a chebyshev based rectangular polar integral solver for scattering by general geometries described by non overlapping patches this paper introduces a high order accurate strategy for integration of singular kernels and edge singular integral densities that appear in the context of boundary integral equation formulations of the problem of acoustic scattering in particular the proposed method is designed for use in conjunction with geometry descriptions given by a set of arbitrary non overlapping logically quadrilateral patches which makes the algorithm particularly well suited for treatment of cad generated geometries fejer s first quadrature rule is incorporated in the algorithm to provide a spectrally accurate method for evaluation of contributions from far integration regions while highly accurate precomputations of singular and near singular integrals over certain surface patches together with two dimensional chebyshev transforms and suitable surface varying rectangular polar changes of variables are used to obtain the contributions for singular and near singular interactions the overall integration method is then used in conjunction with the linear algebra solver gmres to produce solutions for sound soft open and closed surface scattering obstacles including an application to an aircraft described by means of a cad representation the approach is robust fast and highly accurate use of a few points per wavelength suffices for the algorithm to produce far field accuracies of a fraction of a percent and slight increases in the discretization densities give rise to significant accuracy improvements

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

functional compression through graph coloring motivated by applications to sensor networks and privacy preserving databases we consider the problem of functional compression the objective is to separately compress possibly correlated discrete sources such that an arbitrary but fixed deterministic function of those sources can be computed given the compressed data from each source we consider both the lossless and lossy computation of a function specifically we present results of the rate regions for three instances of the problem where there are two sources 1 lossless computation where one source is available at the decoder 2 under a special condition lossless computation where both sources are separately encoded and 3 lossy computation where one source is available at the decoder for all of these instances we present a layered architecture for distributed coding first preprocess data at each source using colorings of certain characteristic graphs and then use standard distributed source coding a la slepian and wolfs scheme to compress them for the first instance our results extend the approach developed by orlitsky and roche 2001 in the sense that our scheme requires simpler structure of coloring rather than independent sets as in the previous case as an intermediate step to obtain these results we obtain an asymptotic characterization of conditional graph coloring for an or product of graphs generalizing a result of korner 1973 which should be of interest in its own right

code design for the noisy slepian wolf problem we consider a noisy slepian wolf problem where two correlated sources are separately encoded using codes of fixed rate and transmitted over two independent binary memoryless symmetric channels the capacity of each channel is characterized by a single parameter that is not known at the transmitter system performance is evaluated by computing the set of channel parameters for which the system can successfully decode this set is called the achievable channel parameter region acpr the goal is to design systems whose acprs are as large as possible the main result is the design of irregular low density parity check ldpc ensembles whose acprs are significantly larger than previous designs some previous attempts to achieve large acprs with ldpc codes failed because systematic codes were used in this work we start with systematic encoders but puncture all the systematic bits before transmission we also show that additional gains are possible using a staggered structure which enables codes optimized for single user channels to perform well under symmetric channel conditions the main analysis tool is a generic density evolution framework for the analysis of joint iterative decoding for this problem

group ordered sprt for decentralized detection the problem of decentralized detection in a large wireless sensor network is considered an adaptive decentralized detection scheme group ordered sequential probability ratio test go sprt is proposed this scheme groups sensors according to the informativeness of their data fusion center collects sensor data sequentially starting from the most informative data and terminates the process when the target performance is reached wald s approximations are shown to be applicable even though the problem setting deviates from that of the traditional sequential probability ratio test sprt to analyze the efficiency of go sprt the asymptotic equivalence between the average sample number of go sprt which is a function of a multinomial random variable and a function of a normal random variable is established closed form approximations for the average sample number are then obtained compared with fixed sample size test and traditional sprt the proposed scheme achieves significant savings in the cost of data fusion

the optimal p version approximation of singularities on polyhedra in the boundary element method we consider elliptic boundary value problems on three dimensional polyhedral domains we describe the three types of singular components that arise in the solution edge vertex and edge vertex singularities we analyze the approximation of the traces of each of each of these different types of singularities by polynomial subspaces on the boundary as the polynomial degree p tends to infinity the p version we establish asymptotic rates of convergence that are optimal in the h t norm over the boundary for 0 leq t leq 1 we apply these results to a galerkin boundary element method bem formulation for a model neumann problem obtaining the optimal convergence rate for the p version bem over polyhedral domains

on the joint source channel coding error exponent for discrete memoryless systems we investigate the computation of csisza spl acute r s bounds for the joint source channel coding jscc error exponent e sub j of a communication system consisting of a discrete memoryless source and a discrete memoryless channel we provide equivalent expressions for these bounds and derive explicit formulas for the rates where the bounds are attained these equivalent representations can be readily computed for arbitrary source channel pairs via arimoto s algorithm when the channel s distribution satisfies a symmetry property the bounds admit closed form parametric expressions we then use our results to provide a systematic comparison between the jscc error exponent e sub j and the tandem coding error exponent e sub t which applies if the source and channel are separately coded it is shown that e sub t spl les e sub j spl les 2e sub t we establish conditions for which e sub j e sub t and for which e sub j 2e sub t numerical examples indicate that e sub j is close to 2e sub t for many source channel pairs this gain translates into a power saving larger than 2 db for a binary source transmitted over additive white gaussian noise awgn channels and rayleigh fading channels with finite output quantization finally we study the computation of the lossy jscc error exponent under the hamming distortion measure

