on optimal and achievable fix free codes fix free codes are prefix condition codes which can also be decoded in the reverse direction they have attracted attention from several communities and are used in video standards two variations with additional constraints have also been considered for joint source channel coding 1 symmetric codes which require the codewords to be palindromes 2 codes with distance constraints on pairs of codewords approaches to determine the existence of a fix free code with a given set of codeword lengths for each of the three variations are proposed these appear to involve the first use of boolean satisfiability sat for the existence and design of source codes branch and bound algorithms to find the collection of optimal codes for asymmetric and symmetric fix free codes are described the first bound for the performance of optimal symmetric binary fix free codes is provided an earlier conjecture on optimal symmetric binary fix free codes is proven and related results for asymmetric fix free codes are presented a variation of the 3 4 conjecture for fix free codes is introduced a key idea in the first conjecture and the new one is a definition of how one sequence of nondecreasing natural numbers dominates another

the beta model maximum likelihood cramer rao bounds and hypothesis testing we study the maximum likelihood estimator in a setting where the dependent variable is a random graph and covariates are available on a graph level the model generalizes the well known beta model for random graphs by replacing the constant model parameters with regression functions cramer rao bounds are derived for special cases of the undirected beta model the directed beta model and the covariate based beta model the corresponding maximum likelihood estimators are compared with the bounds by means of simulations moreover examples are given on how to use the presented maximum likelihood estimators to test for directionality and significance finally the applicability of the model is demonstrated using temporal social network data describing communication among healthcare workers

joint estimation of porosity and saturation using stochastic rock physics modeling sediment porosity and saturation affect bulk modulus shearmodulus anddensity consequently estimatinghydrocarbon saturation and reservoir porosity from seismic data is a joint estimation problem uncertainty in porosity will lead toerrorsinsaturationprediction andviceversa porosityand saturation can be jointly estimated using stochastic rockphysicsmodelingandformalbayesianestimationmethodology knowledge of shear impedance reduces the uncertainty inporosityandthusalsoreducesuncertaintyinsaturationestimation this study investigates joint estimation of porosity and saturation by using rock physics stochastic modeling and bayesian estimation theory to derive saturation and porosity maps of expected pay sands in the field example the uncertainty in porosity quantified by the standard deviation stdassociatedwiththeposteriorprobabilitydensityfunctionpdf derivedfrominversionofseismicdataismuchless than the uncertainty in the derived saturation for a typical case the std associated with saturation is 24 while porositystdisabout1 34porosityunitsgivenseismic derived inversionattributeswithreasonableaccuracy comparisonof these numbers with prior estimates showed that inversion of seismic data decreased the uncertainty in porosity to 15 of the prior uncertainty while saturation uncertainty was only reduced to 92 of the prior uncertainty although these resultsmayvaryfromonelocationtoanother themethodology isgeneralandcanbeappliedtootherlocations

limits of sensing temporal concentration changes by single cells berg and purcell biophys j 20 193 1977 calculated how the accuracy of concentration sensing by single celled organisms is limited by noise from the small number of counted molecules here we generalize their results to the sensing of concentration ramps which is often the biologically relevant situation e g during bacterial chemotaxis we calculate lower bounds on the uncertainty of ramp sensing by three measurement devices a single receptor an absorbing sphere and a monitoring sphere we contrast two strategies simple linear regression of the input signal versus maximum likelihood estimation and show that the latter can be twice as accurate as the former finally we consider biological implementations of these two strategies and identify possible signatures that maximum likelihood estimation is implemented by real biological systems

optimal designs for space time linear precoders and decoders we introduce a new paradigm for the design of transmitter space time coding that we refer to as linear precoding it leads to simple closed form solutions for transmission over frequency selective multiple input multiple output mimo channels which are scalable with respect to the number of antennas size of the coding block and transmit average peak power the scheme operates as a block transmission system in which vectors of symbols are encoded and modulated through a linear mapping operating jointly in the space and time dimension the specific designs target minimization of the symbol mean square error and the approximate maximization of the minimum distance between symbol hypotheses under average and peak power constraints the solutions are shown to convert the mimo channel with memory into a set of parallel flat fading subchannels regardless of the design criterion while appropriate power bits loading on the subchannels is the specific signature of the different designs the proposed designs are compared in terms of various performance measures such as information rate ber and symbol mean square error

tight bounds on the redundancy of huffman codes a method for deriving optimal upper bounds on the redundancy of binary huffman codes in terms of the probability p sub 1 of the most likely source letter is presented this method will be used to compute bounds for all p sub 1 or 1 127 which were previously known only for a few special cases furthermore the known optimal lower bound for binary huffman codes is generalized to arbitrary code alphabets and some upper bounds for d ary huffman codes 2 or 1 2

kraft inequality and zero error source coding with decoder side information for certain source coding problems it is well known that the kraft inequality provides a simple sufficient condition for the existence of codes with given codeword lengths motivated by this fact a sufficient condition based on the kraft inequality can also be sought for the problem of zero error instantaneous coding with decoder side information more specifically it can be envisioned that a sufficient condition for the existence of such codes with codeword lengths l x is that for some 0 alphales 1 sigmaxepsivfscr 2 l x lesalpha for each clique fscr in the characteristic graph g of the source side information pair in this correspondence it is shown that 1 if the above is indeed a sufficient condition for a class g of graphs then it is possible to come as close as 1 log2 alpha bits to the asymptotic limits for each graph in g 2 there exist graph classes of interest for which such a can indeed be found and finally 3 no such n can be found for the class of all graphs

