nonlinear kolmogorov equations in infinite dimensional spaces the backward stochastic differential equations approach and applications to optimal control solutions of semilinear parabolic differential equations in infinite dimensional spaces are obtained by means of forward and backward infinite dimensional stochastic evolution equations parabolic equations are intended in a mild sense that reveals to be suitable also towards applications to optimal control

joint source channel coding with side information using hybrid digital analog codes we study the joint source channel coding problem of transmitting a gaussian source over a gaussian channel in two cases i the presence of interference known only to the transmitter and ii in the presence of side information about the source known only to the receiver we introduce hybrid digital analog forms of the costa and wyner ziv coding schemes we present the random coding counterpart of schemes based on lattices proposed by kochman and zamir then we discuss applications of the hybrid digital analog schemes in the case of channel signal to noise ratio mismatch and for lossy multicasting of a common source with bandwidth compression

transmitter optimization for the multi antenna downlink with per antenna power constraints this paper considers the transmitter optimization problem for a multiuser downlink channel with multiple transmit antennas at the base station in contrast to the conventional sum power constraint on the transmit antennas this paper adopts a more realistic per antenna power constraint because in practical implementations each antenna is equipped with its own power amplifier and is limited individually by the linearity of the amplifier assuming perfect channel knowledge at the transmitter this paper investigates two different transmission schemes under the per antenna power constraint a minimum power beamforming design for downlink channels with a single antenna at each remote user and a capacity achieving transmitter design for downlink channels with multiple antennas at each remote user it is shown that in both cases the per antenna downlink transmitter optimization problem may be transformed into a dual uplink problem with an uncertain noise this generalizes previous uplink downlink duality results and transforms the per antenna transmitter optimization problem into an equivalent minimax optimization problem further it is shown that various notions of uplink downlink duality may be unified under a lagrangian duality framework this new interpretation of duality gives rise to efficient numerical optimization techniques for solving the downlink per antenna transmitter optimization problem

duality between channel capacity and rate distortion with two sided state information we show that the duality between channel capacity and data compression is retained when state information is available to the sender to the receiver to both or to neither we present a unified theory for eight special cases of channel capacity and rate distortion with state information which also extends existing results to arbitrary pairs of independent and identically distributed i i d correlated state information s sub 1 s sub 2 available at the sender and at the receiver respectively in particular the resulting general formula for channel capacity c max sub p u x s sub 1 i u s sub 2 y i u s sub 1 assumes the same form as the generalized wyner ziv 1976 rate distortion function r d min sub p u x s sub 1 p x spl i cap u s sub 2 i u s sub 1 x 1 u s sub 2

a proof of marton s coding theorem for the discrete memoryless broadcast channel corresp a simple proof using random partitions and typicality is given for marton s coding theorem for broadcast channels

global regular solutions of second order hamilton jacobi equations in hilbert spaces with locally lipschitz nonlinearities abstract this paper is devoted to the study of a second order hamilton jacobi equation in infinite dimensions with a locally lipschitz continuous hamiltonian h related with a stochastic optimal control problem driven by white noise in an earlier paper the author studied the case of globally lipschitz continuous hamiltonian h this paper is concerned with the case of locally lipschitz continuous h that include e g the quadratic case which appears very frequently in the applications existence uniqueness and c 2 regularity of a local solution follow by methods given previously the heart of the work is the proof of a priori estimates of the c 1 norm of the local solution this has been done by studying properties of nonlinear transition semigroups and by a careful application of them to our problem the results have been applied to a stochastic optimal control problem proving existence of feedback optimal controls

sharp lp estimates for discrete second order riesz transforms we show that multipliers of second order riesz transforms on products of discrete abelian groups enjoy the lp estimate p 1 where p max p q and p and q are conjugate exponents this estimate is sharp if one considers all multipliers of the form i iriri with i 1 and infinite groups in the real valued case we obtain better sharp estimates for some specific multipliers such as i iriri with 0 i 1 these are the first known precise lp estimates for discrete calderon zygmund operators