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

on non cooperative block faded orthogonal multiple access schemes with correlated sources in this paper we study the performance of non cooperative multiple access systems with noisy separated channels where correlated sources communicate to an access point ap through block faded links in the considered scenario perfect channel state information csi is assumed at the receiver while no csi is available at the transmitters we first consider uncoded transmissions from the sources to the ap which exploits the source correlation to carry out joint channel detection jcd in this scenario we propose an analytical approach to evaluate the achievable performance in terms of average bit error rate ber we then investigate the impact of coding considering the same fixed coding scheme at each source then we consider an extrinsic information transfer exit chart based framework to optimize the design of concatenated and low density parity check ldpc codes for jcd schemes

distributed source coding using syndromes discus design and construction we address the problem of compressing correlated distributed sources i e correlated sources which are not co located or which cannot cooperate to directly exploit their correlation we consider the related problem of compressing a source which is correlated with another source that is available only at the decoder this problem has been studied in the information theory literature under the name of the slepian wolf 1973 source coding problem for the lossless coding case and as rate distortion with side information for the lossy coding case we provide a constructive practical framework based on algebraic trellis codes dubbed as distributed source coding using syndromes discus that can be applicable in a variety of settings simulation results are presented for source coding of independent and identically distributed i i d gaussian sources with side information available at the decoder in the form of a noisy version of the source to be coded our results reveal the promise of this approach using trellis based quantization and coset construction the performance of the proposed approach is 2 5 db from the wyner ziv 1976 bound

source coding and graph entropies a sender wants to accurately convey information to a receiver who has some possibly related data we study the expected number of bits the sender must transmit for one and for multiple instances in two communication scenarios and relate this number to the chromatic and korner 1973 entropies of a naturally defined graph

new performance bounds for turbo codes we derive a new upper bound on the word and bit error probabilities of turbo codes with maximum likelihood decoding by using the gallager bound since the derivation of the bound for a given interleaver is intractable we assume uniform interleaving as in the derivation of the standard union bound for turbo codes the result is a generalization of the transfer function bound and remains useful for a wider range of signal to noise ratios particularly for some range below the channel cutoff rate the new bound is also applicable to other linear codes

distributed coding using punctured quasi arithmetic codes for memory and memoryless sources this correspondence considers the use of punctured quasi arithmetic qa codes for the slepian wolf problem these entropy codes are defined by finite state machines for memoryless and first order memory sources puncturing an entropy coded bit stream leads to an ambiguity at the decoder side the decoder makes use of a correlated version of the original message in order to remove this ambiguity a complete distributed source coding dsc scheme based on qa encoding with side information at the decoder is presented together with iterative structures based on qa codes the proposed schemes are adapted to memoryless and first order memory sources simulation results reveal that the proposed schemes are efficient in terms of decoding performance for short sequences compared to well known dsc solutions using channel codes

a network information theory for wireless communication scaling laws and optimal operation how much information can be carried over a wireless network with a multiplicity of nodes and how should the nodes cooperate to transfer information to study these questions we formulate a model of wireless networks that particularly takes into account the distances between nodes and the resulting attenuation of radio signals and study a performance measure that weights information by the distance over which it is transported consider a network with the following features i n nodes located on a plane with minimum separation distance spl rho sub min 0 ii a simplistic model of signal attenuation e sup spl gamma spl rho spl rho sup spl delta over a distance spl rho where spl gamma spl ges 0 is the absorption constant usually positive unless over a vacuum and spl delta 0 is the path loss exponent iii all receptions subject to additive gaussian noise of variance spl sigma sup 2 the performance measure we mainly but not exclusively study is the transport capacity c sub t sup spl sigma on sub spl lscr 1 sup m r sub spl lscr spl middot spl rho sub spl lscr where the supremum is taken over m and vectors r sub 1 r sub 2 r sub m of feasible rates for m source destination pairs and spl rho sub spl lscr is the distance between the spl lscr th source and its destination it is the supremum distance weighted sum of rates that the wireless network can deliver we show that there is a dichotomy between the cases of relatively high and relatively low attenuation when spl gamma 0 or spl delta 3 the relatively high attenuation case the transport capacity is bounded by a constant multiple of the sum of the transmit powers of the nodes in the network however when spl gamma 0 and spl delta 3 2 the low attenuation case we show that there exist networks that can provide unbounded transport capacity for fixed total power yielding zero energy priced communication examples show that nodes can profitably cooperate over large distances using coherence and multiuser estimation when the attenuation is low these results are established by developing a coding scheme and an achievable rate for gaussian multiple relay channels a result that may be of interest in its own right

on the sum rate of gaussian multiterminal source coding new proofs and results we show that the lower bound on the sum rate of the direct and indirect gaussian multiterminal source coding problems can be derived in a unified manner by exploiting the semidefinite partial order of the distortion covariance matrices associated with the minimum mean squared error mmse estimation and the so called reduced optimal linear estimation through which an intimate connection between the lower bound and the berger tung upper bound is revealed we give a new proof of the minimum sum rate of the indirect gaussian multiterminal source coding problem i e the gaussian ceo problem for the direct gaussian multiterminal source coding problem we derive a general lower bound on the sum rate and establish a set of sufficient conditions under which the lower bound coincides with the berger tung upper bound we show that the sufficient conditions are satisfied for a class of sources and distortion constraints in particular they hold for arbitrary positive definite source covariance matrices in the high resolution regime in contrast with the existing proofs the new method does not rely on shannon s entropy power inequality

zero delay joint source channel coding for a bivariate gaussian on a gaussian mac in this paper delay free low complexity joint source channel coding jscc for transmission of two correlated gaussian memoryless sources over a gaussian multiple access channel gmac is considered the main contributions of the paper are two distributed jscc schemes one discrete scheme based on nested scalar quantization and one hybrid discrete analog scheme based on a scalar quantizer and a linear continuous mapping the proposed schemes show promising performance which improves with increasing correlation and are robust against variations in noise level both schemes also exhibit a constant gap to the performance upper bound when the channel signal to noise ratio gets large