robust linear channel estimation methods for per subcarrier transmit antenna selection the linear minimum mean squared error mse channel estimator for systems employing per subcarrier transmit antenna selection is developed frequency domain correlations after the selection process are shown to be approximated well using a simple function which makes near optimal channel estimation practically possible however the resultant estimators are not robust to errors in the assumed model in terms of the antenna to subcarrier assignment used at transmission as we motivate both analytically and via simulations this is an issue when the channels for conveying this information to the receiver are severely constrained we present windowed channel estimations and new robust estimation algorithms either individually or in combination as solutions to counter this sensitivity the robust estimators are developed based on the principles of 1 minimising the worst case mse over the set of possible models and 2 minimising the expected mse over the set of possible models the latter estimator is preferred due to the lower implementation complexity and better mse performance we also prove theoretical asymptotic in signal to noise ratio performances of the two estimators used with the proposed correlation model simulation results illustrate the performance gains and improved robustness offered by the developed estimators

active learning applied to rcs computations with nonuniform sampling using different objective functions an active learning framework is introduced to reduce the number of frequencies and angles one must consider for wideband monostatic scattering computations or measurements this method is used to optimally select those frequencies and angles that would be most informative resulting in nonuniform sampling and often a reduced number of points vis agrave vis uniform sampling in this paper we focus on jointly two dimensional optimal sampling in frequency and incident angle thetas for monostatic scattering the method consists of two basic steps one step involves estimation of model parameters using a least square ls algorithm the next step is to optimally choose the next point frequency and thetas for analysis by the computational model or experiment this new point is selected with the goal of reducing uncertainty in the parametric model quantified via the fisher information matrix iterating these two steps a sequence of numerical computations or measurements are performed each at the most informative point for learning the parameters of the associated simpler parametric model this idea is demonstrated here in the context of reducing the number of points frequencies and orientations at which a computational model must be employed and in order to avoid repeatedly gathering samplings at the edge of the input space an alternative objective function is applied which makes the actively selected points closer to a region of interest

sequentially constructible reversible variable length codes dominant codelength sequences for reversible variable length codes rvlcs have been recently introduced and studied as a means to looking into optimal rvlcs however obtaining the dominant sequences for rvlcs is computationally challenging in this paper we consider a special subset of all rvlcs namely the sequentially constructible sc rvlcs for which the dominant sequences can be obtained with less computational complexity of course this time saving is achieved at the cost of losing the optimality however it is shown that the dominant sequences for sc rvlcs provide acceptable performance in terms of the redundancy specifically it is seen that the worst case penalty in using the optimal sc rvlcs with respect to the optimal rvlcs is at most 2 9 bit per symbol for alphabet size of up to 16 while obtaining the dominant sequences of sc rvlcs is relatively faster it will still become challenging as the search space of the relevant branch and bound algorithm gets larger when the source alphabet size increases in order to further reduce the time complexity we propose an alternative approach to a table of sc rvl codelength sequences which avoids the branch and bound algorithm it is shown that the codes obtained by this approach perform almost as well as the sc dominant sequences specifically for an alphabet size of up to 21 the redundancy of this approach is at most 2 19 bit more than the optimal sc rvlcs

blended ausm method for all speeds and all grid aspect ratios an ausm based discretization method using an explicit third order discretization for the convective part and a line implicit central discretization for the acoustic part and for the diffusive part has been developed for incompressible and low speed compressible navier stokes equations the lines are chosen in the direction of the gridpoints with shortest connection the semi implicit line method is used in multistage form because of the explicit third order discretization of the convective part multigrid is used as acceleration technique because of the implicit treatment of the acoustic and the diffusive terms the stiffness otherwise caused by high aspect ratio cells is removed low mach number stiffness is treated by a preconditioning technique to ensure physical correct behavior of the discretization for vanishing mach number extreme care has been taken for vanishing mach number stabilization terms are added to the mass flux pressure and temperature stabilization terms are necessary the coefficients of these terms are chosen so that correct scaling with mach number is obtained a blend of the low speed algorithm with the original ausm algorithm developed for high speed applications has been constructed so that the resulting algorithm can be used at all speeds

on the effect of receiver estimation error upon channel mutual information our goal in this paper is to study the effect of the receiver structure upon the achievable data rates we consider transmission of linearly precoded data symbols over a frequency selective block fading multiple input multiple output mimo wireless channel to encompass a number of transmission schemes we study this problem utilizing affine precoding which is a unified model of linearly precoded data symbols with superimposed training we focus on bayesian receivers that estimate both the unknown fading coefficients and the data symbols the receiver may adopt either of the following strategies to retrieve the data symbols strategy i the receiver obtains joint bayesian channel and symbol estimates strategy ii the receiver obtains a bayesian channel estimate initially and the channel measurement is utilized to estimate the data symbols for both strategies we provide lower bounds on the mutual information between the data symbols and their corresponding estimates and we relate these bounds to the symbol cramer rao bound crb matrices in contrast to strategy ii for strategy i the lower bound does not depend on either the channel estimate or the covariance of the channel estimation error for strategy ii we show that asymptotically as the size of the transmission block grows there is no loss of information after the maximum a posteriori map estimate of gaussian symbols we also provide guidelines to design affine precoders that maximize the derived lower bounds under the total average transmit power constraint

tight upper bounds on the redundancy of huffman codes bounds on the redundancy of huffman codes in terms of the probability p sub 1 of the most likely source letter are provided in particular upper bounds are presented that are sharper than the bounds given recently by r g gallager ibid vol it 24 no 6 p 668 74 nov 1978 and by r m capocelli et al ibid vol it 32 no 6 p 854 857 nov 1986 for an interval 2 2 sup l 1 1 or 2 it is shown that the new bounds are the tightest possible for these intervals

preconditioning applied to variable and constant density flows a time derivative preconditioning of the navier stokes equations suitable for both variable and constant density fluids is developed the ideas of low mach number preconditioning and artificial compressibility are combined into a unified approach designed to enhance convergence rates of density based time marching schemes for solving flows of incompressible and variable density fluids at all speeds the preconditioning is coupled with a dual time stepping scheme implemented within an explicit multistage algorithm for solving time accurate flows the resultant time integration scheme is used in conjunction with a finite volume discretization designed for unstructured solution adaptive mesh topologies this method is shown to provide accurate steady state solutions for transonic and low speed flow of variable density fluids the time accurate solution of unsteady incompressible flow is also demonstrated

