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

tauberian theorems and the central limit theorem 1 results let xn be independent and identically distributed random variables with law p mean 0 and variance a2 00 s 1 xk write p qn 1 for the laws of sn sn nyi a n and the standard normal n o 1 thus qn 1d weak convergence by the global central limit theorem we shall need the local central limit theorem see e g ibragimov and linnik 1971 theorems 4 4 1 4 2 1 4 2 2 we shall assume either llt i some pk has an absolutely continuous component in which case qn 11 3 0 as n x oo variation norm or llt ii p is lattice supported by some arithmetic progression a hk with k integer and h maximal we shall suppose for simplicity that a 0 and h 1 when writing pnk for pn k

analytic formulation and numerical implementation of an acoustic pressure gradient prediction two new analytical formulations of the acoustic pressure gradient have been developed and implemented in the psu wopwop rotor noise prediction code the pressure gradient can be used to solve the boundary condition for scattering problems and it is a key aspect to solve acoustic scattering problems the first formulation is derived from the gradient of the ffowcs williams hawkings fw h equation this formulation has a form involving the observer time differentiation outside the integrals in the second formulation the time differentiation is taken inside the integrals analytically this formulation avoids the numerical time differentiation with respect to the observer time which is computationally more efficient the acoustic pressure gradient predicted by these new formulations is validated through comparison with available exact solutions for a stationary and moving monopole sources the agreement between the predictions and exact solutions is excellent the formulations are applied to the rotor noise problems for two model rotors a purely numerical approach is compared with the analytical formulations the agreement between the analytical formulations and the numerical method is excellent for both stationary and moving observer cases

weighted versions of beurling s tauberian theorem wiener s well known tauberian theorem is equivalent to the following assertion for f l the relation lim k f x 0 holds true for the convolution with x coo any k e l 1 whenever it holds true for some k1 li r having a fourier transform which does not vanish at any point beurling suggested such an implication to be true if convolution is replaced by certain related methods of taking moving averages with variable band widths cf 5 6 for details appropriately reformulated results and proofs as given in 6 even hold true in the m dimensional setting m 1 in the present note weighted quantitative versions are to be discussed showing that a certain speed of convergence for a sufficiently smooth kernel k with nonvanishing fourier transform implies the same order of convergence for all kernels satisfying an appropriate decay condition for an illustrating set of equivalent conditions for m 1 the reader is referred to theorem 3 below

asymmetric slepian wolf coding of nonstationarily correlated m ary sources with sliding window belief propagation asymmetric slepian wolf coding aswc of m ary sources with nonstationary correlation is a very useful model for many practical problems an effective implementation of this coding scheme is to binarize each m ary source into multiple bitplanes which are then compressed by a single binary low density parity check ldpc code though the inter bitplane correlation of m ary sources can be exploited at the decoder by the joint bitplane belief propagation jbbp algorithm accurate online estimation of varying local source correlation still remains a major challenge to tackle this problem this paper proposes an m ary counterpart of the sliding window belief propagation swbp algorithm to realize simultaneous source recovery and correlation estimation to search for the optimal sliding window size the expected rate is raised as a new criterion moreover an adaptive method is proposed to decide whether correlation reestimation is necessary the m ary swbp mswbp algorithm is then generalized to obtain its 2d form which can be used to tackle the aswc of 2d m ary sources with nonstationary correlation the developed 1d 2d mswbp algorithm inherits all merits of the original binary swbp algorithm e g near optimal coding efficiency low complexity insensitivity to initial settings etc making it a very attractive technique in practice

pointwise i convergence and i convergence in measure of sequences of functions let i p n be an ideal we say that a sequence yn n n of real numbers is i convergent to y r if for every neighborhood u of y the set of n s satisfying yn u is in i basing upon this notion we define pointwise i convergence and i convergence in measure of sequences of measurable functions defined on a measure space with finite measure we discuss the relationship between these two convergences in particular we show that for a wide class of ideals including erd s ulam ideals and summable ideals the pointwise i convergence implies the i convergence in measure we also present examples of very regular ideals such that this implication does not hold

ldpc based lossless compression of nonstationary binary sources using sliding window belief propagation low density parity check ldpc codes have been used to implement lossless distributed or conventional source coding however block wise ldpc codes are difficult to adapt to varying source statistics as traditional symbol wise entropy coding techniques in this paper we propose the sliding window belief propagation swbp algorithm which is able to simultaneously recover the source and refine the estimate of varying source statistics the swbp is easy to implement and performs well in simulations

