approximately optimal solutions to the finite dimensional witsenhausen counterexample recently a vector version of witsenhausen s counterexample was considered and it was shown that in the asymptotic limit of infinite vector length certain vector quantization based control strategies are provably within a constant factor of the asymptotically optimal cost for all possible problem parameters while suggestive a constant factor result for the finite dimensional problem has remained elusive in this paper we provide a resolution to this issue by applying a large deviation sphere packing philosophy we derive a lower bound to the optimal cost for the finite dimensional case that uses appropriate shadows of an existing vector lower bound that is the same for all dimensions using this new lower bound we show that good lattice quantization based control strategies achieve within a constant factor of the optimal cost uniformly over all possible problem parameters including the vector length for witsenhausen s original problem which is the scalar case the gap between regular lattice quantization based strategies and the lower bound is provably never more than a factor of 100 and computer calculations strongly suggest that the factor in fact may be no larger than 8 finally to obtain a numerical understanding of the possible room for improvement in costs using alternative strategies we also include numerical comparison with strategies that are conjectured to be optimal using this comparison we posit that there is more room for improvement in our lower bounds than in our upper bounds

why do block length and delay behave differently if feedback is present for output symmetric discrete memoryless channels dmcs at even moderately high rates fixed block length communication systems show no improvements in their error exponents with feedback this paper studies systems with fixed end to end delay and shows that feedback generally provides dramatic gains in the error exponents a new upper bound the uncertainty focusing bound is given on the probability of symbol error in a fixed delay communication system with feedback this bound turns out to have a form similar to viterbi s bound used for the block error probability of convolutional codes as a function of the fixed constraint length the uncertainty focusing bound is shown to be asymptotically achievable with noiseless feedback for erasure channels as well as for any output symmetric dmc that has strictly positive zero error capacity furthermore it can be achieved in a delay universal anytime fashion even if the feedback itself is delayed by a small amount finally it is shown that for end to end delay it is generally possible at high rates to beat the sphere packing bound for general dmcs thereby providing a counterexample to a conjecture of pinsker

the mixed order bcgs fft method for the scattering of three dimensional inhomogeneous anisotropic magnetodielectric objects this paper presents the first fft based fast volume integral equation solver for inhomogeneous anisotropic magnetodielectric objects the volume integral equations are formulated by employing mixed order basis functions that expand the flux densities and vector potentials in the coupled field integral equations in terms of different sets of basis functions with different orders volumetric roof top basis functions are used for flux densities whereas second order curl conforming basis functions are used for vector potentials a fast volume integral equations solver namely the bcgs fft method is then applied to accelerate the solution of this mixed order weak form formulation examples show that the mixed order bcgs fft method has high accuracy compared to both analytical and numerical solutions examples also show the mixed order bcgs fft method has high computational efficiency compared to commercial software

fast periodic interpolation method for periodic unit cell problems a fast periodic interpolation method fpim is presented for rapidly computing fields in a unit cell of an infinitely periodic array for low and moderate frequencies for unit cells smaller than or on the order of the wavelength the fpim has the computational cost of o n and it requires only o 1 periodic green s function pgf evaluations for n sources and observers for higher mixed frequencies the computational cost scales as o d 3 log d n where d is the domain size within the unit cell and is the wavelength fpim is based on splitting the field into the near field from the sources around the unit cell and the far field from the remaining sources the near field component can be evaluated rapidly using any available fast method the far field component is computed by tabulating the pgf at sparse source and observer grids using this table to calculate the field at the observation grid and interpolating from the observation grid to the actual observers the fpim is kernel independent and allows using any method for evaluating the pgf including simple floquet expansions the computational times can be comparable to those of conventional non periodic n body electromagnetic problems the presented method can be used to accelerate integral equations for periodic unit cell problems with many applications in microwave engineering and optics

exact moderate deviation asymptotics in streaming data transmission in this paper a streaming transmission setup is considered where an encoder observes a new message in the beginning of each block and a decoder sequentially decodes each message after a delay of t blocks in this streaming setup the fundamental interplay between the coding rate the error probability and the blocklength in the moderate deviations regime is studied for output symmetric channels the moderate deviations constant is shown to improve over the block coding or non streaming setup by exactly a factor of t for a certain range of moderate deviations scalings for the converse proof a more powerful decoder to which some extra information is fedforward is assumed the error probability is bounded first for an auxiliary channel and this result is translated back to the original channel by using a newly developed change of measure lemma where the speed of decay of the remainder term in the exponent is carefully characterized for the achievability proof a known coding technique that involves a joint encoding and decoding of fresh and past messages is applied with some manipulations in the error analysis

composite scheme lr th for decoding with erasures and its effective equivalence to forney s rule for decoding with erasures forney s scheme is known to be optimal in the sense that no other scheme can make the erasure probability p sub ers and undetected error probability p sub uer simultaneously smaller we propose a scheme for erasure decision which tests the likelihood ratio as well as the likelihood itself and show that the attainable upper bounds on p sub ers and p sub uer are the same as those proved for the optimal scheme up to a constant factor we also show that the scheme gives when applied to convolutional codes a bound which is related to the block coding bound via forney s inverse concatenation construction we show that this bound is the same as the one which naturally arises when we apply raghavan and baum s 1998 optimal scheme to convolutional code