retinal vessel centerline extraction using multiscale matched filters confidence and edge measures motivated by the goals of improving detection of low contrast and narrow vessels and eliminating false detections at nonvascular structures a new technique is presented for extracting vessels in retinal images the core of the technique is a new likelihood ratio test that combines matched filter responses confidence measures and vessel boundary measures matched filter responses are derived in scale space to extract vessels of widely varying widths a vessel confidence measure is defined as a projection of a vector formed from a normalized pixel neighborhood onto a normalized ideal vessel profile vessel boundary measures and associated confidences are computed at potential vessel boundaries combined these responses form a six dimensional measurement vector at each pixel a training technique is used to develop a mapping of this vector to a likelihood ratio that measures the vesselness at each pixel results comparing this vesselness measure to matched filters alone and to measures based on the hessian of intensities show substantial improvements both qualitatively and quantitatively the hessian can be used in place of the matched filter to obtain similar but less substantial improvements or to steer the matched filter by preselecting kernel orientations finally the new vesselness likelihood ratio is embedded into a vessel tracing framework resulting in an efficient and effective vessel centerline extraction algorithm

generalized linear precoder and decoder design for mimo channels using the weighted mmse criterion we address the problem of designing jointly optimum linear precoder and decoder for a mimo channel possibly with delay spread using a weighted minimum mean squared error mmse criterion subject to a transmit power constraint we show that the optimum linear precoder and decoder diagonalize the mimo channel into eigen subchannels for any set of error weights furthermore we derive the optimum linear precoder and decoder as functions of the error weights and consider specialized designs based on specific choices of error weights we show how to obtain 1 the maximum information rate design 2 qos based design we show how to achieve any set of relative snrs across the subchannels and 3 the unweighted mmse and equal error design for fixed rate systems

everything you always wanted to know about training guidelines derived using the affine precoding framework and the crb in this paper affine precoding is used to investigate the tradeoffs that exist while using the transmitter resources on training versus information symbols the channel input is a training vector superimposed on a linearly precoded vector of symbols a block fading frequency selective multi input multi output mimo channel is considered to highlight the tradeoffs between training and data symbols the fisher information matrix fim is derived under two circumstances the random parameter vector to be estimated contains 1 only fading channel coefficients and 2 unknown data symbols as well as the channel coefficients while strategy 1 corresponds to the receiver structure in which the channel is estimated initially and the channel measurement is utilized to retrieve the data symbols strategy 2 corresponds to the structure in which channel and symbol estimations are performed jointly the interesting outcome of the study in this paper is that minimizing the channel cramer rao bound crb for strategies 1 and 2 under a total average transmit power constraint leads to different affine precoder design guidelines

iterative cdma multiuser receiver with soft decision directed channel estimation we develop an iterative code division multiple access cdma receiver for multipath block fading channels in the uplink the mean square error mse of the channel estimates is reduced iteratively by using soft data estimates as additional pilots the multiuser detector performs parallel interference cancellation pic with subsequent linear filtering we consider a single user matched filter sumf and develop a low complexity linear minimum mse lmmse filter for intersymbol interference isi channels that allows for 33 more users than the sumf we investigate two choices of training sequences for initial channel estimation the first is a random pilot symbol sequence modulated by a short spreading sequence rand and the second is a perfect root of unity sequence prus used as long sounding chip sequence we observe that the rand scheme approaches the single user bound up to 2 db and in case of prus up to 1 db at a target bit error rate ber of 10 3 further several channel estimators are developed that use various combinations of soft decision symbols and statistical a priori knowledge about the channel these are the approximated least squares als approximated linear mmse almmse and linear mmse lmmse estimators the iterative estimators show an improvement of 2 5 and 5 db with prus and rand pilots respectively over estimators that do not exploit soft feedback symbols at a ber of 10 3 the als is sacrificing less than 0 6 db to obtain a ber of 10 3 in a system at load 1 5 when compared with the almmse and lmmse schemes the load is understood as the ratio of the number of users to the spreading factor this paper shows that significant improvements in system capacity can be achieved in multipath scenarios with low complexity choices of multiuser detectors and channel estimators

on constructing the huffman code based reversible variable length codes in this letter we propose a generic and efficient algorithm that can construct both asymmetrical and symmetrical reversible variable length codes rvlcs starting from a given huffman code the construction is based on two developed codeword selection mechanisms for the symmetrical case and the asymmetrical case respectively it is shown that the two mechanisms possess simple features and can generate efficient rvlcs easily in addition two new asymmetrical rvlcs are constructed and shown to be very efficient for further reducing the coding overheads in mpeg 4 when operating in the reversible decoding mode

an a based algorithm for constructing reversible variable length codes with minimum average codeword length variable length codes vlcs are widely adopted in many compression standards due to their good coding efficiency on average codeword length however an inherent problem with a vlc is that an error of even one bit can cause serious error propagation and thus loss of synchronization at the receiver which would lead to a series of non correctly decoded symbols reversible variable length codes rvlcs were introduced to significantly mitigate this phenomenon in this work a method to find an optimal rvlc in terms of the minimum average codeword length is first formulated as a tree searching problem and then instead of performing an exhaustive search an a based construction algorithm is proposed to find an optimal rvlc the proposed algorithm has been applied to several benchmarks for sources and has found respective optimal symmetric and asymmetric rvlcs

