design of capacity approaching irregular low density parity check codes we design low density parity check ldpc codes that perform at rates extremely close to the shannon capacity the codes are built from highly irregular bipartite graphs with carefully chosen degree patterns on both sides our theoretical analysis of the codes is based on the work of richardson and urbanke see ibid vol 47 no 2 p 599 618 2000 assuming that the underlying communication channel is symmetric we prove that the probability densities at the message nodes of the graph possess a certain symmetry using this symmetry property we then show that under the assumption of no cycles the message densities always converge as the number of iterations tends to infinity furthermore we prove a stability condition which implies an upper bound on the fraction of errors that a belief propagation decoder can correct when applied to a code induced from a bipartite graph with a given degree distribution our codes are found by optimizing the degree structure of the underlying graphs we develop several strategies to perform this optimization we also present some simulation results for the codes found which show that the performance of the codes is very close to the asymptotic theoretical 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

an effective mom solution with nested complex source beam method for electromagnetic scattering problems a nested complex source beam ncsb method based on octree structure is proposed to accelerate the method of moments mom solution for three dimensional 3 d electromagnetic scattering analysis at the finest level the far field contribution of each basis function is expressed with that of complex source beams csbs distributed on the equivalent sphere surface for every group furthermore the far field radiated by csbs of the source group at child level can be represented by that radiated by csbs of the source group at parent level similarly the received field of csbs for each observation group at the parent level can be expressed with that of csbs belong to their child level group an equivalent relationship of csbs between every two adjacent levels is built to obtain the nested equivalent process for ncsb method and only the csbs at the finest level have the direct association with the basis functions in their group the ncsb method is shown to be o nlogn computational complexity for both matrix vector product mvp time and memory storage by numerical examples with appropriate parameters and numerical results demonstrate the better efficiency of the proposed method than the current multilevel csb method

extremal channels of gallager s e_ 0 under the basic polarization transformations we study the extremality of the binary erasure channel and the binary symmetric channel for gallager s reliability function e0 of binary input discrete memoryless channels evaluated under the uniform input distribution from the aspect of channel polarization in particular we show that amongst all binary discrete memoryless channels of a given e0 value for a fixed 0 the binary erasure channel and the binary symmetric channel are extremal in the evolution of e0 under the one step polarization transformations

fast iterative solution of integral equations with method of moments and matrix decomposition algorithm singular value decomposition the multilevel matrix decomposition algorithm mlmda was originally developed by michielsen and boag for 2d tmz scattering problems and later implemented in 3d by rius et al the 3d mlmda was particularly efficient and accurate for piece wise planar objects such as printed antennas however for arbitrary 3d problems it was not as efficient as the multilevel fast multipole algorithm mlfma and the matrix compression error was too large for practical applications this paper will introduce some improvements in 3d mlmda like new placement of equivalent functions and svd postcompression the first is crucial to have a matrix compression error that converges to zero as the compressed matrix size increases as a result the new mda svd algorithm is comparable with the mlfma and the adaptive cross approximation aca in terms of computation time and memory requirements remarkably in high accuracy computations the mda svd approach obtains a matrix compression error one order of magnitude smaller than aca or mlfma in less computation time like the aca the mda svd algorithm can be implemented on top of an existing mom code with most commonly used green s functions but the mda svd is much more efficient in the analysis of planar or piece wise planar objects like printed antennas

extrinsic information transfer functions model and erasure channel properties extrinsic information transfer exit charts are a tool for predicting the convergence behavior of iterative processors for a variety of communication problems a model is introduced that applies to decoding problems including the iterative decoding of parallel concatenated turbo codes serially concatenated codes low density parity check ldpc codes and repeat accumulate ra codes exit functions are defined using the model and several properties of such functions are proved for erasure channels one property expresses the area under an exit function in terms of a conditional entropy a useful consequence of this result is that the design of capacity approaching codes reduces to a curve fitting problem for all the aforementioned codes a second property relates the exit function of a code to its helleseth klove levenshtein information functions and thereby to the support weights of its subcodes the relation is via a refinement of information functions called split information functions and via a refinement of support weights called split support weights split information functions are used to prove a third property that relates the exit function of a linear code to the exit function of its dual

on broadcast channels with binary inputs and symmetric outputs we establish capacity regions for some classes of broadcast channels with binary inputs and symmetric outputs we investigate the more capable partial order and establish that the binary erasure channel and the binary symmetric channel form the two extremes for channels having the same capacity further we apply the results to identify a class of broadcast channels for which the best known inner and outer bounds on the capacity region differ

nested equivalent source approximation for the modeling of penetrable bodies a multiregion nested equivalent source approximation nesa is presented for the fast analysis of electromagnetic scattering by piecewise homogeneous media nesa was introduced for the analysis of metallic problems at low and moderate frequencies and later extended to the fully dynamic case with the introduction of a directional scheme in this communication we modify the wideband scheme for the analysis of arbitrary penetrable media the asymptotic computational costs of the algorithm are compatible with the state of the art factorizations namely linear and quasi linear o n and o n log n for moderate and high frequency problems respectively numerical examples validate the accuracy and favorable computational cost of nesa when applied to penetrable bodies