sending a bivariate gaussian over a gaussian mac we study the power versus distortion tradeoff for the distributed transmission of a memoryless bivariate gaussian source over a two to one average power limited gaussian multiple access channel in this problem each of two separate transmitters observes a different component of a memoryless bivariate gaussian source the two transmitters then describe their source component to a common receiver via an average power constrained gaussian multiple access channel from the output of the multiple access channel the receiver wishes to reconstruct each source component with the least possible expected squared error distortion our interest is in characterizing the distortion pairs that are simultaneously achievable on the two source components we focus on the equal bandwidth case where the source rate in source symbols per second is equal to the channel rate in channel uses per second we present sufficient conditions and necessary conditions for the achievability of a distortion pair these conditions are expressed as a function of the channel signal to noise ratio snr and of the source correlation in several cases the necessary conditions and sufficient conditions are shown to agree in particular we show that if the channel snr is below a certain threshold then an uncoded transmission scheme is optimal moreover we introduce a source channel vector quantizer scheme which is asymptotically optimal as the snr tends to infinity

shannon kotel nikov mappings in joint source channel coding this paper deals with lossy joint source channel coding for transmitting memoryless sources over awgn channels the scheme is based on the geometrical interpretation of communication by kotel nikov and shannon where amplitudecontinuous time discrete source samples are mapped directly onto the channel using curves or planes the source and channel spaces can have different dimensions and thereby achieving either compression or error control depending on whether the source bandwidth is smaller or larger than the channel bandwidth we present a general theory for 1 n and m 1 dimension changing mappings and provide two examples for a gaussian source and channel where we optimize both a 2 1 bandwidth reducing and a 1 2 bandwidth expanding mapping both examples show high spectral efficiency and provide both graceful degradation and improvement for imperfect channel state information at the transmitter

ldpc based channel coding of correlated sources with iterative joint decoding this letter considers low density parity check ldpc coding of correlated binary sources and a novel iterative joint channel decoding without communication of any side information we demonstrate that depending on the extent of the source correlation additional coding gains can be obtained two stages of iterative decoding are employed during global iterations updated estimates of the source correlation are obtained and passed on to the sum product decoder that performs local iterations with a predefined stopping criterion and or a maximum number of local decoding iterations simulation results indicate that very few global iterations 2 5 are sufficient to reap significant benefits from implicit knowledge of source correlation finally we provide analytical performance bounds for our iterative joint decoder and comparisons with sample simulation results

lossless and near lossless source coding for multiple access networks a multiple access source code masc is a source code designed for the following network configuration a pair of correlated information sequences x sub i sub i 1 sup spl infin and y sub i sub i 1 sup spl infin is drawn independent and identically distributed i i d according to joint probability mass function p m f p x y the encoder for each source operates without knowledge of the other source the decoder jointly decodes the encoded bit streams from both sources the work of slepian and wolf describes all rates achievable by mascs of infinite coding dimension n spl rarr spl infin and asymptotically negligible error probabilities p sub e sup n spl rarr 0 in this paper we consider the properties of optimal instantaneous mascs with finite coding dimension n spl infin and both lossless p sub e sup n 0 and nearlossless p sub e sup n spl rarr 0 performance the interest in near lossless codes is inspired by the discontinuity in the limiting rate region at p sub e sup n 0 and the resulting performance benefits achievable by using near lossless mascs as entropy codes within lossy mascs our central results include generalizations of huffman and arithmetic codes to the masc framework for arbitrary p x y n and p sub e sup n and polynomial time design algorithms that approximate these optimal solutions

analog transmission of correlated sources over fading simo multiple access channels joint source channel coding for discrete time analog sources is an appealing transmission approach because of its extremely low delay and complexity when the users access the channel orthogonally analog transmission of correlated information over fading multiple access channels macs using modulo like mappings provides better performance than uncoded transmission in this paper we propose a simplified decoder for modulo mappings in possibly non orthogonal mac scenarios with a single antenna users and a multiple antenna receiver sphere decoding is investigated to reduce the computational complexity when the number of users is large in addition affordable strategies are proposed to optimize the mapping parameters according to the channel conditions and the source correlation the obtained results show that the use of modulo mappings is suitable when the number of antennas at the receiver is larger than the number of users and for high correlation between user data

iterative joint channel decoding of correlated sources employing serially concatenated convolutional codes this correspondence looks at the problem of joint decoding of serially concatenated convolutional codes scccs used for channel coding of multiple correlated sources we assume a simple model whereby two correlated sources transmit sccc encoded data to a single destination receiver we do not assume the existence of nor do we use channel side information at the receiver in particular we present a novel iterative joint channel decoding algorithm for correlated sources by using the empirical cross correlation measurements at successive decoding iterations to provide extrinsic information to the outer codes of the sccc configuration two levels of soft metric iterative decoding are used at the receiver 1 iterative maximum a posteriori probability map decoding is used for efficient decoding of individual sccc codes local iterations and 2 iterative extrinsic information feedback generated from the estimates of the empirical cross correlation in partial decoding steps is used to pass soft information to the outer decoders of the global joint sccc decoder global iterations we provide analytical results followed by simulation studies confirming the robustness of the cross correlation estimates to channel induced errors justifying the use of such estimates in iterative decoding experimental results suggest that relatively few global iterations two to five during which multiple local iterations are conducted are sufficient to reap significant gains using this approach specially when the sources are highly correlated

characteristics of the process zone at sharp notch roots the classical williams solution for the state of stress at the tip of a semi infinite notch is re visited and the two term singular solution re written in a form making the mode mixity and load magnitude explicit this is used to show that for a 270 solid angle the majority of notch problems exhibit a process zone which is entirely or substantially mode i in character which in turn means that the notch strength may practically be governed by a single elastic parameter a method for finding the practical limit on the load and stress intensity ratio where this holds is described

efficient encoding of low density parity check codes low density parity check ldpc codes can be considered serious competitors to turbo codes in terms of performance and complexity and they are based on a similar philosophy constrained random code ensembles and iterative decoding algorithms we consider the encoding problem for ldpc codes more generally we consider the encoding problem for codes specified by sparse parity check matrices we show how to exploit the sparseness of the parity check matrix to obtain efficient encoders for the 3 6 regular ldpc code for example the complexity of encoding is essentially quadratic in the block length however we show that the associated coefficient can be made quite small so that encoding codes even of length n spl sime 100000 is still quite practical more importantly we show that optimized codes actually admit linear time encoding