fading channels how perfect need perfect side information be the analysis of flat fading channels is often performed under the assumption that the additive noise is white and gaussian and that the receiver has precise knowledge of the realization of the fading process these assumptions imply the optimality of gaussian codebooks and of scaled nearest neighbor decoding here we study the robustness of this communication scheme with respect to errors in the estimation of the fading process we quantify the degradation in performance that results from such estimation errors and demonstrate the lack of robustness of this scheme for some situations we suggest the rule of thumb that in order to avoid degradation the estimation error should be negligible compared to the reciprocal of the signal to noise ratio snr

on minimum variance unbiased estimation of clock offset in a two way message exchange mechanism for many applications distributed networks require the local clocks of the constituent nodes to run close to an agreed upon notion of time most of the widely used clock synchronization algorithms in such systems employ the sender receiver protocol based on a two way timing message exchange paradigm maximum likelihood estimator mle of the clock offset based on the timing message exchanges between two clocks was derived in d r jeske on maximum likelihood estimation of clock offset ieee trans commun vol 53 pp 53 54 jan 2005 when the fixed delays are symmetric and the variable delays in each direction assume an exponential distribution with an unknown mean herein the best linear unbiased estimate using order statistics blue os of the clock offset between two nodes is derived assuming both symmetric and asymmetric exponential network delays respectively the rao blackwell lehmann scheffe theorem is then exploited to obtain the minimum variance unbiased estimate mvue for the clock offset which it is shown to coincide with the blue os in addition it is found that the mvue of the clock offset in the presence of symmetric network delays also coincides with the mle finally in the presence of asymmetric network delays although the mle is biased it is shown to achieve lesser mean square error mse than the mvue in the region around the point where the bidirectional network link delays are symmetric and hence its merit as the most versatile estimator is fairly justified

representation of mutual information via input estimates a relationship between information theory and estimation theory was recently shown for the gaussian channel relating the derivative of mutual information with the minimum mean square error this paper generalizes the link between information theory and estimation theory to arbitrary channels giving representations of the derivative of mutual information as a function of the conditional marginal input distributions given the outputs we illustrate the use of this representation in the efficient numerical computation of the mutual information achieved by inputs such as specific codes or natural language

improvement of tdoa position fixing using the likelihood curvature a conventional multilateration is a two step process where in the first step the time difference of arrivals tdoa of a signal at multiple sensors are estimated and in the second step these tdoas are used in some position fixing technique to estimate the location of an emitter several estimators have been proposed over the years for the estimation of the tdoas many techniques have been proposed for position fixing as well much of the research on position fixing has been focused on obtaining a simplified closed form solution for the unknown deterministic signal model stein had derived the maximum likelihood estimator mle for the tdoa between two sensors which is the peak location of the cross correlation function since the asymptotic variance of an mle approaches the cramer rao lower bound crlb which is the inverse of the negative of the expected value of the curvature of the log likelihood function using this as a motivation we propose a weighted least squares type position fixing technique where the weights are computed from the curvature of the log likelihood function

optimum 1 ended binary prefix codes the problem of finding a binary prefix code of minimum average codeword length for a given finite probability distribution subject to the requirement that each codeword must end with a 1 is considered lower and upper bounds to the performance of the optimum code are derived the lower bound is tight for certain probability distributions an algorithm that generates an optimum code for any given distribution is described

more efficient algorithms and analyses for unequal letter cost prefix free coding there is a large literature devoted to the problem of finding an optimal min cost prefix free code with an unequal letter cost encoding alphabet of size while there is no known polynomial time algorithm for solving it optimally there are many good heuristics that all provide additive errors to optimal the additive error in these algorithms usually depends linearly upon the largest encoding letter size this paper was motivated by the problem of finding optimal codes when the encoding alphabet is infinite because the largest letter cost is infinite the previous analyses could give infinite error bounds we provide a new algorithm that works with infinite encoding alphabets when restricted to the finite alphabet case our algorithm often provides better error bounds than the best previous ones known

the risk unbiased cramer rao bound for non bayesian multivariate parameter estimation how accurately can one estimate a deterministic parameter subject to other unknown deterministic model nuisance parameters the most popular answer to this question is given by the cramer rao bound crb the main assumption behind the derivation of the crb is local unbiased estimation of all model parameters the foundations of this paper rely on doubting this assumption generally in multivariate parameter estimation each parameter in its turn can be treated as a single parameter of interest whereas the other model parameters are treated as nuisance as their misknowledge interferes with the estimation of the parameter of interest this approach is utilized in this paper to provide a fresh look at deterministic parameter estimation a new cramer rao cr type bound is derived without assuming unbiased estimation of the nuisance parameters rather than that we apply lehmann s concept of unbiasedness for a risk that measures the distance between the estimator and the locally best unbiased estimator which assumes perfect knowledge of the nuisance parameters the proposed risk unbiased crb rucrb is proven to be asymptotically attainable by the maximum likelihood estimator while being tighter than the conventional crb furthermore simulations verify the asymptotic achievability of the rucrb by the maximum likelihood estimator for an array processing problem

simultaneous solution algorithms for eulerian eulerian gas solid flow models stability analysis and convergence behaviour of a point and a plane solver simultaneous solution algorithms for eulerian eulerian gas solid flow models are presented and their stability analyzed the integration algorithms are based on dual time stepping with fourth order runge kutta in pseudo time the domain is solved point or plane wise the discretization of the inviscid terms is based on a low mach limit of the multi phase preconditioned advection upstream splitting method mp ausmp the numerical stability of the simultaneous solution algorithms is analyzed in 2d with the fourier method stability results are compared with the convergence behaviour of 3d riser simulations the impact of the grid aspect ratio preconditioning artificial dissipation and the treatment of the source terms is investigated a particular advantage of the simultaneous solution algorithms is that they allow a fully implicit treatment of the source terms which are of crucial importance for the eulerian eulerian gas solid flow models and their solution the numerical stability of the optimal simultaneous solution algorithm is analyzed for different solids volume fractions and gas solid slip velocities furthermore the effect of the grid resolution on the convergence behaviour and the simulation results is investigated finally simulations of the bottom zone of a pilot scale riser with a side solids inlet are experimentally validated