about riesz transforms on the heisenberg groups see also m1 subsequently several other proofs have been given of probabilistic b ba see also g v or analytic d r p nature also p a meyer has given in m2 a similar result in the gaussian setting the aim of this work is to prove analogous inequalities for the family of heisenberg groups h n instead of the family of euclidean spaces r n the euclidean proofs do not adapt to the non commutative situation of h however our method is reminiscent of some ideas of the proofs by duoandikoetxearubio de francia d r and pisier p a new feature is however the central r6te played by the heat kernel and our proof heavily relies on its explicit expression in h n given by gavean g and hulanicki h let us recall finally that apart from any question of uniformity the boundedness of the riesz transforms on every nilpotent lie group is a well known issue see l v

state dependent parallel gaussian networks with a common state cognitive helper state dependent parallel networks with a common state cognitive helper is studied in which k transmitters wish to send k messages to their corresponding receivers over k state corrupted parallel channels and a helper who knows the state information noncausally wishes to assist these receivers to cancel state interference furthermore the helper also has its own message to be sent simultaneously to its corresponding receiver since the state information is known only to the helper but not to other transmitters transmitter side state cognition and receiver side state interference are mismatched our focus is on the high state power regime i e the state power goes to infinity three sub models are studied model i serves as a basic model which consists of only one transmitter receiver with state corruption pair in addition to a helper that assists the receiver to cancel state in addition to transmitting its own message model ii consists of two transmitter receiver pairs in addition to a helper and only one receiver is interfered by a state sequence model iii generalizes model i to include multiple transmitter receiver pairs with each receiver corrupted by independent state for all models the inner and outer bounds on the capacity region are derived and comparison of the two bounds yields characterization of either full or partial boundary of the capacity region under various channel parameters

the optimal control of a new class of impulsive stochastic neutral evolution integro differential equations with infinite delay abstractin this paper we introduce the optimal control problems governed by a new class of impulsive stochastic partial neutral evolution equations with infinite delay in hilbert spaces first by using stochastic analysis the analytic semigroup theory fractional powers of closed operators and suitable fixed point theorems we prove an existence result of mild solutions for the control systems in the norm without the assumptions of compactness next we derive the existence conditions of optimal pairs of these systems finally application to a nonlinear impulsive stochastic parabolic optimal control system is considered

infinite horizon backward stochastic differential equations and elliptic equations in hilbert spaces solutions of semilinear elliptic differential equations in infinite dimensional spaces are obtained by means of forward and backward infinite dimensional stochastic evolution equations the backward equation is considered on an infinite time horizon and a suitable growth condition replaces the final condition elliptic equations are intended in a mild sense suitable also for applications to optimal control we finally notice that due to the lack of smoothing properties the elliptic partial differential equation considered here could not be treated by analytic methods

approximate capacity of the dirty multiple access channel with partial state information at the encoders in this paper we consider the k user gaussian multiple access channel with multiple independent additive white gaussian interferences each interference is known to exactly one transmitter non causally the capacity region is characterized to within a bounded gap regardless of channel parameters these results are based on a layered modulo lattice scheme which realizes distributed interference cancellation

stochastic optimal control problems and parabolic equations in banach spaces we consider stochastic optimal control problems in banach spaces these problems are related to nonlinear controlled equations with dissipative nonlinearity and are treated via the backward stochastic differential equation approach which also allows us to solve in a mild sense hamilton jacobi bellman equations in banach spaces we apply the results to controlled stochastic heat and wave equations with a cost functional that is well defined on continuous functions and to delay equations in spaces of p integrable functions

on backward stochastic evolution equations in hilbert spaces and optimal control abstract in this paper a new result on the existence and uniqueness of the adapted solution to a backward stochastic evolution equation in hilbert spaces under a non lipschitz condition is established the applicability of this result is then illustrated in a discussion of a concrete backward stochastic partial differential equation furthermore a stochastic maximum principle for optimal control problems of stochastic systems governed by backward stochastic evolution equations in hilbert spaces is obtained