uniform asymptotic stability of abstract functional differential equations abstract this paper considers a class of abstract functional differential equations by using razumikhin technique we establish several stability criteria in terms of two measures which improve some earlier results found in the literature several examples are also worked out to demonstrate the advantages of our results

loop tree implementation of the adaptive integral method aim for numerically stable broadband fast electromagnetic modeling the adaptive integral method aim is implemented in conjunction with the loop tree lt decomposition of the electric current density in the method of moments approximation of the electric field integral equation the representation of the unknown currents in terms of its solenoidal and irrotational components allows for accurate broadband electromagnetic em simulation without low frequency numerical instability problems while scaling of computational complexity and memory storage with the size of the problem are of the same order as in the conventional aim algorithm the proposed algorithm is built as an extension to the conventional aim formulation that utilizes roof top expansion functions thus providing direct and easy way for the development of the new stable formulation when the roof top based aim is available a new preconditioning strategy utilizing near interactions in the system which are typically available in the implementation of fast solvers is proposed and tested the discussed preconditioner can be used with both roof top and lt formulations of aim and other fast algorithms the resulting aim implementation is validated through its application to the broadband em analysis of large microstrip antennas and planar interconnect structures

performance bounds for erasure list and decision feedback schemes with linear block codes a message independence property and some new performance upper bounds are derived in this work for erasure list and decision feedback schemes with linear block codes transmitted over memoryless symmetric channels similar to the classical work of forney this work is focused on the derivation of some gallager type bounds on the achievable tradeoffs for these coding schemes where the main novelty is the suitability of the bounds for both random and structured linear block codes or code ensembles the bounds are applicable to finite length codes and to the asymptotic case of infinite block length and they are applied to low density parity check code ensembles

a fast full wave analysis of scattering and radiation from large finite arrays of microstrip antennas a fast full wave analysis technique that can be used to analyze the scattering and radiation from large finite arrays of microstrip antennas is presented the technique discretizes the mixed potential integral equation mpie in the spatial domain by means of a full wave discrete complex image method the del operators on the green s functions are transferred from the singular kernel to the expansion and testing functions the resultant system of equations is solved using the biconjugate gradient bcg method in which the matrix vector product is evaluated efficiently using the fast fourier transform fft this results in an efficient and accurate computation of the scattering and radiation from finite arrays of microstrip antennas several numerical results are presented demonstrating the accuracy efficiency and capability of this technique

recurrent multiple repetition coding for channels with feedback we consider multiple repetition strategies with fixed delay decoding for discrete memoryless channels with noiseless feedback existing binary schemes by schalkwijk and zigangirov are analyzed and their results are extended the general error exponents are computed and presented by elegant expressions in the strictly symmetric case an important class of precoded sequences so called flip sequences is found and their degrading effect on the error exponent is investigated this effect is shown negligible when the repetition parameters are chosen such that the transmission rate is maximized even when signalling at channel capacity the error exponent is shown to be strictly positive

scattering by cavity backed antennas on a circular cylinder conformal arrays are popular antennas for aircraft spacecraft and land vehicle platforms due to their inherent low weight drag and observables however to date there has been a dearth of rigorous analytical or numerical solutions to aid the designer in fact it has been common practice to use limited measurements and planar approximations in designing such nonplanar antennas we extend the finite element boundary integral method to scattering by cavity backed structures in an infinite metallic cylinder in particular we discuss the formulation specifics such as weight functions dyadic green s function implementation details and particular difficulties inherent to cylindrical structures special care is taken to ensure that the resulting computer program has low memory demand and minimal computational requirements scattering results are presented and validated as much as possible

functional differential equations and jensen s inequality on etudie les proprietes de stabilite et de limitation de l equation differentielle fonctionnelle x t f t x t ou x t s x t s pour h s 0 et h une constante positive fixee on utilise la methode de lyapunov directe

anytime characteristics of protograph based ldpc convolutional codes anytime transmission has been shown to be an effective means of stabilizing an unstable system over noisy channels a crucial issue in implementing anytime transmission strategies is the design of anytime codes that offer good finite length performance and asymptotic anytime properties this paper introduces an efficient anytime code derived from protograph based low density parity check convolutional codes known as extended s ldpcc xs ldpcc codes the asymptotic anytime properties of xs ldpcc codes over both the binary erasure channel bec and the binary input additive white gaussian noise biawgn channel are demonstrated through density evolution by means of certain observations verified by simulations we provide accurate estimates of the delay exponents of xs ldpcc codes over the bec and the biawgn channel through simulations the finite length performance of xs ldpcc codes and the effects of different code design parameters are quantified

curl conforming hierarchical vector bases for triangles and tetrahedra a new family of hierarchical vector bases is proposed for triangles and tetrahedra these functions span the curl conforming reduced gradient spaces of nedelec the bases are constructed from orthogonal scalar polynomials to enhance their linear independence which is a simpler process than an orthogonalization applied to the final vector functions specific functions are tabulated to order 6 5 preliminary results confirm that the new bases produce reasonably well conditioned matrices