bounds on the redundancy of huffman codes corresp new upper bounds on the redundancy of huffman codes are provided a bound that for 2 9 leq p 1 leq 0 4 is sharper than the bound of gallager when the probability of the most likely source letter p 1 is the only known probability is presented the improved bound is the tightest possible for 1 3 leq p 1 leq 0 4 upper bounds are presented on the redundancy of huffman codes when the extreme probabilities p 1 and p n are known

optimal binary one ended codes binary prefix free codes in which all codewords end with a 1 have been introduced by berger and yeung 1990 a recursive method is given here for the construction of all optimal 1 ended codes with n codewords it is shown that the set of codes obtained by the construction contains only optimal codes we also compute recursively the number of essentially different optimal 1 ended codes with n codewords and show that their number grows faster than any polynomial in n

analogue signalling by phase shifting this paper presents a novel method for overlaying an analogue value on top of a digital signal by adding a phase rotation and a signature sequence to a block of digitally modulated data symbols this analogue value can be conveyed to a receiver without significant degradation to the underlying digital data a near ml estimator is derived which is non data driven and hence independent of the digital data sequence it is shown that this method of signalling a value is superior to quantising it and adding it to the digital data stream we analyse the performance of the analogue and digital methods and also compare them using simulations

on the penalty of optimal fix free codes in this paper the difference between the redundancy of the optimal asymmetric symmetric fix free code and that of the optimal prefix free code is considered as the penalty of benefiting from the desired properties of fix free codes this penalty is studied from different perspectives in particular it is shown that the average penalty of asymmetric fix free codes is less than 0 21 bit per symbol moreover it is proved that when the source alphabet size is sufficiently large for almost all sources the penalty is less than or equal to 0 182 bit per symbol regarding symmetric fix free codes it is shown that the average penalty tends to infinity as the source alphabet size increases

robust precoding with limited feedback design based on precoding mse for mu miso systems for the separation of the signals in the vector broadcast channel bc some information about the channel state is necessary at the transmitter in many cases this channel state information csi must be fed back from the receivers to the transmitter we jointly design the channel estimators and the quantizers at the receivers together with the precoder at the transmitter based on a precoder centric criterion i e the minimization of a mean square error mse metric appropriate for the precoder design this is in contrast to our previous works where the quantizer design was based on a csi mse metric i e based on the minimization of the mse between the true channel and the channel recovered by the transmitter using a feedback channel interestingly the estimators resulting from this joint formulation are independent of the used codebook the codebook entries are the employed precoders therefore each receiver feeds back the index of a set of precoders and the intersection of the sets gives the appropriate precoder since the quantizers of the different receivers have to work separately the metric for the computation of the partition cells cannot be expressed as a simple squared error depending on the quantizer output the proposed system based on a joint optimization clearly outperforms previous designs with separate optimization of feedback and precoding

some basic properties of fix free codes a variable length code is a fix free code if no codeword is a prefix or a suffix of any other codeword this class of codes is applied to speed up the decoding process for the decoder can decode from both sides of the compressed file simultaneously we study some basic properties of fix free codes we prove a sufficient and a necessary condition for the existence of fix free codes and we obtain some new upper bounds on the redundancy of optimal fix free codes

binary prefix codes ending in a 1 binary prefix codes with the constraint that each codeword must end with a 1 have been recently introduced by berger and yeung 1990 we analyze the performance of such codes by investigating their average codeword length in particular we show that a very simple strategy permits the construction of a 1 ended binary prefix code whose average codeword length is less than h 1 for any discrete source with entropy h we also prove a tight lower bound on the optimal average codeword length in terms of h and of the minimum letter probability of the source finally we discuss the problem of finding an optimum feasible code

a kraft type sufficient condition for the existence of d ary fix free codes a greedy scheme called greedy codeword assignment scheme gcas is proposed to assign d ary codewords to the given code lengths 1 2 n so that they satisfy the fix free property this scheme guarantees that a d ary fix free code can be obtained whenever i 1 n d d where d is equal to 5 8 for d even and very close to 5 8 for d odd this result can be regarded as an extension of yekhanin s theorem on the existence of binary fix free codes in the special case d 2 the greediness of gcas enables us to prove that if mini i 2 the inequality i 1 n 2 i 21 32 implies the existence of a binary fix free code with code lengths 1 2 n

sufficient conditions for existence of binary fix free codes two sufficient conditions are given for the existence of binary fix free codes i e both prefix free and suffix free let l be a finite multiset of positive integers whose kraft sum is at most 3 4 it is shown that there exists a fix free code whose codeword lengths are the elements of l if either of the following two conditions holds i the smallest integer in l is at least 2 and no integer in l except possibly the largest one occurs more than 2 sup min l 2 times ii no integer in l except possibly the largest one occurs more than twice the results move closer to the ahlswede balkenhol khachatrian conjecture that kraft sums of at most 3 4 suffice for the existence of fix free codes

the most likely optimal symmetric rvlc for each alphabet size up to 30 a symmetric reversible variable length code rvlc is determined which is most likely to be optimal in average codeword length it is shown that these codes are optimal for more than half of all the possible sources

auditory motivated level crossing approach to instantaneous frequency estimation we address the problem of estimating the instantaneous frequency if of a phase signal using its level crossing lc information based on front end auditory processing motivation we show that the problem of if estimation using lc information can be cast in the framework of estimation from irregularly sampled data the formulation has the generality of estimating different types of if without the need for a quasistationary assumption we consider two types of if polynomial and bandlimited we use polynomial interpolating functions for the former and for the latter we propose a novel line plus sum of sines model the model parameters are estimated by linear regression considering the noisy case lc data for different levels is analyzed and methods for combining different estimators from lcs are discussed theoretical and extensive simulation results show that the performance of the zero crossing zc based if estimator and the level crossing based if estimator with smaller level values is better than those obtained with higher level values or their combinations the new technique reaches the crame spl acute r rao bound crb roughly above 4 db signal to noise ratio snr and its performance does not deteriorate rapidly with mismatch in the if order compared with the other techniques in the literature