achievable rates of multi antenna downlink channels with peak power constraints this paper considers a gaussian multiple input single output miso broadcast channel with a per antenna peak power constraint or simply peak power constraint it is more realistic to consider the peak power constraint on each transmit antenna because in many practical implementations each antenna is equipped with its own power amplifier assuming the perfect knowledge of the channel state information csi at the transmitter we propose an achievable scheme using dirty tape coding dtc the ideal dirty paper coding dpc which is a capacity achieving scheme for the gaussian multiple input multiple output mimo broadcast channel cannot be used for our model because its optimal input distribution is gaussian and thus the peak power constraint is violated on the other hand the channel input of dtc is uniformly distributed in a fixed range which helps to control the peak power of the transmit signal easily we also present an algorithm that finds capacity achieving beamforming vectors and power allocation factors under a per antenna average power constraint and use the optimized parameters in the proposed scheme simulation results show that the proposed scheme provides gains of 2 7db over a non dtc scheme based on minimum mean square error mmse beamforming at high signal to noise ratio snr when there are three receivers and the transmitter has three antennas

quantization based methods additive attacks performance analysis the main goal of this study consists in the development of the worst case additive attack wcaa for ary quantization based data hiding methods using as design criteria the error probability and the maximum achievable rate of reliable communications our analysis focuses on the practical scheme known as distortion compensated dither modulation dc dm from the mathematical point of view the problem of the worst case attack wca design using probability of error as a cost function is formulated as the maximization of the average probability of error subject to the introduced distortion for a given decoding rule when mutual information is selected as a cost function a solution of the minimization problem should provide such an attacking noise probability density function pdf that will maximally decrease the rate of reliable communications for an arbitrary decoder structure the obtained results demonstrate that within the class of additive attacks the developed attack leads to a stronger performance decrease for the considered class of embedding techniques than the additive white gaussian or uniform noise attacks

superposition coding for side information channels we present simple practical codes designed for the binary and gaussian dirty paper channels we show that the dirty paper decoding problem can be transformed into an equivalent multiple access decoding problem for which we apply superposition coding our concept is a generalization of the nested lattices approach of zamir shamai and erez in a theoretical setting our constructions are capable of achieving capacity using random component codes and maximum likelihood decoding we also present practical implementations of the constructions and simulation results for both dirty paper channels our results for the gaussian dirty paper channel are on par with the best known results for nested lattices we discuss the binary dirty tape channel for which we present a simple effective coding technique finally we propose a framework for extending our approach to general gel fand pinsker channels

hybrid mu miso scheduling with limited feedback using hierarchical codebooks the multiuser mimo mu mimo systems tend to have inter user interference in practical systems with limited feedback practical mu mimo systems with limited feedback can be divided into two classes in general one is zero forcing beamforming zfbf and the other is per user unitary rate control pu2rc which is an extended version of random beamforming rbf to improve performance zfbf needs more feedback bits and pu2rc needs a larger number of users we propose a new hybrid mu miso system which has the advantages of the two mu mimo schemes simultaneously and analyze the sum rate performance and the quantization error of the hybrid scheme the analysis shows how the number of feedback bits the number of users and the signal power affect the sum rate the throughput scaling laws are also derived in the high and the medium snr regimes simulation results show that the proposed hybrid mu miso system performs better than either of the two mu mimo systems with the same number of feedback bits another advantage is that it has lower complexity for codeword search since it has a hierarchical codebook structure

gundy varopoulos martingale transforms and their projection operators on manifolds and vector bundles this paper proves the l p boundedness of generalized first order riesz transforms obtained as conditional expectations of martingale transforms a la gundy varopoulos for quite general diffusions on manifolds and vector bundles several specific examples and applications are presented lie groups of compact type the heisenberg group mathbb su 2 and riesz transforms on forms and spinors