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

bounds on information combining when the same data sequence is transmitted over two independent channels or when a data sequence is transmitted twice but independently over the same channel the independent observations can be combined at the receiver side from an information theory point of view the overall mutual information between the data sequence and the received sequences represents a combination of the mutual information of the two channels this concept is termed information combining a lower bound and an upper bound on the combined information is presented and it is proved that these bounds are tight furthermore this principle is extended to the computation of extrinsic information on single code bits for a repetition code and for a single parity check code of length three respectively for illustration of the concept and the bounds on information combining two applications are considered first bounds on the information processing characteristic ipc of a parallel concatenated code are derived from its extrinsic information transfer exit chart second bounds on the exit chart for an outer repetition code and for an outer single parity check code of a serially concatenated coding scheme are computed

extremes of error exponents this paper determines the range of feasible values of standard error exponents for binary input memoryless symmetric channels of fixed capacity c and shows that extremes are attained by the binary symmetric and the binary erasure channel the proof technique also provides analogous extremes for other quantities related to gallager s e0 function such as the cutoff rate the bhattacharyya parameter and the channel dispersion

extremes of information combining extreme densities for information combining are found for two important channel models the binary input symmetric parallel broadcast channel and the parity constrained input symmetric parallel channels following upper and lower mutual information thresholds are stated for per bit maximum a posteriori probability map decoding and low density parity check ldpc code ensembles

multilevel codes theoretical concepts and practical design rules this paper deals with 2 sup l ary transmission using multilevel coding mlc and multistage decoding msd the known result that mlc and msd suffice to approach capacity if the rates at each level are appropriately chosen is reviewed using multiuser information theory it is shown that there is a large space of rate combinations such that mlc and full maximum likelihood decoding mld can approach capacity it is noted that multilevel codes designed according to the traditional balanced distance rule tend to fall in the latter category and therefore require the huge complexity of mld the capacity rule the balanced distances rules and two other rules based on the random coding exponent and cutoff rate are compared and contrasted for practical design simulation results using multilevel binary turbo codes show that capacity can in fact be closely approached at high bandwidth efficiencies moreover topics relevant in practical applications such as signal set labeling dimensionality of the constituent constellation and hard decision decoding are emphasized bit interleaved coded modulation proposed by caire et al see ibid vol 44 p 927 46 1998 is reviewed in the context of mlc finally the combination of signal shaping and coding is discussed significant shaping gains are achievable in practice only if these design rules are taken into account

multilevel fast multipole algorithm based direct solution for analysis of electromagnetic problems in this communication a multilevel fast multipole algorithm mlfma based direct method is proposed for solving electromagnetic scattering problems that are formulated using the electric field integral equation efie approach the method is based on the multilevel compressed block decomposition mlcbd algorithm previously the matrix filling procedure of the mlcbd is based on the matrix decomposition algorithm singular value decomposition mda svd method although the mda svd is more efficient than direct filling it requires a longer filling time for the far field matrix than for the mlfma the problems are used to demonstrate that the matrix filling memory requirement of the mda svd is also higher than that of the mlfma hence the mlfma is utilized to reduce both the matrix filling time and memory of the mlcbd numerical results are presented to demonstrate the accuracy and efficiency of the proposed method

parity check density versus performance of binary linear block codes over memoryless symmetric channels we derive lower bounds on the density of parity check matrices of binary linear codes which are used over memoryless binary input output symmetric mbios channels the bounds are expressed in terms of the gap between the rate of these codes for which reliable communications is achievable and the channel capacity they are valid for every sequence of binary linear block codes if there exists a decoding algorithm under which the average bit error probability vanishes for every mbios channel we construct a sequence of ensembles of regular low density parity check ldpc codes so that an upper bound on the asymptotic density of their parity check matrices scales similarly to the lower bound the tightness of the lower bound is demonstrated for the binary erasure channel by analyzing a sequence of ensembles of right regular ldpc codes which was introduced by shokrollahi and which is known to achieve the capacity of this channel under iterative message passing decoding we show that this sequence of ensembles is asymptotically optimal in a sense to be defined in this paper strengthening a result of shokrollahi finally we derive lower bounds on the bit error probability and on the gap to capacity for binary linear block codes which are represented by bipartite graphs and study their performance limitations over mbios channels the latter bounds provide a quantitative measure for the number of cycles of bipartite graphs which represent good error correction codes