the error exponent of variable length codes over markov channels with feedback the error exponent of markov channels with feedback is studied in the variable length block coding setting burnashev s classic result is extended to finite state ergodic markov channels for these channels a single letter characterization of the reliability function is presented under the assumption of full causal output feedback and full causal observation of the channel state both at the transmitter and at the receiver side tools from stochastic control theory are used in order to treat channels with intersymbol interference isi specifically the convex analytic approach to markov decision processes is adopted in order to handle problems with stopping time horizons induced by variable length coding schemes

scalar estimation and control with noisy binary observations we consider a simple one dimensional system whose observations are sent to a state estimator over a noisy binary communication link the interesting thing about the system is that it is unstable the problem is to design an encoding scheme and a decoder such that the estimation error is stable we explicitly construct a simple but efficient estimator for the binary symmetric channel bsc we are not aware of any such previous codes for the bsc we compare our results to the nonconstructive bounds of sahai

variations on a theme by schalkwijk and kailath schalkwijk and kailath 1966 developed a class of block codes for gaussian channels with ideal feedback for which the probability of decoding error decreases as a second order exponent in block length for rates below capacity this well known but surprising result is explained and simply derived here in terms of a result by elias 1956 concerning the minimum mean square distortion achievable in transmitting a single gaussian random variable over multiple uses of the same gaussian channel a simple modification of the schalkwijk kailath scheme is then shown to have an error probability that decreases with an exponential order which is linearly increasing with block length in the infinite bandwidth limit this scheme produces zero error probability using bounded expected energy at all rates below capacity a lower bound on error probability for the finite bandwidth case is then derived in which the error probability decreases with an exponential order which is linearly increasing in block length at the same rate as the upper bound

the biconjugate gradient method for electromagnetic scattering the biconjugate gradient bcg method for solving linear systems is shown to be more efficient than the conjugate gradient cg method for several examples from electromagnetic scattering a remedy for the occasional stagnation of the algorithm is proposed the potential flaw in the bcg algorithm may be avoided when encountered by restarting the algorithm with a perturbed estimate of the solution

a helmholtz stable fast solution of the electric field integral equation a new fast matrix vector multiplication scheme for the solution of the electric field integral equation is presented in this work similarly to other fast methods our approach reduces the matrix vector multiplication cost from o n2 to o n logn differently from other fast solvers however the effectiveness of efie preconditioning techniques such as quasi helmholtz decompositions or calderon approaches is maintained by our method even for very high matrix compression rates this is thanks to the fact that in the scheme we are proposing the contribution from the scalar potential when applied to or tested with solenoidal functions is always zero independent of the compression error in addition the new method will take advantage of the redundancies of the efie matrix in the low frequency dense discretization regime and it will further decrease both the memory storage and the multiplication cost with respect to currently available fast solvers numerical results will show the effectiveness of our approach and its impact on the solution of realistic problems

characteristic basis function method for solving electromagnetic scattering problems over rough terrain profiles a computationally efficient algorithm which combines the characteristic basis function method cbfm the physical optics po approach when applicable with the forward backward method fbm is applied for the investigation of electromagnetic scattering from and propagation over large scale rough terrain problems the algorithm utilizes high level basis functions defined on macro domains blocks called the characteristic basis functions cbfs that are constructed by aggregating low level basis functions i e conventional sub domain basis functions the fbm as well as the po approach when applicable are used to construct the aforementioned cbfs the conventional cbfm is slightly modified to handle large terrain problems and is further embellished by accelerating it as well as reducing its storage requirements via the use of an extrapolation procedure numerical results for the total fields as well as for the path loss are presented and compared with either measured or previously published reference solutions to assess the efficiency and accuracy of the algorithm

rcs computation of large inhomogeneous objects using a fast integral equation solver in this paper we apply a fast fourier transform fft accelerated volume integral equation solver to compute the radar cross section of large scale inhomogeneous objects this method is related to bojarski s k space method and the subsequent conjugate cg and biconjugate gradient bcg fft algorithms the method developed here combines the weak form discretization with the bcg and stabilized bcg bcgs solvers we show that this method has marked improvements over related algorithms the numerical method has been validated by mie series for multilayer spheres and applied to some practical problems with this method we are currently able to solve a three dimensional problem with a volume of size 3648 spl lambda sup 3 21 23 million unknowns on a single workstation

real time coding with limited lookahead a real time coding system with lookahead consists of a memoryless source a memoryless channel an encoder which encodes the source symbols sequentially with knowledge of future source symbols up to a fixed finite lookahead d with or without feedback of the past channel output symbols and a decoder which sequentially constructs the source symbols using the channel output the objective is to minimize the expected per symbol distortion for a fixed finite lookahead d 1 we invoke the theory of controlled markov chains to obtain an average cost optimality equation acoe the solution of which denoted by d d is the minimum expected per symbol distortion with increasing d d d bridges the gap between causal encoding d 0 where symbol by symbol encoding decoding is optimal and the infinite lookahead case d where shannon theoretic arguments show that separation is optimal we extend the analysis to a system with finite state decoders with or without noise free feedback for a bernoulli source and binary symmetric channel under hamming loss we compute the optimal distortion for various source and channel parameters and thus obtain computable bounds on d d we also identify regions of source and channel parameters where symbol by symbol encoding decoding is suboptimal finally we demonstrate the wide applicability of our approach by applying it in additional coding scenarios such as the case where the sequential decoder can take cost constrained actions affecting the quality or availability of side information about the source