general regular variation popa groups and quantifier weakening abstract we introduce general regular variation a theory of regular variation containing the existing karamata bojanic karamata de haan and beurling theories as special cases the unifying theme is the popa groups of our title viewed as locally compact abelian ordered topological groups together with their haar measure and fourier theory the power of this unified approach is shown by the simplification it brings to the whole area of quantifier weakening so important in this field

computation of acoustic scattering from a moving rigid surface application of the kirchhoff formula for subsonically moving surfaces to scattering of sound from a moving rigid body is described the formulation leads to a singular integral equation that yields surface values of the field the integral equation is solved using a boundary element technique in conjunction with the galerkin method several checks on the accuracy and validity of the scheme are discussed numerical results are obtained for scattering of sound from a harmonic point source co moving with a thin winglike body

statistical gap tauberian theorems in metric spaces abstract by using the concept of statistical convergence we present statistical tauberian theorems of gap type for the cesaro euler borel family and the hausdorff families applicable in arbitrary metric spaces in contrast to the classical gap tauberian theorems we show that such theorems exist in the statistical sense for the convolution methods which include the taylor and the borel matrix methods we further provide statistical analogs of the gap tauberian theorems for the hausdorff methods and provide an explanation as to how the tauberian rates over the gaps may differ from those of the classical tauberian theorems

noise adaptive ldpc decoding using particle filtering belief propagation bp is a powerful algorithm to decode low density parity check ldpc codes over additive white gaussian noise awgn channels however the traditional bp algorithm cannot adapt efficiently to the statistical change of snr in an awgn channel this paper proposes an adaptive scheme that incorporates a particle filtering pf algorithm into the bp based ldpc decoding process the proposed scheme is capable to perform online estimation of time varying snr at the bit level and enhance the bp decoding performance simultaneously

strong and a statistical comparisons for sequences abstract let t and a be two nonnegative regular summability matrices and w t p l and ca b denote the spaces of all bounded strongly t summable sequences with index p 0 and bounded summability domain of a respectively in this paper we show among other things that n is a multiplier from w t p l into ca b if and only if any subset k of positive integers that has t density zero implies that k has a density zero these results are used to characterize the a statistical comparisons for both bounded as well as arbitrary sequences using the concept of a statistical tauberian rate we also show that n is not a multiplier from w t p l into ca b that leads to a steinhaus type result

performance of belief propagation for decoding ldpc codes in the presence of channel estimation error in this paper we investigate the performance of the belief propagation bp algorithm for decoding low density parity check codes over the additive white gaussian noise channel when there is an incorrect estimate of the channel signal to noise ratio snr referred to as snr mismatch at the decoder at the extremes for over and underestimation of snr the performance of bp tends to that of min sum algorithm and the channel bit error rate respectively our results for regular codes indicate that the sensitivity to mismatch increases by increasing the variable node degree and by decreasing the check node degree the effect of variable node degree however appears to be more profound such that at a given rate the codes with the smallest variable and check degrees are more robust against snr mismatch for irregular codes by comparing the thresholds of a few ensembles we demonstrate that the ensemble which performs better in the absence of mismatch can perform worse in the presence of it to obtain our asymptotic results we propose a computationally efficient method based on the gaussian approximation of density evolution in the presence of snr mismatch we also show that the asymptotic results are consistent with simulation results for codes with finite block lengths

bounded multipliers of bounded a statistically convergent sequences abstract in this paper we provide an alternate proof of a result of kline it claims that the set of all a statistically convergent sequences cannot be given a locally convex fk topology where a is a nonnegative regular matrix whose rows spread we also study the bounded multiplier space of all bounded a statistically convergent sequences and using the n program we give an analogue of a result of fridy and miller for bounded multipliers

abelian tauberian and mercerian theorems for arithmetic sums we consider abelian results passing from behaviour of f to that of single or double sums as above tauberian theorems converse implications under additional conditions tauberian conditions and mercerian theorems in which we pass from some comparison statement between f and a sum to a conclusion on f alone this line of work may be traced to a seminal paper of polya in 1917 p see also polya szego ps part ii ch 4 no 156 our two main tools are the karamata theory of regular variation originated in 1930 see bgt and the wiener tauberian theory originated in 1932 see hardy h widder w polya s achievement is all the more striking in that neither of these tools was available to him this study arises from a fusion of two recent lines of work on the arithmetic sums side our interest was stimulated by a series of studies by de koninck ivic deki1 2 3 on the abelian tauberian mercerian side we make use of recent work of our own bi5