a new achievable rate region for the interference channel a new achievable rate region for the general interference channel which extends previous results is presented and evaluated the technique used is a generalization of superposition coding to the multivariable case a detailed computation for the gaussian channel case clarifies to what extent the new region improves previous ones the capacity of a class of gaussian interference channels is also established

viscosity solutions of fully nonlinear second order equations and optimal stochastic control in infinite dimensions part i the case of bounded stochastic evolutions on etudie des equations elliptiques degenerees d ordre 2 non lineaires de la forme f d 2 u du u x 0 dans h ou h est un espace de hilbert separable x un point generique dans h u une fonction de h r

lp harmonic analysis and radon transforms on the heisenberg group in this paper harmonic analysis in the heisenberg group heisn cn r with group law z t z t z z t t 12im z z is taken to mean the joint spectral theory of the operators l heisenberg laplacian and t t the spectral decomposition of e l2 is given explicitly as e 0 e d where e 1 k 0 1 2 and e z t n 2 n 1 n 2k n 1 exp ie tn 2k exp z 24 n 2k lkn 1 z 22 n 2k where lkn 1 denotes the laguerre polynomial the eigenvalues are it e e n 2k e and l k e k e this decomposition is essentially well known but has not previously been described in this light it is also the decomposition into irreducibles of the representation of the heisenberg motion group semi direct product of heisn and u n on l2 heisn the main result is a summability in lp of the decomposition for e lp 1 p limr 1 rk 0 ed for p 1 only a weaker substitute is available and for p the decomposition is false there is also a plancherel formula for l2 2 2 k e n 2k 0 k e z 0 2dzd a number of explicit examples of the decomposition are computed including part of the schrodinger propagator eisl the heisenberg radon transform is defined by r z t n z t w 0 dw this operator was studied by geller and stein it is shown to be bounded from lp to lq if and only if p 2n 2 2n 1 and q 2n 2 some generalizations of these results to the free step two nilpotent lie groups are given but the results are not as complete

adapted solution of a backward stochastic differential equation abstract let wt t 0 1 be a standard k dimensional weiner process defined on a probability space f p and let ft denote its natural filtration given a f1 measurable d dimensional random vector x we look for an adapted pair of processes x t y t t 0 1 with values in rd and rd k respectively which solves an equation of the form x t t 1 f s x s y s ds t 1 g s x s y s dw s x a linearized version of that equation appears in stochastic control theory as the equation satisfied by the adjoint process we also generalize our results to the following equation x t t 1 f s x s y s ds t 1 g s x s y s dw s x under rather restrictive assumptions on g

on a class of stochastic optimal control problems related to bsdes with quadratic growth in this paper we study a class of stochastic optimal control problems where the drift term of the equation has a linear growth on the control variable the cost functional has a quadratic growth and the control process takes values in a closed set not necessarily compact this problem is related to some backward stochastic differential equations bsdes with quadratic growth and unbounded terminal value we prove that the optimal feedback control exists and the optimal cost is given by the initial value of the solution of the related bsde

viscosity solutions of fully nonlinear second order equations and optimal stochastic control in infinite dimensions iii uniqueness of viscosity solutions for general second order equations we prove here the uniqueness and existence of viscosity solutions for a general class of fully nonlinear second order equations in an infinite dimensional hilbert space the uniqueness is proved using the so called inf and sup convolutions which allow some reduction to finite dimensional problems

analog matching of colored sources to colored channels analog uncoded transmission provides a simple and robust scheme for communicating a gaussian source over a gaussian channel under the mean squared error mse distortion measure unfortunately its performance is usually inferior to the all digital separation based source channel coding solution which requires exact knowledge of the channel at the encoder the loss comes from the fact that except for very special cases e g white source and channel of matching bandwidth bw it is impossible to achieve perfect matching of source to channel and channel to source by linear means we show that by combining prediction and modulo lattice operations it is possible to match any colored gaussian source to any colored gaussian noise channel of possibly different bw hence achieve shannon s optimum attainable performance r d c furthermore when the source and channel bws are equal but otherwise their spectra are arbitrary this scheme is asymptotically robust in the sense that for high signal to noise ratio snr a single encoder independent of the noise variance achieves the optimum performance the derivation is based upon a recent modulo lattice modulation scheme for transmitting a wyner ziv source over a dirty paper channel