performance of viterbi decoding with and without arq on rician fading channels in this paper we investigate the performance of the viterbi decoding algorithm with without automatic repeat request arq over a rician flat fading channel with unlimited interleaving we show that the decay rate of the average bit error probability with respect to the bit energy to noise ratio is at least equal to d f at high bit energy to noise ratio for both cases with arq and without arq where d f is the free distance of the convolutional code the yamamoto itoh flag helps to reduce the average bit error probability by a factor of 4 d f with a negligible retransmission rate we also prove an interesting result that the average bit error probability decays exponentially fast with respect to the rician factor for any fixed bit energy per noise ratio in addition the average bit error exponent with respect to the rician factor is shown to be d f

on haroutunian s exponent for parallel channels and an application to fixed delay codes without feedback the haroutunian exponent arises in the study of channel reliability functions for both block coding with feedback and fixed delay coding without feedback for asymmetric channels such as the z channel the haroutunian exponent is strictly larger than the sphere packing exponent the spherepacking exponent is believed to be an upper bound for the reliability function in the two aforementioned communication problems but in attempting to prove this one gets stuck at the haroutunian exponent because of entanglements between the channel behavior and the input distribution in this paper we present a characteristic of the haroutunian exponent that differentiates it from the random coding and sphere packing exponents we consider the parallel channel the repeated use of the original discrete memoryless channel independently some number of times it is well known that the capacity of the parallel channel is l times the capacity of the original channel and the random coding and sphere packing exponents of the l use parallel channel decompose into l times the exponents of the original channel the main result of this paper is to show that the appropriately normalized haroutunian exponent of the parallel channel asymptotically decomposes to the sphere packing exponent of the original channel as opposed to the haroutunian exponent of the original channel this fact is then used to prove two results first an upper bound for the reliability function for fixed blocklength coding with delayed feedback is proved this upper bound converges to the sphere packing exponent as the delay in the feedback path tends to infinity second the reliability function for fixed delay coding without feedback is shown to be upper bounded by the sphere packing exponent

exact relationship between the locally corrected nystrom scheme and rwg moment method for the mixed potential integral equation the exact relationship between the rao wilton glisson rwg method of moments mom and the locally corrected nystrom lcn method for the mixed potential mp electric field integral equation efie is presented as an extension to our work where we established analogous exact relationship for solving the efie in its vector potential vp form it is shown that in order to achieve one such relationship for the mp efie the first and zeroth order lcn methods must be respectively used for the discretization of the vp and scalar potential terms of the mp efie the resulting numerical scheme is a point based rwg mom discretization of the mp efie via the nystrom method due to the mp formulation of the efie the proposed method establishes notably higher accuracy compared to either rwg mom or lcn discretizations of the efie in the vp form the increased accuracy is attributed to the analytical cancellation of the line charge contributions in the mp formulation as opposed to numerical cancellation inherent in the vp formulation of the efie the detailed study and explanations of the above cancellations is presented along with their impact on the accuracy of the respective schemes for both canonical and realistic scattering targets at different frequencies

simultaneous microwave imaging and parameter estimation using modified level set method a modified level set method mlsm is proposed to simultaneously reconstruct the shape and electrical properties of 2 d objects as a numerical technique the formal level set method lsm can retrieve the shape and position of objects using synthetic measurement data in general the constitutive parameters of an object e g its relative complex permittivity are among the a priori information needed for the lsm for mlsm an evolution strategy is proposed to simultaneously calculate both the shape and complex permittivity of a 2 d object the initial guesses in respect of the complex permittivity and shape of the target object converge on their real values as the cost function is minimized the cost function is regularized with two penalty terms to prevent sudden change in the shape of the object a curvature based regularization is used also laplacian regularizer is used to reduce fluctuations in the object s constitutive parameters during the process using different synthetic data sets the capabilities of mlsm in microwave imaging and parameter estimation are evaluated it is found that using mlsm it is possible to completely separate two adjacent objects separated by a distance of one fifteenth of a wavelength the proposed method can retrieve targets of different relative permittivities with less than 10 error one interesting feature of this method is its high fidelity in retrieving the immersed one tenth wavelength targets in highly contrasting up to as high as 8 1 domains in the case of targets with little contrast 10 the proposed method with more iterations can converge on a value which is 57 more than the actual value these features are valuable in distinguishing malignant tissue from normal tissue

rateless codes for avc models the arbitrarily varying channel avc is a channel model whose state is selected maliciously by an adversary fixed blocklength coding assumes a worst case bound on the adversary s capabilities which leads to pessimistic results this paper defines a variable length perspective on this problem for which achievable rates are shown that depend on the realized actions of the adversary specifically rateless codes are constructed which require a limited amount of common randomness these codes are constructed for two kinds of avc models in the first the channel state cannot depend on the channel input and in the second it can as a by product the randomized coding capacity of the avc with state depending on the transmitted codeword is found and shown to be achievable with a small amount of common randomness the results for this model are proved using a randomized strategy based on list decoding