a note on penalized spline smoothing with correlated errors we investigate the behavior of data driven smoothing parameters for penalized spline regression in the presence of correlated data it has been shown for other smoothing methods that mean squared error minimizers such as generalized cross validation or the akaike information criterion are extremely sensitive to misspecifications of the correlation structure resulting in over or under fitting the data in contrast to this we show that a maximum likelihood based choice of the smoothing parameter is more robust and that for a moderately misspecified correlation structure over or under fitting does not occur this is demonstrated in simulations and data examples and is supported by theoretical investigations

channel coding rate in the finite blocklength regime this paper investigates the maximal channel coding rate achievable at a given blocklength and error probability for general classes of channels new achievability and converse bounds are given which are tighter than existing bounds for wide ranges of parameters of interest and lead to tight approximations of the maximal achievable rate for blocklengths n as short as 100 it is also shown analytically that the maximal rate achievable with error probability isclosely approximated by c v n q 1 where c is the capacity v is a characteristic of the channel referred to as channel dispersion and q is the complementary gaussian cumulative distribution function

mom matrix generation based on frequency and material independent reactions fmir mom a novel and efficient method of moments mom matrix generation technique called the frequency and material independent reactions for the method of moments fmir mom technique is presented this new matrix generation algorithm efficiently calculates impedance matrices while sweeping through frequency permittivity conductivity and or permeability values for frequency sweeps it has computational and memory costs comparable to those of interpolation techniques it has the advantage over interpolation techniques in that it does not divide the frequency range into segments and allows one to dynamically update the precision the technique expands the exponential of the green s function into a taylor series this allows the problem to be formulated as a summation where each term consists of a real valued matrix depending only on the geometry discretization multiplied by a scalar dependent on the propagation constant the algorithm s efficiency is obtained by calculating the geometry dependent matrices prior to sweeping through frequency or material parameters

channel polarization through the lens of blackwell measures each memoryless binary input channel bic can be uniquely described by its blackwell measure which is a probability distribution on the unit interval 0 1 with mean 1 2 conversely any such probability distribution defines a bic the evolution of the blackwell measure under arikan s polar transform is derived for general bics and is analogous to density evolution as cited in the literature the present analysis emphasizes functional equations consequently the evolution of a variety of channel functionals is characterized including the symmetric capacity bhattacharyya parameter moments of information density hellinger affinity gallager s reliability function the hirschfeld gebelein renyi maximal correlation and the bayesian information gain the evolution of measure is specialized for symmetric bics according to their decomposition into binary symmetric sub channels bscs which simplifies iterative computations and the construction of polar codes it is verified that as a consequence of the blackwell sherman stein theorem all channel functionals text i f that can be expressed as an expectation of a convex function f with respect to the blackwell measure of a channel polarize in each iteration due to the polar transformation on the class of symmetric bics moreover for f either convex or non convex a necessary and sufficient condition is established to determine whether the random process associated with each text i f is a martingale submartingale or supermartingale represented via functional inequalities in terms of f this condition is numerically verifiable for all text i f and can generate analytical proofs to exhibit one such proof it is shown that the random process associated with the squared maximal correlation parameter is a supermartingale and converges almost surely on the unit interval 0 1

sparsified adaptive cross approximation algorithm for accelerated method of moments computations this paper presents a modification of the adaptive cross approximation aca algorithm for accelerated solution of the method of moments linear system for electrically large radiation and scattering problems as with aca subblocks of the impedance matrix that represent the interaction between well separated subdomains are substituted by compressed approximations allowing for reduced storage and accelerated iterative solution the modified algorithm approximates the original subblocks with products of sparse matrices constructed with the aid of the aca algorithm and of a sub sampling of the original basis functions belonging to either subdomain because of the sampling an additional error is introduced with respect to aca but this error is controllable just like ordinary aca sparsified aca is kernel independent and needs no problem specific information except for the topology of the basis functions as a numerical example rcs computations of the nasa almond are presented showing an important gain in efficiency furthermore the numerical experiment reveals a computational complexity close to n logn for sparsified aca for a target electrical size of up to 50 wavelengths

hierarchical matrix techniques based on matrix decomposition algorithm for the fast analysis of planar layered structures the matrix decomposition algorithm mda provides an efficient matrix vector product for the iterative solution of the integral equation ie by a blockwise compression of the impedance matrix the mda with a singular value decomposition svd recompression scheme i e so called mda svd method shows strong ability for the analysis of planar layered structures however iterative solution faces the problem of convergence rate an efficient hierarchical h lu decomposition algorithm based on the h matrix techniques is proposed to handle this problem exploiting the data sparse representation of the mda svd compressed impedance matrix h lu decomposition can be efficiently implemented by h matrix arithmetic h matrix techniques provide a flexible way to control the accuracy of the approximate h lu factors h lu decomposition with low accuracy can be used as an efficient preconditioner for the iterative solver due to its low computational cost while h lu decomposition with high accuracy can be used as a direct solver for dealing with multiple right hand side rhs vector problems particularly numerical examples demonstrate that the proposed method is very robust for the analysis of various planar layered structures