an existence and uniqueness result for the navier stokes type equations on the heisenberg group abstract the aim of this paper is to give an existence and uniqueness of solutions for the cauchy problem of the navier stokes type equations associated to the sublaplacian provided by the left invariant vector fields on the heisenberg group to avoid the difficulty of the non commutative which is intrinsic in 2 step stratified lie groups we construct the solenoidal space by using the right invariant vector fields on the heisenberg group

optimal control of nonlocal thermistor equations we are concerned with the optimal control problem of the well known nonlocal thermistor problem i e in studying the heat transfer in the resistor device whose electrical conductivity is strongly dependent on the temperature existence of an optimal control is proved the optimality system consisting of the state system coupled with adjoint equations is derived together with a characterisation of the optimal control uniqueness of solution to the optimality system and therefore the uniqueness of the optimal control is established the last part is devoted to numerical simulations

martingale transforms and related singular integrals byrodrigo banuelosabstract the operators obtained by taking conditional expectation of continuoustime martingale transforms are studied both on the circle t and on r using aburkholder gundy inequality for vector valued martingales it is shown that thevector formed by any number of these operators is bounded on lp r 1 p oo with constants that depend only on p and the norms of the matrices involved as acorollary we obtain a recent result of stein on the boundedness of the riesztransforms on lp k 1 p oo with constants independent of n

on the capacity of the carbon copy onto dirty paper channel the carbon copy onto dirty paper ccdp channel is the compound writing on dirty paper channel in which the channel output is obtained as the sum of the channel input white gaussian noise and a gaussian state sequence randomly selected among a set possible realizations the transmitter has non causal knowledge of the set of possible state sequences but does not know which sequence is selected to produce the channel output we study the capacity of the ccdp channel for two scenarios 1 the state sequences are independent and identically distributed and 2 the state sequences are scaled versions of the same sequence in the first scenario we show that a combination of superposition coding time sharing and gel fand pinsker binning is sufficient to approach the capacity to within 3 bits per channel use for any number of possible state realizations in the second scenario we derive capacity to within 4 bits per channel use for the case of two possible state sequences this result is extended to the ccdp channel with any number of possible state sequences under certain conditions on the scaling parameters which we denote as strong fading regime we conclude by providing some remarks on the capacity of the ccdp channel in which the state sequences have any jointly gaussian distribution

bellman functions and dimension free lp estimates for the riesz transforms in bessel settings abstract in this article we prove dimension free l p boundedness of riesz transforms associated with a bessel differential operator we obtain explicit estimates of the l p norms for the bessel riesz transforms in terms of p establishing a linear behavior with respect to p we use the bellman function technique to prove a bilinear dimension free inequality involving poisson semigroups defined through this bessel operator

optimal control of stochastic differential equations with dynamical boundary conditions in this paper we investigate the optimal control problem for a class of stochastic cauchy evolution problems with nonstandard boundary dynamic and control the model is composed by an infinite dimensional dynamical system coupled with a finite dimensional dynamics which describes the boundary conditions of the internal system in other terms we are concerned with nonstandard boundary conditions as the value at the boundary is governed by a different stochastic differential equation