the streaming dmt of fading channels we study sequential transmission of a stream of messages over a block fading multi input multi output mimo channel a new message arrives in each coherence block and the decoder is required to output each message after a delay of t coherence blocks we establish the optimal diversity multiplexing tradeoff dmt and show that it can be achieved using a simple interleaving of messages the converse is based on an outage amplification technique which appears to be new we also discuss another coding scheme based on a sequential tree code this coding scheme only requires the knowledge of delay at the decoder and yet realizes the optimal dmt we finally discuss some extensions when multiple messages at uniform intervals arrive within each coherence period

lossless coding for distributed streaming sources distributed source coding is traditionally viewed in a block coding context wherein all source symbols are known in advance by the encoders however many modern applications to which distributed source coding ideas are applied are better modeled as having streaming data in a streaming setting source symbol pairs are revealed to separate encoders in real time and need to be reconstructed at the decoder with subject to some tolerable end to end delay in this paper a causal sequential random binning encoder is introduced and paired with maximum likelihood ml and universal decoders the latter uses a novel weighted empirical suffix entropy decoding rule we derive a lower bounds on the error exponent with delay for each decoder we also provide upper bounds for the special case of streaming with decoder side information and discuss when upper and lower bounds match we show that both ml and universal decoders achieve the same positive error exponents for all rate pairs inside the slepian wolf achievable rate region the dominant error events in streaming are different from those in block coding and result in different exponents because the sequential random binning scheme is also universal over delays the resulting code eventually reconstructs every source symbol correctly with probability one

minimax universal decoding with an erasure option motivated by applications of rateless coding decision feedback and automatic repeat request arq we study the problem of universal decoding for unknown channels in the presence of an erasure option specifically we harness the competitive minimax methodology developed in earlier studies in order to derive a universal version of forney s classical erasure list decoder which in the erasure case optimally trades off between the probability of erasure and the probability of undetected error the proposed universal erasure decoder guarantees universal achievability of a certain fraction xi of the optimum error exponents of these probabilities in a sense to be made precise in the sequel a single letter expression for xi which depends solely on the coding rate and the neyman pearson threshold to be defined is provided the example of the binary symmetric channel is studied in full detail and some conclusions are drawn

on gaussian macs with variable length feedback and non vanishing error probabilities we characterize the fundamental limits of transmission of information over a gaussian multiple access channel mac with the use of variable length feedback codes and under a non vanishing error probability formalism we develop new achievability and converse techniques to handle the continuous nature of the channel and the presence of expected power constraints we establish the varepsilon capacity regions and bounds on the second order asymptotics of the gaussian mac with variable length feedback with termination codes and stop feedback codes we show that the former outperforms the latter significantly due to the multi terminal nature of the channel model we leverage tools from renewal theory developed by lai and siegmund to bound the asymptotic behavior of the maximum of a finite number of stopping times

feedback in the non asymptotic regime without feedback the backoff from capacity due to non asymptotic blocklength can be quite substantial for blocklengths and error probabilities of interest in many practical applications in this paper novel achievability bounds are used to demonstrate that in the non asymptotic regime the maximal achievable rate improves dramatically thanks to variable length coding and feedback for example for the binary symmetric channel with capacity 1 2 the blocklength required to achieve 90 of the capacity is smaller than 200 compared to at least 3100 for the best fixed blocklength code even with noiseless feedback virtually all the advantages of noiseless feedback are shown to be achievable even if the feedback link is used only to send a single signal informing the encoder to terminate the transmission stop feedback it is demonstrated that the non asymptotic behavior of the fundamental limit depends crucially on the particular model chosen for the end of packet control signal fixed blocklength codes and related questions concerning communicating with a guaranteed delay are discussed in which situation feedback is demonstrated to be almost useless even non asymptotically

on iterative approaches for electromagnetic rough surface scattering problems iterative techniques developed for solving general systems of linear equations have been applied to systems resulting from electromagnetic rough surface scattering problems previously used iterative procedures that model the multiple scattering of the electromagnetic energy are shown to be mathematically equivalent to the application of stationary iterative procedures to the system of equations resulting from the standard moment method convergence difficulties that are sometimes observed with these approaches are due to the inherent limitations of the stationary techniques the performances of the stationary approaches are compared with that of several conjugate direction based nonstationary iterative procedures through the application to a series of scattering surfaces that yield rapidly changing conditioning of the moment method interaction matrix the stationary algorithms give the quickest convergence when applied to the systems with the best conditioning but the nonstationary techniques prove much more robust in other more ill conditioned situations

nonparametric threshold decision rule coverings and some consequences threshold decision is a decision rule for errors and erasures decoding such that the decoder accepts the decoded codeword if its likelihood is larger than a given threshold value this decision rule involves a parameter that needs to be optimized we propose a nonparametric version of threshold decision and show that this nonparametric threshold decision allows us to extend some results on decision rules known only for restricted cases the relationship between the threshold decision and the rule based on error detection coding and the attainability of forney s 1968 1981 exponent by the likelihood ratio test these results are derived from a covering theorem which is closely related to the nonparametric threshold decision