encoding of correlated observations an important class of engineering problems involves sensing an environment and making estimates based on the phenomena sensed in the traditional model of this problem the sensors observations are available to the estimator without alteration there is growing interest in em distributed sensing systems in which several observations are communicated to the estimator over channels of limited capacity the observations must be separately encoded so that the target can be estimated with minimum distortion two questions are addressed for a special case of this problem wherein there are two sensors which observe noisy data and communicate with a single estimator 1 if the encoder is unlimited in complexity what communication rates and distortions can be achieved 2 if the encoder must be a quantizer a mapping of a single observation sample into a digital output how can it be designed for good performance the first question is treated by the techniques of information theory it is proved that a given combination of rates and distortion is achievable if there exist degraded versions of the observations that satisfy certain formulas the second question is treated by two approaches in the first the outputs of the quantizers undergo a second stage of encoding which exploits their correlation to reduce the output rate algorithms which design the second stage are presented and tested the second approach is based on the em distributional distance a measure of dissimilarity between two probability distributions an algorithm to modify a quantizer for increased distributional distance is derived and tested

rate region of the quadratic gaussian two encoder source coding problem we determine the rate region of the quadratic gaussian two encoder source coding problem this rate region is achieved by a simple architecture that separates the analog and digital aspects of the compression furthermore this architecture requires higher rates to send a gaussian source than it does to send any other source with the same covariance our techniques can also be used to determine the sum rate of some generalizations of this classical problem our approach involves coupling the problem to a quadratic gaussian ldquoceo problem rdquo

network vector quantization we present an algorithm for designing locally optimal vector quantizers for general networks we discuss the algorithm s implementation and compare the performance of the resulting network vector quantizers to traditional vector quantizers vqs and to rate distortion r d bounds where available while some special cases of network codes e g multiresolution mr and multiple description md codes have been studied in the literature we here present a unifying approach that both includes these existing solutions as special cases and provides solutions to previously unsolved examples

general edge asymptotics of solutions of second order elliptic boundary value problems i this is the first of two papers in which we study the singularities of solutions of second order linear elliptic boundary value problems at the edges of piecewise analytic domains in 3 when the opening angle at the edge is variable there appears the phenomenon of crossing of the exponents of singularities for this case we introduce the appropriate combinations of the simple tensor product singularities that allow us to give estimates in ordinary and weighted sobolev spaces for the regular part of the solution and for the coefficients of the singularities these combinations appear in a natural way as sections of an analytic bundle above the edge their behaviour is described with the help of divided differences of powers of the distance to the edge the class of operators considered includes second order elliptic operators with analytic complex valued coefficients with mixed dirichlet neumann or oblique derivative conditions with our description of the singularities we are able to remove some restrictive hypotheses that were previously made in other works in this first part we prove the basic facts in a simplified framework nevertheless the tools we use are essentially the same in the general situation

regularity of the solutions for elliptic problems on nonsmooth domains in r3 part 2 regularity in neighborhoods of edges this paper is the second in a series of three devoted to the analysis of the regularity of solutions of elliptic problems on nonsmooth domains in 3 the present paper concentrates on the regularity of solutions of the poisson equation in neighbourhoods of edges of a polyhedral domain in the framework of the weighted sobolev spaces and countably normed spaces these results can be generalised to elliptic problems arising from mechanics and engineering for instance the elasticity problem on polyhedral domains hence the results are not only important to understand comprehensively the qualitative and quantitative aspects of the behaviours of the solution and its derivatives of all orders in neighbourhoods of edges but also essential to design an effective computation and analyse the optimal convergence of the finite elements solutions for these problems

weighted norm least squares finite element method for poisson equation in a polyhedral domain this paper concerns poisson equation in a polyhedral domain with corners and edges we apply the least squares finite element method to the reformulated first order system of poisson equation to overcome the difficulties from boundary singularities a weighted norm technique is used to define the least squares functional the method prevents the loss of global accuracy numerical simulations are given to demonstrate the theoretical estimates

orthogonal multiple access with correlated sources achievable region and pragmatic schemes in this paper we consider orthogonal multiple access coded schemes with correlated sources the sources are distributedly encoded and their correlation is exploited at the access point ap in particular we assume that each source uses a classical channel code to transmit through an additive white gaussian noise awgn channel its information to the ap here component decoders associated with the source encoders iteratively exchange soft information by taking into account the source correlation the key goal of this paper is to investigate the ultimate achievable performance limits in terms of a multidimensional feasible region in the space of channel parameters deriving insights on the impact of the number of sources in order to analyze the performance of given coded schemes we propose an extrinsic information transfer exit based approach which allows to determine the corresponding multi dimensional feasible regions on the basis of the proposed analytical framework the performance of pragmatic schemes based on serially concatenated convolutional codes scccs and low density parity check ldpc codes is discussed

a linear encoding approach to index assignment in lossy source channel coding we present a general scheme for the lossy transmission of a source with arbitrary statistics through a noisy channel under the mean square error fidelity criterion our approach is based on transform coding scalar quantization of the transform coefficients and linear encoding of the quantization indices entropy coding and channel coding are merged into a single linear encoding function such that the catastrophic behavior of conventional entropy coding is avoided and the full power of modern coding techniques and iterative belief propagation decoding can be exploited we show that this approach is asymptotically optimal in the limit of large block length for arbitrary source statistics and binary input output symmetric channel in the practical regime of finite block length and low decoding complexity we show through the explicit construction of codes for the lossy transmission of digital images over a binary symmetric channel that our approach yields significant improvements with respect to previously proposed channel optimized quantization schemes and also with respect to the conventional concatenation of state of the art image coding with state of the art channel coding although our constructive example focuses on a special case the approach is general and can be applied to other classes of sources of practical interest