a multigrid semi implicit line method for viscous incompressible and low mach number flows on high aspect ratio grids abstract discretization of viscous incompressible and viscous low mach number flows often leads to a system of equations which is very difficult to solve there are two reasons first the use of high aspect ratio grids results in a very numerically anisotropic behaviour of the diffusive and acoustic terms and second in low mach number flow the ratio of the convective and acoustic eigenvalues of the inviscid system becomes very high we implemented an ausm based discretization method using an explicit third order discretization for the convective part and a line implicit central discretization for the acoustic part and for the diffusive part the lines are chosen in the direction of the grid points with shortest connection the preconditioned semi implicit line method is used in multistage form because of the explicit third order discretization of the convective part multigrid is used as an acceleration technique it is shown that the convergence is very good independent of grid aspect ratio and mach number

low complexity lmmse based mimo ofdm channel estimation via angle domain processing in many situations multiple input multiple output with orthogonal frequency division multiplexing mimo ofdm channels tend to be spatially correlated due for example to limited scattering prior knowledge of this channel spatial correlation and the channel frequency correlation can be exploited by using the linear minimum mean square error lmmse technique however the complexity of the 2 d lmmse technique which fully utilizes both the channel spatial and frequency correlation is quite high to solve this problem this paper presents and analyzes several low complexity suboptimal approximated lmmse channel estimation techniques in the angle domain where the channel model lends itself to a physical interpretation the choice of angle domain techniques is largely dependent on the extent of channel stochastic information e g channel correlation or power that is available to the receiver nevertheless all the proposed angle domain techniques have much lower complexity compared to the 2 d lmmse technique further all the angle domain techniques improve over the conventional least square ls technique for all the typical mimo ofdm models under consideration more importantly our simulation results show that the angle domain quasi 1 d ql d lmmse technique can achieve similar performance compared to the 2 d lmmse technique for all typical mimo ofdm models with significantly lower complexity

development of low diffusion flux splitting methods for dense gas solid flows the development of a class of low diffusion upwinding methods for computing dense gas solid flows is presented in this work an artificial compressibility low mach preconditioning strategy is developed for a hyperbolic two phase flow equation system consisting of separate solids and gas momentum and continuity equations the eigenvalues of this system are used to devise extensions of the ausm 1 and ldfss 2 flux splitting methods that provide high resolution capturing of bubble growth and collapse in gas solid fluidized beds applications to several problems in fluidization are presented

preconditioned methods for solving the incompressible low speed compressible equations abstract acceleration methods are presented for solving the steady state incompressible equations these systems are preconditioned by introducing artificial time derivatives which allow for a faster convergence to the steady state we also consider the compressible equations in conservation form with slow flow two arbitrary functions and are introduced in the general preconditioning an analysis of this system is presented and an optimal value for is determined given a constant it is further sown that the resultant incompressible equations form a symmetric hyperbolic system and so are well posed several generalizations to the compressible equations are presented which extend previous results

on the construction of statistically synchronizable codes the problem of constructing statistically synchronizable codes over arbitrary alphabets and for any finite source is considered it is shown how to efficiently construct a statistically synchronizable code whose average codeword length is within the least likely codeword probability from that of the huffman code for the same source moreover a method is given for constructing codes having a synchronizing codeword the method yields synchronous codes that exhibit high synchronizing capability and low redundancy

fundamentals of statistical signal processing estimation theory minimum variance unbiased estimation cramer rao lower bound linear models general minimum variance unbiased estimation best linear unbiased estimators maximum likelihood estimation least squares method of moments the bayesian philosophy general bayesian estimators linear bayesian estimators kalman filters summary of estimators extension for complex data and parameters

modified symmetrical reversible variable length code and its theoretical bounds reversible variable length codes rvlcs have been adopted in emerging video coding standards h 263 and mpeg 4 to enhance their error resilience capabilities which are important and essential in error prone environments this study proposes an efficient algorithm to construct a symmetrical rvlc from a given huffman code in addition theoretical bounds on the maximum codeword length for fixed length huffman codes and on the optimal average codeword lengths for sources with exponential distribution are provided

fundamental limits of linear equalizers diversity capacity and complexity linear equalizers les have been widely adopted for practical systems due to their low computational complexity however it is also well known that les provide inferior performance relative to a maximum likelihood equalizer mle or other near mles because les usually cannot collect the diversity order enabled by the transmitter and at the same time they lose mutual information more importantly unlike mle or near mles the performance of les has not been well quantified this hinders more general applications of les in wireless systems in this paper we reveal a fundamental link between a channel parameter orthogonality deficiency od of the channel matrix and the diversity and capacity of les we identify that when the od of channel matrix has an upper bound strictly less than 1 the same diversity order as that of mles is collected by les and the outage capacity loss relative to mles is also a constant over signal to noise ratio snr these results can be applied to designing a framework for hybrid equalizers furthermore by studying the statistical properties of the od and comparing the complexity of different equalizers we show that hybrid equalizers can trade off between performance and complexity by tuning the channel matrix od the theoretical analysis is corroborated by computer simulations

a new flux splitting scheme a new flux splitting scheme is proposed the scheme is remarkably simple and yet its accuracy rivals and in some cases surpasses that of roe s solver in the euler and navier stokes solutions carried out in this study the scheme is robust and converges as fast as the roe splitting we propose an appropriately defined cell face advection mach number using values from the two straddling cells via associated characteristic speeds this interface mach number is then used to determine the upwind extrapolation for the convective quantities accordingly the name of the scheme is coined as the advection upstream splitting method ausm we also introduce a new pressure splitting which is shown to behave successfully yielding much smoother results than other existing pressure splittings of particular interest is the supersonic blunt body problem in which the roe scheme gives anomalous solutions the ausm produces correct solutions without difficulty for a wide range of flow conditions as well as grids