error exponents of erasure list decoding revisited via moments of distance enumerators the analysis of random coding error exponents pertaining to erasure list decoding due to forney is revisited instead of using jensen s inequality as well as some other inequalities in the derivation we demonstrate that an exponentially tight analysis can be carried out by assessing the relevant moments of certain distance enumerators the resulting bound has the following advantages i it is at least as tight as forney s bound ii under certain symmetry conditions associated with the channel and the random coding distribution it is simpler than forney s bound in the sense that it involves an optimization over one parameter only rather than two and iii in certain special cases like the binary symmetric channel bsc the optimum value of this parameter can be found in closed form and so there is no need to conduct a numerical search we have not found yet a numerical example where this new bound is strictly better than forney s bound and this may provide an additional evidence to support forney s conjecture that his bound is tight for the average code however when applying the proposed analysis technique to a certain universal decoder with erasures we demonstrate that it may yield significantly tighter exponential error bounds we believe that this technique can be useful in simplifying and improving exponential error bounds in other problem settings as well

numerical accuracy of multipole expansion for 2d mlfma a numerical study of the multipole expansion for the multilevel fast multipole algorithm mlfma is presented in the numerical implementation of mlfma the error comes from three sources the truncation of the addition theorem the approximation of the integration the aggregation and disaggregation process these errors are due to the factorization of the green s function which is the mathematical core of the algorithm among the three error sources we focus on the truncation error and a new approach of selecting truncation numbers for the addition theorem is proposed using this approach the error prediction and control can be improved for the small buffer sizes and high accuracy requirements

on stability in terms of two measures for impulsive systems of functional differential equations this paper considers the stability problem for a class of impulsive systems of functional differential equations by using lyapunov functions and the razumikhin technique several stability criteria in terms of two measures are established some examples are worked out to illustrate the theorems

evaluating the performance of convolutional codes over block fading channels this correspondence considers union upper bound techniques for error control codes with limited interleaving over block fading rician channels a modified bounding technique is presented that relies on limiting the conditional union bound before averaging over the fading process this technique although analytically not very attractive provides tight and hence useful numerical results

on the error exponent of convolutionally coded arq forney s 1968 exponent is effectively the best one for the block coded automatic repeat request systems arq and it has been conjectured that a counterpart of forney s exponent is attainable by convolutional codes with reasonable decoder complexity in the paper it is show that the scheme of yamamoto and itoh 1980 which is known to be one of the simplest convolutionally coded arq schemes actually gives a better performance than ever expected and that it has an error exponent quite close to the conjectured counterpart of forney s exponent at relatively low rates it is further shown that the likelihood ratio test used by yamamoto and itoh gives forney s exponent in the case of block coded arq

exact random coding exponents for erasure decoding random coding of channel decoding with an erasure option is studied by analyzing the large deviations behavior of the code ensemble we obtain exact single letter formulas for the error exponents in lieu of forney s lower bounds the analysis technique we use is based on an enhancement and specialization of tools for assessing the statistical properties of certain distance enumerators we specialize our results to the setup of the binary symmetric channel case with uniform random coding distribution and derive an explicit expression for the error exponent which unlike forney s bounds does not involve optimization over two parameters we also establish the fact that for this setup the difference between the exact error exponent corresponding to the probability of undetected decoding error and the exponent corresponding to the erasure event is equal to the threshold parameter numerical calculations indicate that for this setup as well as for a z channel forney s bound coincides with the exact random coding exponent

a simple class of capacity achieving strategies for discrete memoryless channels with feedback a class of multiple repetition strategies is presented for discrete memoryless channels with noiseless feedback this extends results obtained by schalkwijk 1971 to nonbinary asymmetric memoryless channels an interesting characterization of the attainability of a rate is presented in terms of a generating polynomial from which follows that for each strategy in our class there exists a discrete memoryless channel such that capacity can be achieved on this channel

channel combining and splitting for cutoff rate improvement the cutoff rate r0 w of a discrete memoryless channel dmc w is often used as a figure of merit alongside the channel capacity c w if a channel w is split into two possibly correlated subchannels w1 w2 the capacity function always satisfies c w1 c w2 lesc w while there are examples for which r0 w1 r0 w2 r0 w the fact that cutoff rate can be created by channel splitting was noticed by massey in his study of an optical modulation system this paper gives a general framework for achieving similar gains in the cutoff rate of arbitrary dmcs by methods of channel combining and splitting the emphasis is on simple schemes that can be implemented in practice we give several examples that achieve significant gains in cutoff rate at little extra system complexity theoretically as the complexity grows without bound the proposed framework is capable of boosting the cutoff rate of a channel to arbitrarily close to its capacity in a sense made precise in the paper apart from massey s work the methods studied here have elements in common with forney s concatenated coding idea a method by pinsker for cutoff rate improvement and certain coded modulation techniques namely ungerboeck s set partitioning idea and imai hirakawa multilevel coding these connections are discussed in the paper