algebraic constructions of shannon codes for regular channels the problem of the explicit construction of encoders achieving shannon s capacity and admitting a simple decoding algorithm is considered a solution based on justesen s idea of variable concatenated codes is given for the case of a symmetric memoryless channel with an input alphabet of prime power order under the assumption that the information messages are equiprobable this construction remains good for a nonsymmetric channel provided the encoding rate is smaller than a well defined pseudocapacity in case the channel is regular it is shown that the error probability after decoding is an exponentially decreasing function of the block length for any encoding rate less than the channel capacity

distributed arithmetic coding for the slepian wolf problem distributed source coding schemes are typically based on the use of channels codes as source codes in this paper we propose a new paradigm named ldquodistributed arithmetic coding rdquo which extends arithmetic codes to the distributed case employing sequential decoding aided by the side information in particular we introduce a distributed binary arithmetic coder for the slepian wolf coding problem along with a joint decoder the proposed scheme can be applied to two sources in both the asymmetric mode wherein one source acts as side information and the symmetric mode wherein both sources are coded with ambiguity at any combination of achievable rates distributed arithmetic coding provides several advantages over existing slepian wolf coders especially good performance at small block lengths and the ability to incorporate arbitrary source models in the encoding process e g context based statistical models in much the same way as a classical arithmetic coder we have compared the performance of distributed arithmetic coding with turbo codes and low density parity check codes and found that the proposed approach is very competitive

quantization as histogram segmentation optimal scalar quantizer design in network systems an algorithm for scalar quantizer design on discrete alphabet sources is proposed the proposed algorithm can be used to design fixed rate and entropy constrained conventional scalar quantizers multiresolution scalar quantizers multiple description scalar quantizers and wyner ziv scalar quantizers the algorithm guarantees globally optimal solutions for conventional fixed rate scalar quantizers and entropy constrained scalar quantizers for the other coding scenarios the algorithm yields the best code among all codes that meet a given convexity constraint in all cases the algorithm run time is polynomial in the size of the source alphabet the algorithm derivation arises from a demonstration of the connection between scalar quantization histogram segmentation and the shortest path problem in a certain directed acyclic graph

iterative decoding threshold analysis for ldpc convolutional codes an iterative decoding threshold analysis for terminated regular ldpc convolutional ldpcc codes is presented using density evolution techniques the convergence behavior of an iterative belief propagation decoder is analyzed for the binary erasure channel and the awgn channel with binary inputs it is shown that for a terminated ldpcc code ensemble the thresholds are better than for corresponding regular and irregular ldpc block codes

extracting edge flux intensity functions for the laplacian the solution to the laplace operator in three dimensional domains in the vicinity of straight edges is presented as an asymptotic expansion involving eigenpairs with their coefficients called edge flux intensity functions efifs the eigenpairs are identical to their two dimensional counterparts over a plane perpendicular to the edge extraction of efifs however cannot be obtained in a straightforward manner over this two dimensional plane a method based on l 2 projection and richardson extrapolation is presented for point wise extraction of efifs from p finite element solutions and illustrated by examples a similar but more efficient method based on energy projection for extracting efifs is proposed

zero error instantaneous coding of correlated sources with length constraints is np complete it is well known that the kraft inequality gives a necessary and sufficient condition on the codeword lengths of a zero error instantaneous code for a single source however generalization for two correlated sources is nontrivial we show that in the slepian wolf configuration even if one source is known at the decoder designing a zero error instantaneous code with given codeword lengths for the other source is np complete

generalized coset codes for distributed binning in many multiterminal communication problems constructions of good source codes involve finding distributed partitions into bins of a collection of quantizers associated with a group of source encoders further computationally efficient procedures to index these bins are also required in this work we consider a constructive approach for distributed binning in an algebraic framework several application scenarios fall under the scope of this paper including the ceo problem distributed source coding and n channel symmetric multiple description source coding with n 2 specifically in this exposition we consider the case of two codebooks while focusing on the gaussian ceo problem with mean squared error reconstruction and with two symmetric observations this problem deals with distributed encoding of correlated noisy observations of a source into descriptions such that the joint decoder having access to them can reconstruct the source with a fidelity criterion we employ generalized coset codes constructed in a group theoretic setting for this approach and analyze the performance in terms of distance properties and decoding algorithms

a new method for derivation of statistical weight of the gentile statistics abstract we present a new method for obtaining the statistical weight of the gentile statistics in a recent paper perez and tun presented an approximate combinatoric and an exact recursive formula for the statistical weight of gentile statistics beginning from bosonic and fermionic cases respectively hernandez perez and tun 2007 in this paper we obtain two exact one combinatoric and one recursive formulae for the statistical weight of gentile statistics by another approach the combinatoric formula is valid only for special cases whereas recursive formula is valid for all possible cases moreover for a given q maximum number of particles that can occupy a level for gentile statistics the recursive formula we have derived gives the result much faster than the recursive formula presented in hernandez perez and tun 2007 when one uses a computer program moreover we obtained the statistical weight for the distribution proposed by dai and xie 2009

