on the error probability of coded frequency hopped spread spectrum multiple access systems a simple exact calculation is presented of the probability distribution of the number of hits in a block of n symbols in a frequency hopped spread spectrum multiple access communication system while the sequence of hits is not markovian there is an underlying markovian structure that allows the probability distribution of the number of hits to be calculated in a recursive fashion knowing the probability distribution of the number of hits makes it possible to calculate the probability of error for a system employing error correcting codes for several different types of receivers including receivers with both errors and erasures the numerical results show that both the approximation obtained by assuming the actual sequence of hits is markovian and the approximation obtained by assuming the hits are independent are very good when the number of frequency slots is not too small less than five calculations show that assuming the independence of hits gives an error probability accurate to within 1 of the actual error probability assuming the hits are markovian gives error probabilities which are accurate to within 0 001

mixed finite elements for second order elliptic problems in three variables two families of mixed finite elements one based on simplices and the other on cubes are introduced as alternatives to the usual raviart thomas nedelec spaces these spaces are analogues of those introduced by brezzi douglas and marini in two space variables error estimates inl2 andh s are derived

error exponents of modulo additive noise channels with side information at the transmitter consider the optimum strategy for using channel state side information in transmission over a modulo additive noise channel with state dependent noise where the receiver does not have access to the side information si previous work showed that capacity wise the optimum transmitter shifts each code letter by a prediction of the noise sample based on the si we show that this structure achieves also the random coding error exponent and therefore is optimum at some range of rates below capacity specifically the optimum transmitter predictor minimizes the renyi entropy of the prediction error the renyi order depends on the rate and goes to one corresponding to shannon entropy for rates close to capacity in contrast it is shown that this prediction strategy may not be optimal at low transmission rates

wiretap channels implications of the more capable condition and cyclic shift symmetry characterization of the rate equivocation region of a general wiretap channel involves two auxiliary random variables u for rate splitting and v for channel prefixing in this paper we explore specific classes of wiretap channels for which the evaluation of the rate equivocation region is simpler we show that if the wiretap channel is more capable v x is optimal and the boundary of the rate equivocation region is achieved by varying rate splitting u alone conversely we show under a mild condition that if the wiretap channel is not more capable then v x is strictly suboptimal next we focus on the class of cyclic shift symmetric wiretap channels we show that optimal rate splitting u that achieves the boundary of the rate equivocation region is uniform with cardinality vert cal x vert and the prefix channel between optimal u and v is expressed as cyclic shifts of the solution of an auxiliary optimization problem over a single variable we provide a special class of cyclic shift symmetric wiretap channels for which u phi is optimal we apply our results to the binary input cyclic shift symmetric wiretap channels and thoroughly characterize the rate equivocation regions of the bsc bec and bec bsc wiretap channels

modeling diffusion in random heterogeneous media data driven models stochastic collocation and the variational multiscale method in recent years there has been intense interest in understanding various physical phenomena in random heterogeneous media any accurate description simulation of a process in such media has to satisfactorily account for the twin issues of randomness as well as the multilength scale variations in the material properties an accurate model of the material property variation in the system is an important prerequisite towards complete characterization of the system response we propose a general methodology to construct a data driven reduced order model to describe property variations in realistic heterogeneous media this reduced order model then serves as the input to the stochastic partial differential equation describing thermal diffusion through random heterogeneous media a decoupled scheme is used to tackle the problems of stochasticity and multilength scale variations in properties a sparse grid collocation strategy is utilized to reduce the solution of the stochastic partial differential equation to a set of deterministic problems a variational multiscale method with explicit subgrid modeling is used to solve these deterministic problems an illustrative example using experimental data is provided to showcase the effectiveness of the proposed methodology

probabilistic collocation method for flow in porous media comparisons with other stochastic methods 1 an efficient method for uncertainty analysis of flow in random porous media is explored in this study on the basis of combination of karhunen loeve expansion and probabilistic collocation method pcm the random log transformed hydraulic conductivity field is represented by the karhunen loeve expansion and the hydraulic head is expressed by the polynomial chaos expansion probabilistic collocation method is used to determine the coefficients of the polynomial chaos expansion by solving for the hydraulic head fields for different sets of collocation points the procedure is straightforward and analogous to the monte carlo method but the number of simulations required in pcm is significantly reduced steady state flows in saturated random porous media are simulated with the probabilistic collocation method and comparisons are made with other stochastic methods monte carlo method the traditional polynomial chaos expansion pce approach based on galerkin scheme and the moment equation approach based on karhunen loeve expansion klme this study reveals that pcm and klme are more efficient than the galerkin pce approach while the computational efforts are greatly reduced compared to the direct sampling monte carlo method the pcm and klme approaches are able to accurately estimate the statistical moments and probability density function of the hydraulic head