on universal properties of capacity approaching ldpc code ensembles this paper is focused on the derivation of some universal properties of capacity approaching low density parity check ldpc code ensembles whose transmission takes place over memoryless binary input output symmetric mbios channels properties of the degree distributions graphical complexity and the number of fundamental cycles in the bipartite graphs are considered via the derivation of information theoretic bounds these bounds are expressed in terms of the target block bit error probability and the gap in rate to capacity most of the bounds are general for any decoding algorithm and some others are proved under belief propagation bp decoding proving these bounds under a certain decoding algorithm validates them automatically also under any suboptimal decoding algorithm a proper modification of these bounds makes them universal for the set of all mbios channels which exhibit a given capacity bounds on the degree distributions and graphical complexity apply to finite length ldpc codes and to the asymptotic case of an infinite block length the bounds are compared with capacity approaching ldpc code ensembles under bp decoding and they are shown to be informative and are easy to calculate finally some interesting open problems are considered

mixed form nested approximation for wideband multiscale simulations we propose a mixed skeleton and equivalence nested approximation method to compress the impedance matrix of the method of moments for the wideband multiscale simulations we first introduce a nested skeleton approximation where the impedance matrix is expressed recursively by sampling the dominant basis functions e g skeletons with a fully algebraic implementation from the original basis functions the idea is to introduce the automatically constructed test surface around the interface between near and far field regions for each group the dominant rwgs are sampled recursively with the adaptive cross approximation to compress the matrix against the test surface second we introduce a mixed form algorithm of skeleton and equivalence nested approximation method at low levels the nested skeleton approximation is employed and it is smoothly transferred to standard wideband nested equivalence approximation wnesa at high levels an accurate number of skeletons can be always found with a predetermined threshold at a low level which will improve computation efficiency with respect to wnesa the computational complexity of the proposed algorithm is mathcal o n log n n is the number of unknowns numerical wideband multiscale simulations demonstrate the efficiency of the proposed algorithm

polarization improves e_ 0 we prove that channel combining and splitting via arikan s polarization transformation improves gallager s reliability function e0 for binary input channels in this sense polarization creates e0 this observation gives yet another justification as to why the polar transform yields capacity achieving and low complexity codes the improvement in e0 translates to an improvement in complexity error probability trade off in analyzing polar codes one examines auxiliary random processes that follow the evolution of information measures as an underlying communication channel undergoes a sequence of transformations the conclusion of this paper shows that the e0 process associated to such an analysis is a submartingale

approximation of boundary element matrices this article considers the problem of approximating a general asymptotically smooth function in two variables typically arising in integral formulations of boundary value problems by a sum of products of two functions in one variable from these results an iterative algorithm for the low rank approximation of blocks of large unstructured matrices generated by asymptotically smooth functions is developed this algorithm uses only few entries from the original block and since it has a natural stopping criterion the approximative rank is not needed in advance

wideband fast kernel independent modeling of large multiscale structures via nested equivalent source approximation we propose a wideband fast kernel independent modeling of large multiscale structures we employ a nested equivalent source approximation nesa to compress the dense system matrix the nesa was introduced by these authors for low and moderate frequency problems smaller than a few wavelengths here we introduce a high frequency nesa algorithm and propose a hybrid version with extreme wideband properties the equivalent sources of the wideband nesa wnesa are obtained by an inverse source process enforcing equivalence of radiated fields on suitably defined testing surfaces in the low frequency region the nesa is used unmodified with a complexity of mathcal o n in the high frequency region in order to obtain a fixed rank matrix compression we hierarchically divide the far coupling space into pyramids with angles related to the peer coupling group size and the nesa testing surfaces are defined as the boundaries of the pyramids this results in a directional nested low rank fixed rank approximation with mathcal o n log n computational complexity that is kernel independent overall the approach yields wideband fast solver for the modeling of large structures that inherits the efficiency and accuracy of low frequency nesa for multiscale problems numerical results and discussions demonstrate the validity of the proposed work

generalized partial orders for polar code bit channels we study partial orders pos for the synthesized bit channels of polar codes first we give an alternative proof of an existing po for bit channels with the same hamming weight and use the underlying idea to extend the bit channel ordering to some additional cases in particular the bit channel ordering for a given code block length is used to generate additional bit channel ordering relationships for larger block lengths generalizing previously known pos next we consider pos especially for the binary erasure channel bec we identify a symmetry property of the bhattacharyya parameters of complementary bit channel pairs on the bec and provide a condition for the alignment of polarized sets of bit channels for the bec and general binary input memoryless symmetric bms channels numerical examples and further properties about the pos for the bit channels with different hamming weights are provided to illustrate the new pos the bit channels with universal ordering positions which are independent of the channel erasure probability are verified for all of the code block lengths finally we show the threshold behavior of the bhattacharyya parameters of some bit channels by approximating the threshold values the corresponding value for a bit channel can be used to determine whether it is good or bad when the underlying channel is known