map decoding for multi antenna systems with non uniform sources exact pairwise error probability and applications we study the maximum a posteriori map decoding of memoryless non uniform sources over multiple antenna channels our model is general enough to include space time coding blast architectures and single transmit multi receive antenna systems which employ any type of channel coding we derive a closed form expression for the codeword pairwise error probability pep of general multi antenna codes using moment generating function and laplace transform arguments we then consider space time orthogonal block stob coding and prove that similar to the maximum likelihood ml decoding case detection of symbols is decoupled in map decoding we also derive the symbol pep in closed form for stob codes we apply these results in several scenarios first we design a binary antipodal signaling scheme which minimizes the system bit error rate ber under stob coding at a ber of 10 6 this constellation has a channel signal to noise ratio csnr gain of 4 7 db over conventional bpsk signaling for a binary nonuniform source with p0 delta p 0 0 9 we next design space time linear dispersion ld codes which are optimized for the source distribution under the criterion of minimizing the union upper bound on the frame error rate fer two codes are given here one outperforms v blast by 3 5 db and alamouti s code by 12 3 db at an fer of 10 2 for a binary source with p0 0 9 and the other outperforms v blast by 4 2 db at an fer of 10 3 for a uniform source these codes also outperform the ld codes of constructed under a different criteria finally the problem of bit to signal mapping is studied it is shown that for a binary source with p0 0 9 64 qam signaling and ser 10 3 a gain of 3 7 db can be achieved using a better than gray mapping for a system with one transmit and two receive antennas that uses trellis coding with 16 qam signaling a 1 8 db gain over quasi gray mapping and ml decoding is observed when map decoding is used for binary sources with p0 0 9

optimality and approximate optimality of source channel separation in networks we consider the source channel separation architecture for lossy source coding in communication networks it is shown that the separation approach is optimal in two general scenarios and is approximately optimal in a third scenario the two scenarios for which separation is optimal complement each other the first is when the memoryless sources at source nodes are arbitrarily correlated each of which is to be reconstructed at possibly multiple destinations within certain distortions but the channels in this network are synchronized orthogonal and memoryless point to point channels the second is when the memoryless sources are mutually independent each of which is to be reconstructed only at one destination within a certain distortion but the channels are general including multi user channels such as multiple access broadcast interference and relay channels possibly with feedback the third scenario for which we demonstrate approximate optimality of source channel separation generalizes the second scenario by allowing each source to be reconstructed at multiple destinations with different distortions for this case the loss from optimality using the separation approach can be upper bounded when a difference distortion measure is taken and in the special case of quadratic distortion measure this leads to universal constant bounds

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

deterministic annealing based optimization for zero delay source channel coding in networks this paper studies the problem of global optimization of zero delay source channel codes that map between the source space and the channel space under a given transmission power constraint and for the mean square error distortion particularly we focus on two well known network settings the wyner ziv setting where only a decoder has access to side information and the distributed setting where independent encoders transmit over independent channels to a central decoder prior work derived the necessary conditions for optimality of the encoder and decoder mappings along with a greedy optimization algorithm that imposes these conditions iteratively in conjunction with the heuristic noisy channel relaxation method to mitigate poor local minima while noisy channel relaxation is arguably effective in simple settings it fails to provide accurate global optimization in more complicated settings considered in this paper we propose a powerful nonconvex optimization method based on the concept of deterministic annealing which is derived from information theoretic principles and was successfully employed in several problems including vector quantization classification and regression we present comparative numerical results that show strict superiority of the proposed method over greedy optimization methods as well as prior approaches in literature

the relation between properties of gentile statistics and fractional statistics of anyon abstract in this paper we discuss the relationship of two kinds of intermediate statistics the gentile statistics and the fractional statistics of anyons the anyon winding number representation is introduced we construct the transformation between anyon winding number representation and the occupation number representation of particles of gentile statistics we study intermediate statistics quantum bracket and coherent states for anyons in the winding number representation we demonstrate that anyons can be simulated by gentile statistics with a geometric phase

spatially coupled ldpc codes for decode and forward relaying of two correlated sources over the bec we present a decode and forward transmission scheme based on spatially coupled low density parity check sc ldpc codes for a network consisting of two possibly correlated sources one relay and one destination the links between the nodes are modeled as binary erasure channels joint source channel coding with joint channel decoding is used to exploit the correlation the relay performs network coding we derive analytical bounds on the achievable rates for the binary erasure time division multiple access relay channel with correlated sources we then design bilayer sc ldpc codes and analyze their asymptotic performance for this scenario we prove analytically that the proposed coding scheme achieves the theoretical limit for symmetric channel conditions and uncorrelated sources using density evolution we furthermore demonstrate that our scheme approaches the theoretical limit also for non symmetric channel conditions and when the sources are correlated and we observe the threshold saturation effect that is typical for spatially coupled systems finally we give simulation results for large block lengths which validate the de analysis

a representation of angular momentum su 2 algebra abstract this paper seeks to construct a representation of the algebra of angular momentum su 2 algebra in terms of the operator relations corresponding to gentile statistics in which one quantum state can be occupied by n particles first we present an operator realization of gentile statistics then we propose a representation of angular momenta the result shows that there exist certain underlying connections between the operator realization of the gentile statistics and the angular momentum su 2 algebra

on the scaling laws of dense wireless sensor networks the data gathering channel we consider dense wireless sensor networks deployed to observe arbitrary random fields the requirement is to reconstruct an estimate of the random field at a certain collector node this creates a many to one data gathering wireless channel in this note we first characterize the transport capacity of many to one dense wireless networks subject to a constraint on the total average power in particular we show that the transport capacity scales as theta log n when the number of sensors n grows to infinity and the total average power remains fixed we then use this result along with some information theoretic tools to derive sufficient and necessary conditions that characterize the set of observable random fields by dense sensor networks in particular for random fields that can be modeled as discrete random sequences we derive a certain form of source channel coding separation theorem we further show that one can achieve any desired nonzero mean square estimation error for continuous gaussian and spatially bandlimited fields through a scheme composed of single dimensional quantization distributed slepian wolf source coding and the proposed antenna sharing strategy based on our results we revisit earlier conclusions about the feasibility of data gathering applications using dense sensor networks

optimal control of elliptic equations with pointwise constraints on the gradient of the state in nonsmooth polygonal domains this article is concerned with optimal control problems subject to a second order elliptic pde and additional pointwise constraints on the gradient of the state in particular the existence of solutions on nonsmooth polygonal or polyhedral domains is analyzed in this situation the solution operator for the pde does not provide enough regularity to state the pointwise constraint for any right hand side due to the appearance of singularities associated to the corners edges and vertices of the domain further necessary optimality conditions for the solution of the optimization problem in two and three space dimensions are derived however in the three dimensional case certain critical angles along the edges of the domain have to be circumvented in the derivation of the optimality conditions finally the derived optimality conditions are utilized to deduce additional regularity for the control variable