two level tabulated interaction method for electromagnetic scattering from lossy irregular terrain profiles incorporating back scattering an efficient method is proposed for computing electromagnetic wave propagation over lossy terrain profiles using a coupled surface integral equation formulation the proposed method uses a set of basis functions which can produce a linear system with much fewer unknowns than that created using pulse basis functions in addition the matrix entries can be computed very rapidly using precomputed tabulated values the method improves upon the original tabulated interaction method tim by extending it to lossy profiles allowing for back scatter and by introducing increased accuracy for near field interactions the complexity and numerical analysis demonstrates that the proposed method has an extremely low computational complexity and storage requirement moreover the accuracy of the proposed method is demonstrated by comparing the pathloss against numerically precise solutions and measured data

lanczos type variants of the cocr method for complex nonsymmetric linear systems motivated by the celebrated extending applications of the well established complex biconjugate gradient cbicg method to deal with large three dimensional electromagnetic scattering problems by pocock and walker m d pocock s p walker the complex bi conjugate gradient solver applied to large electromagnetic scattering problems computational costs and cost scalings ieee trans antennas propagat 45 1997 140 146 three lanczos type variants of the recent conjugate a orthogonal conjugate residual cocr method of sogabe and zhang t sogabe s l zhang a cocr method for solving complex symmetric linear systems j comput appl math 199 2007 297 303 are explored for the solution of complex nonsymmetric linear systems the first two can be respectively considered as mathematically equivalent but numerically improved popularizing versions of the bicr and crs methods for complex systems presented in sogabe s ph d dissertation and the last one is somewhat new and is a stabilized and more smoothly converging variant of the first two in some circumstances the presented algorithms are with the hope of obtaining smoother and hopefully faster convergence behavior in comparison with the cbicg method as well as its two corresponding variants this motivation is demonstrated by numerical experiments performed on some selective matrices borrowed from the university of florida sparse matrix collection by davis

fast iterative coding techniques for feedback channels a class of capacity achieving low complexity high reliability variable rate coding schemes is developed for communication over discrete memoryless channels with noiseless feedback algorithms for encoding and decoding that require computations growing linearly with the number of channel inputs used are developed the error exponent associated with the scheme is shown to be optimal and implies that capacity is achievable simulations are performed and support the analytically predicted high performance and low complexity

a conjugate gradient based algorithm to minimize the sidelobe level of planar arrays with element failures element failures increase the sidelobe power level of an array reconfiguring the amplitude and phase distribution of the remaining elements can partially compensate for the failed elements and thus reduce the sidelobe level an algorithm is obtained that yields the reconfigured distribution by minimizing the ratio of the average peak sidelobe power level to the power in the main beam taking into account the defective elements the minimization of this nonlinear function is carried out via a conjugate gradient method the algorithm is applied to the synthesis of sum and difference patterns of planar arrays

an improvement of soft decision maximum likelihood decoding algorithm using hard decision bounded distance decoding a new soft decision maximum likelihood decoding algorithm is proposed which generates a set of candidate codewords using hard decision bounded distance decoding by improving the generating method of input vectors for the bounded distance decoding due to kaneko et al see ibid vol 40 no 3 p 320 27 1994 the decoding time complexity is reduced without degradation of the performance the space complexity is dependent on the bounded distance decoding

a surface integral formulation of maxwell equations for topologically complex conducting domains a general and effective method is presented to numerically solve the electric field integral equation efie for topologically complex conducting domains by the finite element method a new technique is proposed to decompose the surface current density into a solenoidal part and a nonsolenoidal remainder to avoid the low frequency breakdown the surface current density field is approximated through div conforming facet elements the solenoidal part is represented through the null space of the discrete approximation d of the surface divergence operator in the subspace spanned by the facet elements whereas the nonsolenoidal remainder is represented through its complement the basis functions of the null space and its complement are evaluated respectively by the null and pseudo inverse of the matrix d the completeness of the null pinv basis functions is studied unlike the loop star and loop tree basis functions the null pinv basis functions allow to deal with topologically complex conducting domains in a general and readily applicable way a topological interpretation of the null pinv decomposition is given and a general and simple method to evaluate the null and pseudo inverse of d is proposed the computational complexity of the proposed method is discussed

converse theorems for the dmc with mismatched decoding the problem of mismatched decoding with an additive bounded metric q for a discrete memoryless channel w is addressed we study two kinds of decoders the delta margin mismatched decoder outputs a message whose metric with the channel output exceeds that of all the other codewords by at least delta the tau threshold decoder outputs a single message whose metric with the channel output exceeds a threshold tau it is proved that the mismatch capacity with a constant margin decoder is equal to the product space improvement of the random coding lower bound on the mismatch capacity c q infty w which was introduced by csiszar and narayan we next consider sequences of p constant composition codebooks using the central limit theorem it is shown that for such sequences of codebooks the supremum of achievable rates with constant threshold decoding is upper bounded by the supremum of the achievable rates with a constant margin decoder and therefore also by c q infty w further a soft converse is proved stating that if the average probability of error of a sequence of codebooks with ordinary mismatched decoding converges to zero sufficiently fast the rate of the code sequence is upper bounded by c q infty w in particular if q is a bounded rational metric and the average probability of error converges to zero faster than o n 1 then r leq c q infty w finally a max min multi letter upper bound on the mismatch capacity that bears some resemblance to c q infty w is presented