analytical acoustic pressure gradient prediction for moving medium problems in this paper an acoustic pressure gradient formula capable of accounting for constant uniform flow effects is suggested acoustic pressure gradient calculation is key for acoustic scattering prob

tauberian theorems via statistical convergence the concept of statistical convergence which is related to the usual concept of convergence in probability provides a regular summability method for abstract metric spaces by using probabilistic tools we provide some tauberian theorems which have best possible order tauberian conditions furthermore these methods can be used to unify and improve the classical pointwise tauberian theorems of summability theory for the random walk type methods as proved by bingham and hausdorff methods as proved by lorentz

suppressing the onset of instabilities in the time domain equivalent source method using a multistep approach numerical instability is an important issue that should be addressed in the time domain equivalent source method tesm this study proposes a multistep method to stabilize tesm when using the measured acoustic pressure data to optimize equivalent source strengths unlike the conventional single step method that solves each time step in the time marching process of tesm the proposed method performs a one time solution for several time steps the multistep solution can potentially reduce the accumulation rate of error and improves filtering effects by changing the structure of the matrix that needs to be inverted when the truncated singular value decomposition or tikhonov regularization is used in the time marching process numerical simulations with three examples demonstrate the effectiveness of the multistep method in improving the stability of solutions compared with the single step method effects of the number of merged time steps on the solutions are also discussed to guide the selection process finally the sensitivity of the multistep method to numerical parameters is investigated to demonstrate its consistency under different configurations of numerical parameters

matrix maps of statistically convergent sequences abstract let a and d be two nonnegative regular matrices and b be an arbitrary infinite matrix we give the sufficient necessary conditions under which the matrix map b sends a statistically convergent bounded sequences to d statistically convergent sequences these give nice additions to the work of fridy and khan we also provide the limit formula for such a map and evaluate the corresponding operator semi norm our results generalize many well known results

particle filters for joint blind equalization and decoding in frequency selective channels this paper introduces new algorithms for joint blind equalization and decoding of convolutionally coded communication systems operating on frequency selective channels the proposed method is based on particle filters pf recursively approximating maximum a posteriori map estimates of the transmitted data without explicitly determining channel parameters further elaborating on previous works we assume that both the channel order and the noise variance are unknown random variables and develop a new formulation for pf weight propagation which allows these quantities to be analytically integrated out we verify via numerical simulations that the proposed methods lead to near optimal performance closely approximating that of algorithms that require exact knowledge of all channel parameters

fuzzifying ideal convergence in fuzzifying topological linear spaces in this study we propose a framework for fuzzifying ideal convergence in fuzzifying topological linear spaces after defining fuzzifying ideal convergence we discuss many properties of fuzzifying ideal convergence in fuzzifying topological linear spaces we also introduce a stronger convergence than fuzzifying ideal convergence and a sufficient condition called ap fuzzifying condition under which fuzzifying ideal convergence implies the stronger convergence above is proved

statistical convergence and ideal convergence for sequences of functions abstract let i p n stand for an ideal containing finite sets we discuss various kinds of statistical convergence and i convergence for sequences of functions with values in r or in a metric space for real valued measurable functions defined on a measure space x m we obtain a statistical version of the egorov theorem when x we show that in its assertion equi statistical convergence on a big set cannot be replaced by uniform statistical convergence also we consider statistical convergence in measure and i convergence in measure with some consequences of the riesz theorem we prove that outer and inner statistical convergences in measure for sequences of measurable functions are equivalent if the measure is finite

adaptive bayesian multiuser detection for synchronous cdma with gaussian and impulsive noise we consider the problem of simultaneous parameter estimation and data restoration in a synchronous cdma system in the presence of either additive gaussian or additive impulsive white noise with unknown parameters the impulsive noise is modeled by a two term gaussian mixture distribution bayesian inference of all unknown quantities is made from the superimposed and noisy received signals the gibbs sampler a markov chain monte carlo procedure is employed to calculate the bayesian estimates the basic idea is to generate ergodic random samples from the joint posterior distribution of all unknown and then to average the appropriate samples to obtain the estimates of the unknown quantities adaptive bayesian multiuser detectors based on the gibbs sampler are derived for both the gaussian noise synchronous cdma channel and the impulsive noise synchronous cdma channel a salient feature of the proposed adaptive bayesian multiuser detectors is that they can incorporate the a priori symbol probabilities and they produce as output the a posteriori symbol probabilities that is they are soft input soft output algorithms hence these methods are well suited for iterative processing in a coded system which allows the adaptive bayesian multiuser detector to refine its processing based on the information from the decoding stage and vice versa a receiver structure termed the adaptive turbo multiuser detector