transmission of nonuniform memoryless sources via nonsystematic turbo codes we investigate the joint source channel coding problem of transmitting nonuniform memoryless sources over binary phase shift keying modulated additive white gaussian noise and rayleigh fading channels via turbo codes in contrast to previous work recursive nonsystematic convolutional encoders are proposed as the constituent encoders for heavily biased sources we prove that under certain conditions and when the length of the input source sequence tends to infinity the encoder state distribution and the marginal output distribution of each constituent recursive convolutional encoder become asymptotically uniform regardless of the degree of source nonuniformity we also give a conjecture which is empirically validated on the condition for the higher order distribution of the encoder output to be asymptotically uniform irrespective of the source distribution consequently these conditions serve as design criteria for the choice of good encoder structures as a result the outputs of our selected nonsystematic turbo codes are suitably matched to the channel input since a uniformly distributed input maximizes the channel mutual information and hence achieves capacity simulation results show substantial gains by the nonsystematic codes over previously designed systematic turbo codes furthermore their performance is within 0 74 1 17 db from the shannon limit finally we compare our joint source channel coding system with two tandem schemes which employ a fourth order huffman code performing near optimal data compression and a turbo code that either gives excellent waterfall bit error rate ber performance or good error floor performance at the same overall transmission rate our system offers robust and superior performance at low bers 10 sup 4 while its complexity is lower

on the broadcast capacity of wireless networks with cooperative relays a fundamental problem in wireless networks is determining the broadcast capacity i e the maximum data transfer rate from a given node to every other node in a relay network this paper studies the scaling of the broadcast capacity for a network with a single source and n destinations of which f n are randomly selected to also act as relays in high density networks i e the node density goes to infinity the network area is fixed it is shown that the broadcast capacity is upper bounded by log f n schemes are provided that achieve i log f n throughput if the channel fading is spatially continuous ii log log f n throughput if the channel fading is spatially i i d for extended networks i e the node density is fixed the network area goes to infinity the broadcast capacity is upper bounded by 1 under channel models with fading and path loss exponent 2 a multistage cooperative broadcasting scheme which achieves 1 broadcast rate for the high density extended networks with pathloss channel model is proposed these results quantifies the gains obtained due to cooperation compared to multihop noncooperative broadcasting which has a maximum rate that scales as 1 for high density and 1 log f n 2 for extended networks

numerical methods for extracting edge stress intensity functions in anisotropic three dimensional domains the solution to elasticity problems in three dimensional 3 d polyhedral domains in the vicinity of an edge is represented by a family of eigen functions similar to 2 d domains complemented by shadow functions and their associated edge stress intensity functions esifs which are functions along the edge these are of major engineering importance because failure theories directly or indirectly involve them in isotropic materials one may compute analytically the eigen functions and their shadows z yosibash n omer m costabel m dauge edge stress intensity functions in polyhedral domains and their extraction by a quasi dual function method int j fract 136 2005 37 73 used in conjunction with the quasi dual function method m costabel m dauge z yosibash a quasi dual function method for extracting edge stress intensity functions siam j math anal 35 5 2004 1177 1202 for extracting esifs from finite element solutions however in anisotropic materials and multi material interfaces the analytical derivation becomes intractable and numerical methods are mandatory herein we use p finite element methods p fem for the computation of the eigen pairs and shadow functions together with their duals having computed these the p fem is used again to obtain a fe solution from which we extract approximations of the esifs based on a family of adaptive hierarchical jacobi polynomials of increasing order numerical examples for 3 d isotropic and anisotropic materials are provided for which the eigen pairs and shadow functions are numerically computed and esifs extracted these examples show the efficiency and high accuracy of the numerical approximations 2007 elsevier b v all rights reserved

threshold saturation via spatial coupling why convolutional ldpc ensembles perform so well over the bec convolutional low density parity check ldpc ensembles introduced by felstrom and zigangirov have excellent thresholds and these thresholds are rapidly increasing functions of the average degree several variations on the basic theme have been proposed to date all of which share the good performance characteristics of convolutional ldpc ensembles we describe the fundamental mechanism that explains why convolutional like or spatially coupled codes perform so well in essence the spatial coupling of individual codes increases the belief propagation bp threshold of the new ensemble to its maximum possible value namely the maximum a posteriori map threshold of the underlying ensemble for this reason we call this phenomenon threshold saturation this gives an entirely new way of approaching capacity one significant advantage of this construction is that one can create capacity approaching ensembles with an error correcting radius that is increasing in the blocklength although we prove the threshold saturation only for a specific ensemble and for the binary erasure channel bec empirically the phenomenon occurs for a wide class of ensembles and channels more generally we conjecture that for a large range of graphical systems a similar saturation of the dynamical threshold occurs once individual components are coupled sufficiently strongly this might give rise to improved algorithms and new techniques for analysis

weighted regularization of maxwell equations in polyhedral domains we present a new method of regularizing time harmonic maxwell equations by a bf grad div term adapted to the geometry of the domain this method applies to polygonal domains in two dimensions as well as to polyhedral domains in three dimensions in the presence of reentrant corners or edges the usual regularization is known to produce wrong solutions due the non density of smooth fields in the variational space we get rid of this undesirable effect by the introduction of special weights inside the divergence integral standard finite elements can then be used for the approximation of the solution this method proves to be numerically efficient