functional mixed effects spectral analysis in many experiments time series data can be collected from multiple units and multiple time series segments can be collected from the same unit this article introduces a mixed effects cramer spectral representation which can be used to model the effects of design covariates on the second order power spectrum while accounting for potential correlations among the time series segments collected from the same unit the transfer function is composed of a deterministic component to account for the population average effects and a random component to account for the unit specific deviations the resulting log spectrum has a functional mixed effects representation where both the fixed effects and random effects are functions in the frequency domain it is shown that when the replicate specific spectra are smooth the log periodograms converge to a functional mixed effects model a data driven iterative estimation procedure is offered for the periodic smoothing spline estimation of the fixed effects penalized estimation of the functional covariance of the random effects and unit specific random effects prediction via the best linear unbiased predictor

iterative decoding of binary block and convolutional codes iterative decoding of two dimensional systematic convolutional codes has been termed turbo de coding using log likelihood algebra we show that any decoder can be used which accepts soft inputs including a priori values and delivers soft outputs that can be split into three terms the soft channel and a priori inputs and the extrinsic value the extrinsic value is used as an a priori value for the next iteration decoding algorithms in the log likelihood domain are given not only for convolutional codes but also for any linear binary systematic block code the iteration is controlled by a stop criterion derived from cross entropy which results in a minimal number of iterations optimal and suboptimal decoders with reduced complexity are presented simulation results show that very simple component codes are sufficient block codes are appropriate for high rates and convolutional codes for lower rates less than 2 3 any combination of block and convolutional component codes is possible several interleaving techniques are described at a bit error rate ber of 10 sup 4 the performance is slightly above or around the bounds given by the cutoff rate for reasonably simple block convolutional component codes interleaver sizes less than 1000 and for three to six iterations

on the degrees of freedom of scattered fields starting from the observation that fields differing less than a prescribed error cannot be resolved as distinct entities the degrees of freedom of the scattered field are introduced and then computed the degrees of freedom are shown to be practically equal to the nyquist number appropriate to the effective spatial bandwidth of the scattered field and to the extension of the observation domain accordingly a finite number of elements of information can be used to determine the scattered field to a prescribed approximation error it is also shown that the field representation can be made in terms of field values and simple sampling functions provided that a marginal increase in the approximation error is tolerated the results not only completely justify the use of sampling interpolation for representing scattering fields but also demonstrate that such representation is practically an optimal one an algorithm for the reconstruction of scattered fields given the maximum allowed error is then produced

contour fft based spectral domain mbf analysis of large printed antenna arrays a fast spectral domain method is proposed to evaluate the reaction terms between the macro basis functions in regular and non regular arrays made of identical printed antennas the presented technique first exploits the filtering capabilities of the macro basis functions in the spectral domain the method is then strongly accelerated with the help of a newly formulated fast fourier transform fft based technique which is applicable to a contour integration in the complex plane we name the method as contour fft c fft besides an effective homogeneous medium term treated with multipoles a computational complexity of order n log2 n is achieved for the tabulation of substrate related reaction terms for any possible relative positions the complexity of the proposed method is independent from the complexity of the elements numerical results obtained with the proposed method are compared with those from a pre validated reference solution based on the traditional macro basis functions technique an excellent agreement is observed

performance bounds of concatenated polar coding schemes a concatenated coding scheme over binary memoryless symmetric bms channels using a polarization transformation followed by outer sub codes is analyzed achievable error exponents and upper bounds on the error rate are derived the first bound is obtained using outer codes which are typical random linear codes as a byproduct of this bound it determines the rates of the outer codes a lower bound on the error exponent that holds for all bms channels with a given capacity is then derived improved bounds and approximations for finite blocklength codes using channel dispersions normal approximation as well as converse and approximate converse results are also obtained the bounds are compared with actual simulation results from the literature for the cases considered when transmitting over the binary input additive white gaussian noise channel there was only a small gap between the channel dispersion based approximation and the actual error rate of concatenated bch polar codes

a multilevel matrix decomposition algorithm for analyzing scattering from large structures a multilevel algorithm is presented for analyzing scattering from electrically large surfaces the algorithm accelerates the iterative solution of integral equations that arise in computational electromagnetics the algorithm permits a fast matrix vector multiplication by decomposing the traditional method of moment matrix into a large number of blocks with each describing the interaction between distant scatterers the multiplication of each block by a trial solution vector is executed using a multilevel scheme that resembles a fast fourier transform fft and that only relies on well known algebraic techniques the computational complexity and the memory requirements of the proposed algorithm are o n log sup 2 n