stochastic collocation and mixed finite elements for flow in porous media the aim of this paper is to quantify uncertainty of flow in porous media through stochastic modeling and computation of statistical moments the governing equations are based on darcy s law with stochastic permeability starting from a specified covariance relationship the log permeability is decomposed using a truncated karhunen loeve expansion mixed finite element approximations are used in the spatial domain and collocation at the zeros of tensor product hermite polynomials is used in the stochastic dimensions error analysis is performed and experimentally verified with numerical simulations computational results include incompressible and slightly compressible single and two phase flow

capacity and lattice strategies for canceling known interference we consider the generalized dirty paper channel y x s n e x sup 2 spl les p sub x where n is not necessarily gaussian and the interference s is known causally or noncausally to the transmitter we derive worst case capacity formulas and strategies for strong or arbitrarily varying interference in the causal side information si case we develop a capacity formula based on minimum noise entropy strategies we then show that strategies associated with entropy constrained quantizers provide lower and upper bounds on the capacity at high signal to noise ratio snr conditions i e if n is weak relative to the power constraint p sub x these bounds coincide the optimum strategies take the form of scalar lattice quantizers and the capacity loss due to not having s at the receiver is shown to be exactly the shaping gain 1 2log 2 spl pi e 12 spl ap 0 254 bit we extend the schemes to obtain achievable rates at any snr and to noncausal si by incorporating minimum mean squared error mmse scaling and by using k dimensional lattices for gaussian n the capacity loss of this scheme is upper bounded by 1 2log2 spl pi eg spl lambda where g spl lambda is the normalized second moment of the lattice with a proper choice of lattice the loss goes to zero as the dimension k goes to infinity in agreement with the results of costa these results provide an information theoretic framework for the study of common communication problems such as precoding for intersymbol interference isi channels and broadcast channels

solution of stochastic partial differential equations using galerkin finite element techniques this paper presents a framework for the construction of galerkin approximations of elliptic boundary value problems with stochastic input data a variational formulation is developed which allows among others numerical treatment by the finite element method a theory of a posteriori error estimation and corresponding adaptive approaches based on practical experience can be utilized the paper develops a foundation for treating stochastic partial differential equations pdes which can be further developed in many directions

feedback does not increase the capacity of discrete channels with additive noise we consider discrete time finite alphabet channels with additive random noise we show that output feedback does not increase the capacity of such channels this result holds in the most general case i e for arbitrary additive noise processes

channels with block interference a new class of channel models with memory is presented in order to study various kinds of interference phenomena it is shown among other things that when all other parameters are held fixed channel capacity c is an em increasing function of the memory length while the cutoff rate r 0 generally is a em decreasing function calculations with various explicit coding schemes indicate that c is better than r 0 as a performance measure for these channel models as a partial resolution of this c versus r 0 paradox the conjecture is offered that r 0 is more properly a measure of coding delay rather than of coding complexity

an anisotropic sparse grid stochastic collocation method for partial differential equations with random input data this work proposes and analyzes an anisotropic sparse grid stochastic collocation method for solving partial differential equations with random coefficients and forcing terms input data of the model the method consists of a galerkin approximation in the space variables and a collocation in probability space on sparse tensor product grids utilizing either clenshaw curtis or gaussian knots even in the presence of nonlinearities the collocation approach leads to the solution of uncoupled deterministic problems just as in the monte carlo method this work includes a priori and a posteriori procedures to adapt the anisotropy of the sparse grids to each given problem these procedures seem to be very effective for the problems under study the proposed method combines the advantages of isotropic sparse collocation with those of anisotropic full tensor product collocation the first approach is effective for problems depending on random variables which weigh approximately equally in the solution while the benefits of the latter approach become apparent when solving highly anisotropic problems depending on a relatively small number of random variables as in the case where input random variables are karhunen loeve truncations of smooth random fields this work also provides a rigorous convergence analysis of the fully discrete problem and demonstrates sub exponential convergence in the asymptotic regime and algebraic convergence in the preasymptotic regime with respect to the total number of collocation points it also shows that the anisotropic approximation breaks the curse of dimensionality for a wide set of problems numerical examples illustrate the theoretical results and are used to compare this approach with several others including the standard monte carlo in particular for moderately large dimensional problems the sparse grid approach with a properly chosen anisotropy seems to be very efficient and superior to all examined methods