scaling laws for dense gaussian sensor networks and the order optimality of separation we investigate the optimal performance of dense sensor networks by studying the joint source channel coding problem there are n uniformly spaced sensor nodes sampling noiselessly a one dimensional spatial random process over an interval 0 u0 the overall goal of the sensor network is for the sensor nodes to code and transmit the measurement samples to a collector node over a cooperative multiple access channel with noisy feedback and for the collector node to reconstruct the entire random process with minimum expected distortion we provide separation based lower and upper bounds for the minimum achievable expected distortion when the underlying random process is gaussian when the gaussian random process satisfies some general conditions such as the eigenvalues of its karhunen loeve expansion decrease roughly inverse polynomially in order x i e the kth eigenvalue is roughly k x we evaluate the lower and upper bounds explicitly and show that they are of the same order for a wide range of power constraints thus for these random processes under these power constraints we show that the minimum achievable expected distortion decreases as log np n 1 x where p n is the sum power constraint on the sensor nodes further we show that the achievability scheme that achieves the lower bound on the distortion is a separation based scheme that is composed of multiterminal rate distortion coding and amplify and forward channel coding therefore we conclude that separation is order optimal for the dense gaussian sensor network scenario under consideration when the underlying random process satisfies some general conditions

a numerical procedure for the determination of certain quantities related to the stress intensity factors in two dimensional elasticity abstract this work is devoted to the investigation of corner and interface singularities in linear elasticity and to the development of a numerical code that computes certain quantities associated with those singularities we compute several terms of the asymptotic expansion of the solution of the elasticity system near the corner or interface which is of the form knr nfn in particular the n and fn we treat our problem as a non linear eigenvalue problem and we use an approach based on the shooting method for boundary value problems to create an analytic function whose zeros are the n above the zeros of this function are then found using an iteration method and a global method to make sure that no zero was overlooked the program works for the general case of anisotropic non homogeneous wedge with general boundary conditions as well as in the case of crossing interfaces in an internal point we test the convergence accuracy robustness efficiency and reliability of the code from those tests it can be seen that the code works quite well for the majority of the applications

on zero error source coding with decoder side information let x y be a pair of random variables distributed over a finite product set v spl times w according to a probability distribution p x y the following source coding problem is considered the encoder knows x while the decoder knows y and wants to learn x without error the minimum zero error asymptotic rate of transmission is shown to be the complementary graph entropy of an associated graph thus previous results in the literature provide upper and lower bounds for this minimum rate further these bounds are tight for the important class of perfect graphs the algorithmic aspects of instantaneous code design are considered next it is shown that optimal code design is np hard an optimal code design algorithm is derived polynomial time suboptimal algorithms are also presented and their average and worst case performance guarantees are established

dirichlet to neumann map for domains with corners and approximate boundary conditions we present in this paper the dirichlet to neumann operator for the wave equation on a straight wedge in r 2 using fourier integral operators as a consequence we recover the classical approximate boundary conditions of orders 1 and 2

improved image decoding over noisy channels using minimum mean squared estimation and a markov mesh joint source channel jsc decoding based on residual source redundancy is a technique for providing channel robustness to quantized data previous work assumed a model equivalent to viewing the encoder noisy channel tandem as a discrete hidden markov model hmm with transmitted indices the hidden states we generalize this hmm based 1 d approach for images using the more powerful hidden markov mesh random field hmmrf model while previous state estimation methods for hmmrfs base estimates on only a causal subset of the observed data our new method uses both causal and anticausal subsets for jsc based image decoding the new method provides significant benefits over several competing techniques

complete state counting for gentile s generalization of the pauli exclusion principle in the present work we perform the complete state counting for gentile s approach to the generalized pauli exclusion principle gpep which has been lacking in the literature we count the total number of ways to allocate n identical particles occupying a group of g states with up to q particles in each state in order to derive an exact expression for the statistical weight our obtained expression for the statistical weight gives the fermionic one for q 1 and for q41 it tends fast to a bosonic weight moreover we perform a numerical comparison between our state counting and wu s corresponding to the haldane wu s formulation of the gpep which implies that gentile s formulation gives rise to more boson like behavior while haldane wu s approach to more fermion like behavior this difference lies on the fact that each formulation has its own state occupation rules on which correlation plays a key role r 2007 published by elsevier b v pacs 05 30 d

unveiling turbo codes some results on parallel concatenated coding schemes a parallel concatenated coding scheme consists of two simple constituent systematic encoders linked by an interleaver the input bits to the first encoder are scrambled by the interleaver before entering the second encoder the codeword of the parallel concatenated code consists of the input bits to the first encoder followed by the parity check bits of both encoders this construction can be generalized to any number of constituent codes parallel concatenated schemes employing two convolutional codes as constituent codes in connection with an iterative decoding algorithm of complexity comparable to that of the constituent codes have been previously shown to yield remarkable coding gains close to theoretical limits they have been named and are known as turbo codes we propose a method to evaluate an upper bound to the bit error probability of a parallel concatenated coding scheme averaged over all interleavers of a given length the analytical bounding technique is then used to shed some light on some crucial questions which have been floating around in the communications community since the proposal of turbo codes

distributed joint source channel coding using unequal error protection ldpc codes this paper presents a general approach to designing distributed joint source channel djsc codes with arbitrary rates for communication of a pair of correlated binary sources over noisy channels in this approach both distributed compression and channel error correction are simultaneously achieved by transmitting for each source a fraction of the information bits together with the parity bits of a systematic channel code this approach is shown to be asymptotically optimal i e any rate pair in the achievable rate region can be approached as the codeword length is increased the practical realization of such a code requi res the design of a pair of channel codes with unequal error protection uep properties determined by the inter source correlation and the channel capacity available to each source towards this end a linear programming based procedure for jointly optimizing the degree profiles of a pair of irregular ldpc codes to achieve the required uep properties is presented experimental results obtained with both binary symmetric channels and binary input gaussian channels are presented which demonstrate that the proposed uep djsc codes can significantly outperform separate source channel codes as well as previously reported joint source channel coding schemes particularly for short codeword lengths