a high performance upgrade of the perfectly matched layer multilevel fast multipole algorithm for large planar microwave structures an improvement of the perfectly matched layer multilevel fast multipole algorithm pml mlfma for simulating large planar microwave structures is presented by exploiting the low rank property of the pml mlfma multimodal aggregation and disaggregation matrices considerable reductions in memory usage and computation time are obtained the method has been extensively validated demonstrating complete error controllability when simulating large planar microwave structures reductions in memory requirements and cpu time of more than 60 and 40 have been achieved

multiscale compressed block decomposition for fast direct solution of method of moments linear system the multiscale compressed block decomposition algorithm ms cbd is presented for highly accelerated direct non iterative solution of electromagnetic scattering and radiation problems with the method of moments mom the algorithm is demonstrated to exhibit n2 computational complexity and storage requirements scaling with n1 5 for electrically large objects several numerical examples illustrate the efficiency of the method in particular for problems with multiple excitation vectors the largest problem presented in this paper is the monostatic rcs of the nasa almond at 50 ghz for one thousand incidence angles discretized using 442 089 rwg basis functions being entirely algebraic ms cbd is independent of the greens function of the problem

nested equivalent source approximation for the modeling of multiscale structures we introduce a method to compress the impedance matrix of the method of moments mom for the modeling of high fidelity multiscale structures at low to moderate frequencies we start from a method recently proposed to compress static scalar problems proved to have o n computational complexity we represent far coupling between groups through equivalent source distributions on properly defined automatically generated equivalence surfaces the equivalent sources are obtained via an inverse source process that enforces equivalence of radiated fields on testing surfaces within a prescribed accuracy and are intrinsically multiscale this results in an o n complexity scaling of matrix vector products but reduces multiplicative constants i e reduces time and memory requirements for all structures it affords an improved representation of couplings in multiscale structures resulting in a fast convergence of iterative solvers our approach is green s function independent and easy to be implemented in existing mom codes the present version is based on the electric field integral equation efie numerical results prove the effectiveness of the proposed algorithm for complex multiscale structures

fast solution methods in electromagnetics various methods for efficiently solving electromagnetic problems are presented electromagnetic scattering problems can be roughly classified into surface and volume problems while fast methods are either differential or integral equation based the resultant systems of linear equations are either solved directly or iteratively a review of various differential equation solvers their complexities and memory requirements is given the issues of grid dispersion and hybridization with integral equation solvers are discussed several fast integral equation solvers for surface and volume scatterers are presented these solvers have reduced computational complexities and memory requirements

multilevel fast adaptive cross approximation algorithm with characteristic basis functions this paper presents a multilevel fast adaptive cross approximation mlfaca algorithm for accelerated iterative solution of the method of moments mom matrix equation for electrically large targets the mlfaca compresses the impedance submatrices between well separated blocks into products of sparse matrices constructed with the aid of the fast adaptive cross sampling facs scheme and the butterfly algorithm as a result the mlfaca can reduce both the computational time and the storage of the mom to mathbf o mathbf n mathbf log mathbf 2 text n where mathbf n is the number of the rao wilton glisson rwg basis functions in the analyzed target meanwhile the mlfaca maintains the adaptive and kernel independent properties furthermore the characteristic basis function method cbfm is employed to decrease the size of the outer matrices of the mlfaca to further reduce the storage and iteration time numerical results are presented to demonstrate the advantages of the proposed method including a successful solution of a scattering problem involving 10 861 668 rwg basis functions

the generalized area theorem and some of its consequences there is a fundamental relationship between belief propagation bp and maximum a posteriori decoding the case of transmission over the binary erasure channel was investigated in detail in a companion paper c meacuteasson a montanari and r urbanke maxwell s construction the hidden bridge between iterative and maximum a posteriori decoding ieee transactions on information theory submitted for publication this paper investigates the extension to general memoryless channels paying special attention to the binary case an area theorem for transmission over general memoryless channels is introduced and some of its many consequences are discussed we show that this area theorem gives rise to an upper bound on the maximum a posteriori threshold for sparse graph codes in situations where this bound is tight the extrinsic soft bit estimates delivered by the bp decoder coincide with the correct a posteriori probabilities above the maximum a posteriori threshold more generally it is conjectured that the fundamental relationship between the maximum a posteriori probability map and the bp decoder which was observed for transmission over the binary erasure channel carries over to the general case we finally demonstrate that in order for the design rate of an ensemble to approach the capacity under bp decoding the component codes have to be perfectly matched a statement which is well known for the special case of transmission over the binary erasure channel