coded diversity on block fading channels this paper considers coded diversity schemes over block fading rician channels using random coding techniques two random coding upper bounds on the error probability of block codes are derived a new bound and a simpler but looser bound assuming binary input distribution also a new lower bound for any block code is derived using the strong converse to channel coding theorem the lower bound shows that the new random coding upper bound is quite tight furthermore it is shown that the maximum achievable diversity order in a block fading channel with finite interleaving depends not only on the number of subchannels l but also on the code rate r and that the performance can only marginally be improved by increasing the block length of the code the random coding upper bound and the lower bound are shown to converge to the capacity outage for large channel block lengths n demonstrating that the capacity outage can be used for estimating the error probability of coded diversity schemes

a hierarchical fast solver for efie mom analysis of multiscale structures at very low frequencies we present an efie fast solver that is stable down to very low frequencies for very dense meshes and multi scale problems the proposed approach uses a split potentials formulation in association to a hierarchic pre conditioner for the underlying low rank fast factorization potential splitting prevents the numerical cancellation problem that undermines the effectiveness of the low rank factorization negatively impacting on the necessary factorization tolerance the fast method presented in this work can be directly implemented into existing codes

achievable moderate deviations asymptotics for streaming compression of correlated sources motivated by streaming multi view video coding and wireless sensor networks we consider the problem of blockwise streaming compression of a pair of correlated sources which we term streaming slepian wolf coding we study the moderate deviations regime in which the rate pairs of a sequence of codes converge along a straight line to various points on the boundary of the slepian wolf region at a speed slower than the inverse square root of the blocklength n while the error probability decays subexponentially fast in n our main result focuses on the directions of approaches to corner points of the slepian wolf region it states that for each correlated source and all corner points there exists a non empty subset of directions of approaches such that the moderate deviations constant the constant of proportionality for the subexponential decay of the error probability is enhanced over the non streaming case by at least a factor of t the block delay of decoding source block pairs we specialize our main result to the setting of streaming lossless source coding and generalize this result to the setting where we have different delay requirements for each of the two source blocks the proof of our main result involves the use of various analytical tools and amalgamates several ideas from the recent information theoretic streaming literature we adapt the so called truncated memory encoding idea from draper and khisti 2011 and lee tan and khisti 2016 to ensure that the effect of error accumulation is nullified in the limit of large block lengths we also adapt the use of the so called minimum weighted empirical suffix entropy decoder which was used by draper chang and sahai 2014 to derive achievable error exponents for symbolwise streaming slepian wolf coding

reliability output decoding of tail biting convolutional codes we present extensions to raghavan and baum s reliability output viterbi algorithm rova to accommodate tail biting convolutional codes these tail biting reliability output algorithms compute the exact word error probability of the decoded codeword after first calculating the posterior probability of the decoded tail biting codeword s starting state one approach employs a state estimation algorithm that selects the maximum a posteriori state based on the posterior distribution of the starting states another approach is an approximation to the exact tail biting rova that estimates the word error probability a comparison of the computational complexity of each approach is discussed in detail the presented reliability output algorithms apply to both feedforward and feedback tail biting convolutional encoders these tail biting reliability output algorithms are suitable for use in reliability based retransmission schemes with short blocklengths in which terminated convolutional codes would introduce rate loss

the awgn red alert problem consider the following unequal error protection scenario one special message dubbed the red alert message is required to have an extremely small probability of missed detection the remainder of the messages must keep their average probability of error and probability of false alarm below a certain threshold the goal then is to design a codebook that maximizes the error exponent of the red alert message while ensuring that the average probability of error and probability of false alarm go to zero as the blocklength goes to infinity this red alert exponent has previously been characterized for discrete memoryless channels this paper completely characterizes the optimal red alert exponent for additive white gaussian noise channels with block power constraints

equivalent conditions on stability of functional differential equations where x s x t s for h 0 and each 4 e c there is at least one solution x t 4 satisfying 1 on an interval to to a with value at t denoted by x t t 4 moreover if there is an h h and if ix t to d l h for all t 2 to for which x to 4 can be defined then tl co details may be found in 2 7 8 111 for example throughout this paper we work with wedges denoted by wi r r which are continuous strictly increasing and which satisfy wi 0 0 these wedges are related to properties of continuous scalar functionals called liapunov functionals v r x c r which are differentiated along solutions of 1 by the relation

the complex bi conjugate gradient solver applied to large electromagnetic scattering problems computational costs and cost scalings the complex bi conjugate gradient iterative method is applied to an isoparametric boundary integral equation formulation for frequency domain electromagnetic scattering problems it is demonstrated to work well on large and geometrically complex examples including a 20 wavelength slender dipole the nasa almond and a resonant cavity on such problems with asymmetric curvilinear irregular meshes and nontrivial geometries the number of iterations required seems to increase rather more than linearly with body size indicating an overall spl sim sixth power cost scaling this scaling is essentially as for direct methods but with costs still a small fraction of the direct approach a method is proposed for the selection of a termination condition designed to avoid seeking the approximate answer too precisely it typically permits a further halving of costs