of high precision e g 8 12 bits analog to digital conversion adc becomes the limiting factor in modern transceiver architectures based on digital signal processing in this work we explore the impact of lowering the precision of the adc on the performance of the communication link specifically we evaluate the communication limits imposed by low precision adc e g 1 3 bits for transmission over the real discrete time additive white gaussian noise awgn channel under an average power constraint on the input for an adc with k quantization bins i e a precision of log2 k bits we show that the input distribution need not have any more than k 1 mass points to achieve the channel capacity for 2 bin 1 bit symmetric quantization this result is tightened to show that binary antipodal signaling is optimum for any signal to noise ratio snr for multi bit quantization a dual formulation of the channel capacity problem is used to obtain tight upper bounds on the capacity the cutting plane algorithm is employed to compute the capacity numerically and the results obtained are used to make the following encouraging observations a up to a moderately high snr of 20 db 2 3 bit quantization results in only 10 20 reduction of spectral efficiency compared to unquantized observations b standard equiprobable pulse amplitude modulated input with quantizer thresholds set to implement maximum likelihood hard decisions is asymptotically optimum at high snr and works well at low to moderate snrs as well

channel optimized quantization with soft decision demodulation for space time orthogonal block coded channels we introduce three soft decision demodulation channel optimized vector quantizers covqs to transmit analog sources over space time orthogonal block stob coded flat rayleigh fading channels with binary phase shift keying bpsk modulation one main objective is to judiciously utilize the soft information of the stob coded channel in the design of the vector quantizers while keeping a low system complexity to meet this objective we introduce a simple space time decoding structure that consists of a space time soft detector followed by a linear combiner and a scalar uniform quantizer with resolution q the concatenation of the space time encoder modulator fading channel and space time receiver can be described by a binary input 2q output discrete memoryless channel dmc the scalar uniform quantizer is chosen so that the capacity of the equivalent dmc is maximized to fully exploit and capture the system s soft information by the dmc we next determine the statistics of the dmc in closed form and use them to design three covq schemes with various degrees of knowledge of the channel noise power and fading coefficients at the transmitter and or receiver the performance of each quantization scheme is evaluated for memoryless gaussian and gauss markov sources and various stob codes and the benefits of each scheme is illustrated as a function of the antenna diversity and soft decision resolution q comparisons to traditional coding schemes which perform separate source and channel coding operations are also provided

at low snr asymmetric quantizers are better we study the capacity of the discrete time gaussian channel when its output is quantized with a 1 bit quantizer we focus on the low signal to noise ratio snr regime where communication at very low spectral efficiencies takes place in this regime a symmetric threshold quantizer is known to reduce channel capacity by a factor of 2 i e to cause an asymptotic power loss of approximately 2 db here it is shown that this power loss can be avoided by using asymmetric threshold quantizers and asymmetric signaling constellations to avoid this power loss flash signaling input distributions are essential consequently 1 bit output quantization of the gaussian channel reduces spectral efficiency threshold quantizers are not only asymptotically optimal at every fixed snr a threshold quantizer maximizes capacity among all 1 bit output quantizers the picture changes on the rayleigh fading channel in the noncoherent case a 1 bit output quantizer causes an unavoidable low snr asymptotic power loss in the coherent case however this power loss is avoidable provided that we allow the quantizer to depend on the fading level

the capacity of discrete time memoryless rayleigh fading channels we consider transmission over a discrete time rayleigh fading channel in which successive symbols face independent fading and where neither the transmitter nor the receiver has channel state information subject to an average power constraint we study the capacity achieving distribution of this channel and prove it to be discrete with a finite number of mass points one of them located at the origin we numerically compute the capacity and the corresponding optimal distribution as a function of the signal to noise ratio snr the behavior of the channel at low snr is studied and finally a comparison is drawn with the ideal additive white gaussian noise channel

bayesian parameter estimation using single bit dithered quantization the bayesian parameter estimation problem using a single bit dithered quantizer is considered this problem arises e g for channel estimation under low precision analog to digital conversion adc at the receiver based on the bayesian cramer rao lower bound crlb bounds on the mean squared error are derived that hold for all dither strategies with strictly causal adaptive processing of the quantizer output sequence in particular any estimator using the binary quantizer output sequence is asymptotically in the sequence length at least 10 log10 2 1 96 db worse than the minimum mean squared error estimator using continuous observations for any dither strategy moreover dither strategies are designed that are shown by simulation to closely approach the derived lower bounds

on the capacity of the blockwise incoherent mpsk channel the capacity of m ary phase shift keying mpsk over an additive white gaussian noise awgn channel with carrier phase unknown but constant over l symbols is investigated it is shown that capacity achieving channel inputs are uniformly distributed and independent mpsk symbols capacity over a range of signal to noise ratio snr and l is presented for binary phase shift keying bpsk and quaternary phase shift keying qpsk upper and lower easy to compute bounds on capacity are derived it is proven that for large l the coherent capacity is approached an analytic asymptotic expression for low l spl middot snr is derived exhibiting the expected quadratic dependence on the snr