design of quantizers for decentralized estimation systems the authors consider parameter estimation in decentralized systems with distributed processors they restrict the local processors to be quantizers and consider the optimal design of the systems to minimize the estimation error they present necessary conditions for the optimal system based on the bayes distortion functions and fisher s information the numerical results compare the resulting quantizers obtained by different distortion criteria

noise prediction for channels with side information at the transmitter the computation of channel capacity with side information at the transmitter side but not at the receiver side requires in general extension of the input alphabet to a space of strategies and is often hard we consider the special case of a discrete memoryless module additive noise channel y x z sub s where the encoder observes causally the random state s spl isin s that governs the distribution of the noise z sub s we show that the capacity of this channel is given by c log spl chi min sub t s spl rarr spl chi h z sub s t s this capacity is realized by a state independent code followed by a shift by the noise prediction t sub min s that minimizes the entropy of z sub s t s if the set of conditional noise distributions p z s s spl isin s is such that the optimum predictor t sub min spl middot is independent of the state weights then c is also the capacity for a noncausal encoder that observes the entire state sequence in advance furthermore for this case we also derive a simple formula for the capacity when the state process has memory

memoryless multiple access channel with asymmetric noisy state information at the encoders the problem of reliable communication over the memoryless state dependent multiple access channel mac is considered where the encoders and the decoder are provided with various degrees of asymmetric noisy channel state information csi for the case where the encoders observe causal asymmetric noisy csi and the decoder observes complete csi inner and outer bounds to the capacity region which are tight for the sum rate capacity are provided next single letter characterizations for the channel capacity regions under each of the following system settings are established 1 the csi at the encoders are asymmetric deterministic functions of the csi at the decoder and the encoders have noncausal noisy csi 2 the encoders observe asymmetric noisy csi with asymmetric delays and the decoder observes complete csi 3 a degraded message set scenario with asymmetric noisy csi at the encoders and complete and or noisy csi at the decoder the main component in these results is a generalization of a recently introduced converse coding approach for the mac with asymmetric quantized csi at the encoders and herein considerably extended and adapted for the noisy csi setup

writing on dirty paper corresp a channel with output y x s z is examined the state s sim n 0 qi and the noise z sim n 0 ni are multivariate gaussian random variables i is the identity matrix the input x in r n satisfies the power constraint l n sum i 1 n x i 2 leq p if s is unknown to both transmitter and receiver then the capacity is frac 1 2 ln 1 p n q nats per channel use however if the state s is known to the encoder the capacity is shown to be c ast frac 1 2 ln 1 p n independent of q this is also the capacity of a standard gaussian channel with signal to noise power ratio p n therefore the state s does not affect the capacity of the channel even though s is unknown to the receiver it is shown that the optimal transmitter adapts its signal to the state s rather than attempting to cancel it

multiuser demodulation and iterative decoding for frequency hopped networks demodulation and decoding for frequency hopped spread spectrum multiple access fh ssma systems have been traditionally conducted by conventional single user noncollaborative demodulation and error and erasure correcting decoding techniques in this paper we study the demodulation and decoding aspects of collaborative multiuser reception for fh ssma and propose methods which increase the number of users the system can support in particular we propose and analyze the optimum maximum a priori probability demodulation of multiple symbols or type and the use of iterative multiuser decoding after the demodulation since hits from one or two other users are the most likely hit events in fh ssma the joint demodulation of two or of three users is performed based on likelihood ratio tests m ary frequency shift keying modulation with noncoherent demodulation and reed solomon codes with hard decision minimum distance decoding are used in the fh ssma system results are derived for both synchronous and asynchronous frequency hop systems the performance of the proposed multiuser detector in additive white gaussian noise and flat rayleigh fading channels is evaluated scenarios when all simultaneous users or only a subset of them are collaboratively demodulated and decoded are simulated