93 of the 3 over 4 conjecture is already verified one of the most important challenges in the context of fix free codes is proving the 3 4 conjecture which guarantees the existence of fix free codewords of lengths l1 l2 ln if i 1n2 li 3 4 although this conjecture has not become a theorem yet some researchers have proved the problem with some extra constraints on the codelengths one of those we call it yekhanin s constraint is i li 1 2 li 1 2 where minklk in this paper it is shown that such a constraint is not so restrictive we prove that almost 93 8 of the n tuple codelength vectors with kraft sum 3 4 do satisfy yekhanin s constraint one can optimistically interpret this result as almost 93 8 of the road of proving the 3 4 conjecture is paved

on posterior distributions for signals in gaussian noise with unknown covariance matrix a bayesian approach to estimate parameters of signals embedded in complex gaussian noise with unknown color is presented the study specifically focuses on a bayesian treatment of the unknown noise covariance matrix making up a nuisance parameter in such problems by integrating out uncertainties regarding the noise color an enhanced ability to estimate both the signal parameters as well as properties of the error is exploited several noninformative priors for the covariance matrix such as the reference prior the jeffreys prior and modifications to this are considered some of the priors result in analytical solutions whereas others demand numerical approximations in the linear signal model connections are made between the standard adaptive maximum likelihood aml estimate and a bayesian solution using the jeffreys prior with adjustments to the jeffreys prior correspondence to the regularized solution is also established this in turn enables a formal treatment of the regularization parameter simulations indicate that significant improvements compared to the aml estimator can be obtained by considering both the derived regularized solutions as well as the one obtained using the reference prior the simulations also indicate the possibility of enhancing the predictions of properties of the error as uncertainties in the noise color are acknowledged

the redundancy of an optimal binary fix free code is not greater than 1 bit in the context of fix free codes the most important and immediate consequence of the 3 4 conjecture if it is proven is that the redundancy of an optimal binary fix free code never exceeds 1 bit as with the optimal prefix free codes i e huffman codes in this paper this bound on the redundancy is proven without requiring the conjecture to be true to do so we use two known sufficient conditions for the existence of binary fix free codes to derive an improved upper bound on the redundancy of an optimal fix free code in terms of the largest symbol probability

optimal design and placement of pilot symbols for channel estimation the problem of designing and placing pilot symbols for the estimation of frequency selective random channels is considered the channel is assumed to be a block fading model with finite impulse response fir for both single input single output siso and multiple input multiple output mimo channels under the assumption of independent and identical distributed channel taps the cramer rao bound crb on the mean square error mse of semi blind channel estimators is derived and minimized with respect to pilot symbols and their placement it is shown that the optimal strategy is to place pilot symbols satisfying certain orthogonality condition in such a way that data and pilot symbols with higher power are in the middle of the packet the results also indicate that the optimal pilot placements are independent of channel probability distribution for constant modulus symbols we show that the quasi periodic placement and its generalization in the multiuser case turn out to be optimal we further consider estimating channels with correlated taps and show that the previous placement strategy is also optimal among orthogonal pilot sequences

optimal placement of training for frequency selective block fading channels the problem of placing training symbols optimally for orthogonal frequency division multiplexing ofdm and single carrier systems is considered the channel is assumed to be quasi static with a finite impulse response of length l 1 samples under the assumptions that neither the transmitter nor the receiver knows the channel and that the receiver forms a minimum mean square error mmse channel estimate based on training symbols only training is optimized by maximizing a tight lower bound on the ergodic training based independent and identically distributed i i d capacity for ofdm systems it is shown that the lower bound is maximized by placing the known symbols periodically in frequency for single carrier systems under the assumption that the training symbols are placed in clusters of length spl alpha spl ges 2l 1 it is shown that the lower bound is maximized by a family of placement schemes called qpp spl alpha where qpp stands for quasi periodic placement these placement schemes are formed by grouping the known symbols into as many clusters as possible and then placing these clusters periodically in the packet for both ofdm and single carrier systems the optimum energy tradeoff between training and data is also obtained

filterbank transceivers optimizing information rate in block transmissions over dispersive channels optimal finite impulse response fir transmit and receive filterbanks are derived for block based data transmissions over frequency selective additive gaussian noise agn channels by maximizing mutual information subject to a fixed transmit power constraint both fir and pole zero channels are considered the inherent flexibility of the proposed transceivers is exploited to derive as special cases zero forcing zf and minimum mean square error receive filterbanks the transmit filterbank converts transmission over a frequency selective fading channel affected by additive colored noise into a set of independent flat fading subchannels with uncorrelated noise samples two loading algorithms are also developed to distribute transmit power and number of bits across the usable subchannels while adhering to an upper bound on the bit error rate ber reduction of the signal to noise ratio snr margin required to satisfy the prescribed ber is achieved by coding each subchannel s bit stream the potential of the proposed transceivers is illustrated and compared to discrete multitone dmt with simulated examples

some tight lower bounds on the redundancy of optimal binary prefix free and fix free codes the tight lower bound on the redundancy of optimal prefix free codes in terms of a given symbol probability not necessarily the largest or the smallest one has been derived in the literature the first goal of this paper is to derive the tight lower bounds in terms of j j 1 known symbol probabilities of the source using some properties of kullback leibler distance since fix free codes are special prefix free codes for which no codeword is a suffix of the other codewords it is clear that all lower bounds on the redundancy of optimal prefix free codes are also valid for fix free ones accordingly the second question of the paper is on the tightness of the derived lower bounds for optimal fix free codes it is proven that these lower bounds are tight for optimal fix free codes if j leq 3 and are not tight for j geq 4 also it is shown that the tight lower bound in terms of the probability of the most likely symbol is the same for optimal prefix free and optimal fix free codes