polar codes characterization of exponent bounds and constructions polar codes were recently introduced by arikan they achieve the symmetric capacity of arbitrary binary input discrete memoryless channels under a low complexity successive cancellation decoding scheme the original polar code construction is closely related to the recursive construction of reed muller codes and is based on the 2 2 matrix 1 0 1 1 it was shown by arikan telatar that this construction achieves an error exponent of 1 2 i e that for sufficiently large blocklengths the error probability decays exponentially in the square root of the blocklength it was already mentioned by arikan that in principle larger matrices can be used to construct polar codes in this paper it is first shown that any l l matrix none of whose column permutations is upper triangular polarizes binary input memoryless channels the exponent of a given square matrix is characterized upper and lower bounds on achievable exponents are given using these bounds it is shown that there are no matrices of size smaller than 15 15 with exponents exceeding 1 2 further a general construction based on bch codes which for large i achieves exponents arbitrarily close to 1 is given at size 16 16 this construction yields an exponent greater than 1 2

an mse based transfer chart for analyzing iterative decoding schemes using a gaussian approximation an alternative to extrinsic information transfer exit charts called mean square error mse charts that use a measure related to the mse instead of mutual information is proposed using the relationship between mutual information and minimum mean square error mmse for the additive white gaussian noise awgn channel a relationship between the rate of any code and the area under a plot of mmse versus signal to noise ratio snr is obtained when the a priori log likelihood ratio llr is from a binary input gaussian channel using this result a justification is provided for designing concatenated codes by matching the exit curves of the inner and outer decoder when the llrs are assumed to be gaussian which is also the typical assumption used for code design using exit charts even though the gaussian assumption is almost never true the results presented in this paper represent a step toward the analysis of iterative decoding schemes using a single parameter finally for the special case of awgn channel it is shown that any capacity achieving code has an exit curve that is a step function

density evolution for asymmetric memoryless channels density evolution de is one of the most powerful analytical tools for low density parity check ldpc codes and graph codes with message passing decoding algorithms with channel symmetry as one of its fundamental assumptions density evolution has been widely and successfully applied to different channels including binary erasure channels becs binary symmetric channels bscs binary additive white gaussian noise biawgn channels etc this paper generalizes density evolution for asymmetric memoryless channels which in turn broadens the applications to general memoryless channels e g z channels composite white gaussian noise channels etc the central theorem underpinning this generalization is the convergence to perfect projection for any fixed size supporting tree a new iterative formula of the same complexity is then presented and the necessary theorems for the performance concentration theorems are developed several properties of the new density evolution method are explored including stability results for general asymmetric memoryless channels simulations code optimizations and possible new applications suggested by this new density evolution method are also provided this result is also used to prove the typicality of linear ldpc codes among the coset code ensemble when the minimum check node degree is sufficiently large it is shown that the convergence to perfect projection is essential to the belief propagation bp algorithm even when only symmetric channels are considered hence the proof of the convergence to perfect projection serves also as a completion of the theory of classical density evolution for symmetric memoryless channels

nonparametric spectral analysis of heart rate variability through penalized sum of squares frequency domain properties of heart rate variability hrv or the elapsed time between consecutive heart beats are utilized by biomedical researchers in a variety of fields hrv is measured from the electrocardiograph signal through the interbeat interval series popular approaches for estimating power spectra from these interval data apply common spectral analysis methods that are designed for the analysis of evenly sampled time series the application of these methods to the interbeat interval series which is indexed over an uneven time grid requires a bias inducing transformation the goal of this article is to explore the use of penalized sum of squares for nonparametric estimation of the spectrum of hrv directly from the interbeat intervals a novel cross validation procedure is introduced for smoothing parameter selection empirical properties of the proposed estimation procedure are explored and compared to popular methods in a simulation study the proposed method is used in an analysis of data from an insomnia study which seeks to illuminate the association between the power spectrum of hrv during different periods of sleep with response to behavioral therapy

multilevel adaptive cross approximation mlaca the multilevel adaptive cross approximation mlaca is proposed as a fast method to accelerate the matrix vector products in the iterative solution of the linear system that results from the discretization of electromagnetic integral equations ie with the method of moments mom the single level aca already described in the literature is extended with a multilevel recursive algorithm in order to improve the asymptotical complexity of both the computational cost and the memory requirements the main qualities of aca are maintained it is purely algebraic and independent of the integral equation kernel green s function as long as it produces pseudo rank deficient matrix blocks the algorithm is presented in such a way that it can be easily implemented on top of an existing mom code with most commonly used green s functions