scales of fluctuation and the propagation of uncertainty in random porous media the mechanics of transport and flow in a random porous medium are addressed in this paper the hydraulic properties of the porous medium are modeled as spatial random processes the heterogeneity of the medium is modeled as a superposition of scales of heterogeneity that are statistically uncorrelated the stochastic process making up a hydraulic property is thus represented as a linear combination of normalized deterministic shapes multiplied by a set of uncorrelated random variables the karhunen loeve expansion is used to formalize this representation the uncertainty contained in each of these scales is then propagated through the system using the governing differential equation as a constraint the solution process will thus consist of the original scales used to represent the porous medium as well as various interaction between these scales the objective of this paper is to develop a procedure for quantifying the uncertainty in the field variables using the scales of fluctuation of the porous medium as the measuring stick

multiple access capability of frequency hopped spread spectrum revisited an analysis of the effect of unequal power levels a method for the evaluation of the probability of error of uncoded asynchronous frequency hopped spread spectrum multiple access communications is presented for systems with binary fsk modulation this method provides an accurate approximation and a tight upper bound to the bit error probability for systems with m ary fsk modulation it provides tight upper bounds to the symbol error probability the method enables the computationally efficient averaging of the error probability with respect to the delays phase angles and data streams of the different users it relies on the integration of the product of the characteristic function of the envelope of the branch of the bfsk demodulator which carries the desired signal and of the derivative of the characteristic function of the envelope of the other branch for sufficient frequency separation between the bfsk tones the method can achieve any desirable accuracy moreover the computational effort required for its evaluation grows linearly with the number of interfering users in the m ary case tight upper bounds based on the union bound and the results of the binary case are derived the method allows the effect of unequal power levels on other user interference in fh ssma systems to be quantified accurately for the first time the results indicate that the fh ssma systems suffer from the near far problem although less seriously than direct sequence ssma systems

quantization for decentralized hypothesis testing under communication constraints in a decentralized hypothesis testing network several peripheral nodes observe an environment and communicate their observations to a central node for the final decision the presence of capacity constraints introduces theoretical and practical problems the following problem is addressed given that the peripheral encoders that satisfy these constraints are scalar quantizers how should they be designed in order that the central test to be performed on their output indices is most powerful the scheme is called cooperative design separate encoding since the quantizers process separate observations but have a common goal they seek to maximize a system wide performance measure the bhattacharyya distance of the joint index space as such a criterion is suggested and a design algorithm to optimize arbitrarily many quantizers cyclically is proposed a simplified version of the algorithm namely an independent design separate encoding scheme where the correlation is either absent or neglected for the sake of simplicity is outlined performances are compared through worked examples

a stochastic collocation method for elliptic partial differential equations with random input data in this paper we propose and analyze a stochastic collocation method to solve elliptic partial differential equations with random coefficients and forcing terms input data of the model the input data are assumed to depend on a finite number of random variables the method consists in a galerkin approximation in space and a collocation in the zeros of suitable tensor product orthogonal polynomials gauss points in the probability space and naturally leads to the solution of uncoupled deterministic problems as in the monte carlo approach it can be seen as a generalization of the stochastic galerkin method proposed in i babuscka r tempone and g e zouraris siam j numer anal 42 2004 pp 800 825 and allows one to treat easily a wider range of situations such as input data that depend nonlinearly on the random variables diffusivity coefficients with unbounded second moments and random variables that are correlated or even unbounded we provide a rigorous convergence analysis and demonstrate exponential convergence of the probability error with respect to the number of gauss points in each direction in the probability space under some regularity assumptions on the random input data numerical examples show the effectiveness of the method

entropy amplification property and the loss for writing on dirty paper costa s celebrated ldquowriting on dirty paperrdquo wdp shows that the power constrained channel y x s z with gaussian z has the same capacity as the standard awgn channel y x z provided that the ldquointerferencerdquo s no matter how strong it is is known at the transmitter while this ability for perfect interference cancelation is very appealing it relies heavily on the gaussianity of the unknown noise z we construct an example of ldquobadrdquo noise for writing on dirty paper namely ldquodifference set noiserdquo if the interference s is strong then difference set noise limits the wdp capacity to at most 2 bits at the same time like in the awgn case the zero interference capacity grows without bound with the input constraint thus almost 100 of the available capacity is lost in wdp in the presence of difference set noise this high capacity loss is due to the ldquoentropy amplification propertyrdquo eap of noise with an aperiodic probability distribution using the eap and the duality between wdp and wyner ziv source coding we also give an example of dramatic rate loss in quantizing encrypted source