hybrid fm polynomial phase signal modeling parameter estimation and cramer rao bounds parameter estimation for a class of nonstationary signal models is addressed the class contains combination of a polynomial phase signal pps and a frequency modulated fm component of the sinusoidal or hyperbolic type such signals appear in radar and sonar applications involving moving targets with vibrating or rotating components a novel approach is proposed that allows us to decouple estimation of the fm parameters from those of the pps relying on properties of the multilag high order ambiguity function ml haf the accuracy achievable by any unbiased estimator of the hybrid fm pps parameters is investigated by means of the cramer rao lower bounds crlbs both exact and large sample approximate expressions of the bounds are derived and compared with the performance of the proposed methods based on monte carlo simulations

estimation of flows in flow networks abstract let g be a directed graph with an unknown flow on each edge such that the following flow conservation constraint is maintained except for sources and sinks the sum of flows into a node equals the sum of flows going out of a node given a noisy measurement of the flow on each edge the problem we address which we call the m ost p robable f low e stimation problem mpfe is to estimate the most probable assignment of flow for every edge such that the flow conservation constraint is maintained we provide an algorithm called y mpfe for solving the mpfe problem when the measurement error is gaussian g aussian mpfe the algorithm works in o e v 2 when the underlying undirected graph of g is a 2 connected planar graph and in o e v when it is a 2 connected serial parallel graph or a tree this result is applicable to any m inimum c ost f low problem for which the cost function is e x e e 2 for edge e where e and e are constants and x e is the flow on edge e we show that for all topologies the g aussian mpfe s precision for each edge is analogous to the equivalent resistance measured in series to this edge in an electrical network built by replacing every edge with a resistor reflecting the measurement s precision on that edge

quasi ml period estimation from incomplete timing data given a noisy sequence of possibly shifted integer multiples of a certain period it is often of interest to accurately estimate the period with known integer regressors the problem is classical linear regression in many applications however the regressors are unknown integers and only loose bounds on the period are available examples include hop period and timing estimation wherein hops may be missed at the output of the frequency discriminator or the emitter may hop out of band pulse repetition interval pri analysis and passive rotating beam radio scanning we study several pertinent period estimators our emphasis is on a quasi maximum likelihood approach developed herein and an earlier method based on the fourier transform of a dirac delta train representation of the data surprisingly both are capable of attaining the clairvoyant crame spl acute r rao bound at moderate signal to noise ratios snrs even for short e g 10 samples we carefully address parameter identifiability issues and corroborate our findings with extensive simulations

new results on deterministic cramer rao bounds for real and complex parameters the cramer rao bounds crb is a lower bound of great interest for system analysis and design in the asymptotic region high signal to noise ratio snr and or large number of snapshots as it is simple to calculate and it is usually possible to obtain closed form expressions the first part of the paper is a generalization to complex parameters of the barankin rationale for deriving mse lower bounds that is the minimization of a norm under a set of linear constraints with the norm minimization approach the study of fisher information matrix fim singularity constrained crb and regularity conditions become straightforward corollaries of the derivation the second part provides new results useful for system analysis and design a general reparameterization inequality the equivalence between reparameterization and equality constraints and an explicit relationship between parameters unidentifiability and fim singularity

robust rls in the presence of correlated noise using outlier sparsity relative to batch alternatives the recursive least squares rls algorithm has well appreciated merits of reduced complexity and storage requirements for online processing of stationary signals and also for tracking slowly varying nonstationary signals however rls is challenged when in addition to noise outliers are also present in the data due to e g impulsive disturbances existing robust rls approaches are resilient to outliers but require the nominal noise to be white an assumption that may not hold in e g sensor networks where neighboring sensors are affected by correlated ambient noise prewhitening with the known noise covariance is not a viable option because it spreads the outliers to noncontaminated measurements which leads to inefficient utilization of the available data and unsatisfactory performance in this correspondence a robust rls algorithm is developed capable of handling outliers and correlated noise simultaneously in the proposed method outliers are treated as nuisance variables and estimated jointly with the wanted parameters identifiability is ensured by exploiting the sparsity of outliers which is effected via regularizing the least squares ls criterion with the l1 norm of the outlier vectors this leads to an optimization problem whose solution yields the robust rls estimates for low complexity real time operation a suboptimal online algorithm is proposed which entails closed form updates per time step in the spirit of rls simulations demonstrate the effectiveness and improved performance of the proposed method in comparison with the nonrobust rls and its state of the art robust renditions

some upper bounds on the redundancy of optimal binary fix free codes in order to investigate the cost of employing fix free codes instead of the well established prefix free codes some upper bounds on the redundancy of the optimal fix free codes and their difference with the corresponding huffman codes are presented unlike the conventional approach which is based on some shannon like suboptimal codes we examine the redundancy of a better huffman like code an algorithm is proposed for deriving optimal binary codeword lengths with kraft sum 5 8 for a given probability distribution the existence of a fix free code with such codelengths is guaranteed by yekhanin s theorem it is shown that the redundancy of this fix free code is at most 0 8 bit greater than that of the huffman code and does not exceed 8 3 log3 1 0817 bits this upper bound is 4 3 log 5 3 0 5964 bit less than the best known one if the 3 4 conjecture is proved sometime in the future the presented upper bound on the redundancy of the optimal fix free codes i e 1 0817 will be improved by only 5 3 log3 0 0817 in addition to these general bounds all known upper bounds in terms of the largest the smallest and an arbitrary given symbol probability are substantially improved