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

spatially coupled ensembles universally achieve capacity under belief propagation we investigate spatially coupled code ensembles for transmission over the binary erasure channel it was recently shown that spatial coupling increases the belief propagation threshold of the ensemble to essentially the maximum a priori threshold of the underlying component ensemble this explains why convolutional ldpc ensembles originally introduced by felstrom and zigangirov perform so well over this channel we show that the equivalent result holds true for transmission over general binary input memoryless output symmetric channels more precisely given a desired error probability and a gap to capacity we can construct a spatially coupled ensemble that fulfills these constraints universally on this class of channels under belief propagation decoding in fact most codes in this ensemble have this property the quantifier universal refers to the single ensemble code that is good for all channels but we assume that the channel is known at the receiver the key technical result is a proof that under belief propagation decoding spatially coupled ensembles achieve essentially the area threshold of the underlying uncoupled ensemble we conclude by discussing some interesting open problems

does the performance of ldpc codes depend on the channel in this letter we discuss the performance of low density parity check ldpc codes on memoryless channels using a recently proposed analysis technique based on extrinsic information transfer exit charts we present an interpretation of the known fact that the bit error rate ber performance of an ensemble of ldpc codes shows little dependence on the specific memoryless channel this result has been partially observed in the literature for symmetric channels and is here extended to asymmetric channels we conjecture and demonstrate that the performance of an ensemble of ldpc codes depends primarily and solely on the mutual information mi between the input and the output of the channel as a validation of this conjecture we compare the performance of a few ldpc codes with various rates for five representative memoryless both symmetric and asymmetric channels obtaining results in excellent agreement with the exit chart based prediction

random coding techniques for nonrandom codes this work provides techniques to apply the channel coding theorem and the resulting error exponent which was originally derived for totally random block code ensembles to ensembles of codes with less restrictive randomness demands as an example the random coding technique can even be applied for an ensemble that contains a single code for a specific linear code we get an upper bound for the error probability which equals gallager s 1968 random coding bound up to a factor determined by the maximum ratio between the weight distribution of the code and the expected random weight distribution

nonparametric spectral density estimation using penalized whittle likelihood abstract the penalized likelihood approach is not well developed in time series analysis even though it has been applied successfully in a number of nonparametric function estimation problems chow and grenander proposed a penalized likelihood type approach to the nonparametric estimation of the spectral density of gaussian processes in this article this estimator is extended to more general stationary processes its practical implementation is developed in some detail and some asymptotic rates of convergence are established its performance is also compared to more widely used alternatives in the field a computational algorithm involving an iterative least squares initialized by the log periodogram is first developed then motivated by an asymptotic linearization an estimator of the integrated squared error between the estimated and true log spectral densities is proposed from this a data dependent procedure for selection of the amount of smoothing is constructed the methodology is illustrated

channel polarization a method for constructing capacity achieving codes for symmetric binary input memoryless channels a method is proposed called channel polarization to construct code sequences that achieve the symmetric capacity i w of any given binary input discrete memoryless channel b dmc w the symmetric capacity is the highest rate achievable subject to using the input letters of the channel with equal probability channel polarization refers to the fact that it is possible to synthesize out of n independent copies of a given b dmc w a second set of n binary input channels wn i 1 les i les n such that as n becomes large the fraction of indices i for which i wn i is near 1 approaches i w and the fraction for which i wn i is near 0 approaches 1 i w the polarized channels wn i are well conditioned for channel coding one need only send data at rate 1 through those with capacity near 1 and at rate 0 through the remaining codes constructed on the basis of this idea are called polar codes the paper proves that given any b dmc w with i w 0 and any target rate r i w there exists a sequence of polar codes cfrn nges1 such that cfrn has block length n 2n rate ges r and probability of block error under successive cancellation decoding bounded as pe n r les o n 1 4 independently of the code rate this performance is achievable by encoders and decoders with complexity o n logn for each

extension of an entropy property for binary input memoryless symmetric channels the channel output entropy property introduced by a d wyner and j ziv ibid vol it 19 p 769 762 nov 1973 for a binary symmetric channel is extended to arbitrary memoryless symmetric channels with binary inputs and discrete or continuous outputs this yields lower bounds on the achievable information rates of these channels under constrained binary inputs using the interpretation of entropy as a measure of order and randomness the authors deduce that output sequences of memoryless symmetric channels induced by binary inputs are of a higher degree of randomness if the redundancy of the input binary sequence is spread in memory rather than in one dimensional asymmetry it is of interest to characterize the general class of schemes for which this interpretation holds

constrained information combining theory and applications for ldpc coded systems this paper tightens previous information combining bounds on the performance of iterative decoding of binary low density parity check ldpc codes over binary input symmetric output channels by tracking the probability of erroneous bit in conjunction with mutual information evaluation of the new bounds as well as of other known bounds on different ldpc ensembles demonstrates sensitivity of the finite dimensional iterative bounds to lambda2 the fraction of edges connected to degree 2 variable nodes