markov tree model of transport in area preserving maps abstract transport in an area preserving map with a mixture of regular and chaotic regions is described in terms of the flux through invariant cantor sets called cantori a model retaining a discrete set of cantori approaching a boundary circle gives the markov chain description of hanson cary and meiss the inclusion of cantori surrounding island chains and islands about islands etc gives a markov tree model with a slower decay rate the survival probability distribution is shown to decay asymptotically as a power law the decay exponent agrees reasonably well with the computations of karney and of chirikov and shepelyanski

strange objects in the complex plane julia sets are examined as examples of strange objects which arise in the study of long time properties of simple dynamical systems technically they are the closure of the set of unstable cycles of analytic maps physically they are sets of points which lead to chaotic behavior the mapf z z2 p is analyzed for smallp where the julia set is a closed curve and for largep where the julia set is completely disconnected in both cases the hausdorff dimension is calculated in perturbation theory and numerically an expression for the rate at which points escape from the neighborhood of the julia set is derived and tested in a numerical simulation of the escape

differential unitary space time modulation we present a framework for differential modulation with multiple antennas across a continuously fading channel where neither the transmitter nor the receiver knows the fading coefficients the framework can be seen as a natural extension of standard differential phase shift keying commonly used in single antenna unknown channel systems we show how our differential framework links the unknown channel system with a known channel system and we develop performance design criteria as a special ease we introduce a class of diagonal signals where only one antenna is active at any time and demonstrate how these signals may be used to achieve full transmitter diversity and low probability of error

effects of sampling and quantization on single tone frequency estimation the effects of sampling and quantization on frequency estimation for a single sinusoid are investigated the cramer rao bound for 1 bit quantization is derived and compared with the limit of infinite quantization it is found that 1 bit quantization gives a slightly worse performance however with a dramatic increase of variance at certain frequencies this can be avoided by using four times oversampling the effect of sampling when using nonideal antialiasing lowpass filters is therefore investigated through derivation of the cramer rao lower bounds finally fast estimators for 1 bit quantization in particular correlation based estimators are derived and their performance is investigated the paper is concluded with simulation results for four times oversampled 1 bit quantization

repellers semi attractors and long lived chaotic transients abstract we study the chaotic transients observed in many deterministic systems in general they are related to strange repellers or semi attractors if they are repelling in some and attracting in other directions we propose formulas relating the average life time of the transient to dimensions of the repeller and to lyapunov exponents of the flow on it the formulas are tested numerically in a number of cases

decision feedback differential detection of differentially encoded 16apsk signals multiple symbol differential detection dd with reference signal estimation based on the feedback of past detected symbols is presented for differentially encoded 16 level amplitude phase shift keying 16dapsk a suboptimal decision is derived the approximate analysis of the bit error rate ber performance taking into account the decision error propagation effect is presented in an additive white gaussian noise awgn channel and the ber performance is compared with those of 16dpsk and 16 quadrature amplitude modulation 16qam

maximum likelihood differential detection of uncoded and trellis coded amplitude phase modulation over awgn and fading channels spl minus metrics and performance this paper derives metrics for maximum likelihood differential detection of uncoded and trellis coded mpsk and qam transmitted over rayleigh and rician fading channels receiver structures based on these metrics are proposed and their error probability performance analyzed and or simulated the results represent a generalization of the notion of multiple symbol differential detection previously introduced by the authors for mpsk over an awgn to the fading channel and other modulations for the coded cases ideal interleaving deinterleaving is assumed and furthermore the presence or absence of channel state information an interesting side result is that for a constant envelope modulation transmitted over a fading channel with unknown but rapidly varying phase error the other extreme to the slowly varying phase error case normally assumed for differential detection under certain practical assumptions it is shown that the optimum receiver is of the limiter discriminator type

empirical analyses of bold fmri statistics i spatially unsmoothed data collected under null hypothesis conditions temporal autocorrelation spatial coherency and their effects on voxel wise parametric statistics were examined in bold fmri null hypothesis or noise datasets seventeen normal young subjects were scanned using bold fmri while not performing any time locked experimental behavior temporal autocorrelation in these datasets was described well by a 1 frequency relationship voxel wise statistical analysis of these noise datasets which assumed independence i e ignored temporal autocorrelation rejected the null hypothesis at a higher rate than specified by the nominal alpha temporal smoothing in conjunction with the use of a modified general linear model worsley and friston 1995 neuroimage 2 173 182 brought the false positive rate closer to the nominal alpha it was also found that the noise fmri datasets contain spatially coherent time signals this observed spatial coherence could not be fully explained by a continuously differentiable spatial autocovariance function and was much greater for lower temporal frequencies its presence made voxel wise test statistics in a given noise dataset dependent and thus shifted their distributions to the right or left of 0 inclusion of a global signal covariate in the general linear model reduced this dependence and consequently stabilized i e reduced the variance of dataset false positive rates