achievable rates for multiple descriptions consider a sequence of independent identically distributed i i d random variables x l x 2 cdots x n and a distortion measure d x i x i on the estimates x i of x i two descriptions i x in 1 2 cdots 2 nr 1 and j x in 1 2 cdots 2 nr 2 are given of the sequence x x 1 x 2 cdots x n from these two descriptions three estimates i x x2 j x and hat x o i x j x are formed with resulting expected distortions e frac 1 n sum n k 1 d x k hat x mk d m m 0 1 2 we find that the distortion constraints d 0 d 1 d 2 are achievable if there exists a probability mass distribution p x p hat x 1 hat x 2 hat x 0 x with ed x hat x m leq d m such that r 1 i x hat x 1 r 2 i x hat x 2 where i cdot denotes shannon mutual information these rates are shown to be optimal for deterministic distortion measures

multiple description quantization via gram schmidt orthogonalization the multiple description md problem has received considerable attention as a model of information transmission over unreliable channels a general framework for designing efficient md quantization schemes is proposed in this paper we provide a systematic treatment of the el gamal cover egc achievable md rate distortion region and show it can be decomposed into a simplified egc segc region and a superimposed refinement operation furthermore any point in the segc region can be achieved via a successive quantization scheme along with quantization splitting for the quadratic gaussian case the proposed scheme has an intrinsic connection with the gram schmidt orthogonalization which implies that the whole gaussian md rate distortion region is achievable with a sequential dithered lattice based quantization scheme as the dimension of the optimal lattice quantizers becomes large moreover this scheme is shown to be universal for all independent and identically distributed i i d smooth sources with performance no worse than that for an i i d gaussian source with the same variance and asymptotically optimal at high resolution a class of md scalar quantizers in the proposed general framework is also constructed and is illustrated geometrically the performance is analyzed in the high resolution regime which exhibits a noticeable improvement over the existing md scalar quantization schemes

on error exponents of modulo lattice additive noise channels modulo lattice additive noise mlan channels appear in the analysis of structured binning codes for costa s dirty paper channel and of nested lattice codes for the additive white gaussian noise awgn channel in this paper we derive a new lower bound on the error exponents of the mlan channel with a proper choice of the shaping lattice and the scaling parameter the new lower bound coincides with the random coding lower bound on the error exponents of the awgn channel at the same signal to noise ratio snr in the sphere packing and straight line regions this result implies that at least for rates close to channel capacity 1 writing on dirty paper is as reliable as writing on clean paper and 2 lattice encoding and decoding suffer no loss of error exponents relative to the optimal codes with maximum likelihood decoding for the awgn channel

l p dimension free boundedness for riesz transforms associated to hermite functions riesz transforms associated to hermite functions were introduced by s thangavelu who proved that they are bounded operators on 1 p in this paper we give a different proof that allows us to show that the lp norms of these operators are bounded by a constant not depending on the dimension d moreover we define riesz transforms of higher order and free dimensional estimates of the lp bounds of these operators are obtained in order to prove the mentioned results we give an extension of the littlewood paley theory that we believe of independent interest

vector perturbation based on symbol scaling for limited feedback miso downlinks we propose a low complexity vector precoding vp scheme for the downlink of multi user multiple input single output mu miso systems with limited feedback conventional vp requires the use of modulo operation and knowledge of the scaling factor used at the transmitter in order to remove the perturbation quantity at the receiver the latter may be problematic in certain limited feedback scenarios where only quantized versions of the scaling factor can be made available at the receiver to circumvent this shortcoming we propose a modified vp technique where the search of perturbing vectors is limited to the area in the symbol constellation which is constrictive to the information symbols i e the area where the distances from the decision thresholds are increased with respect to a distance threshold by doing this the perturbation quantities can only enhance detection and need not be removed at the receiver successful detection can therefore be done without the use of the modulo operation and the scaling factor which makes the proposed vp scheme applicable to limited feedback scenarios analytical and simulation results show that the performance of the proposed scheme is free of the error floor typically encountered with conventional vp in the presence of limited feedback

exact sum rate analysis of mimo broadcast channels with random unitary beamforming random unitary beamforming rub is an attractive transmission scheme for mimo broadcast channels because of its ability to achieve high sum rate capacity with limited feedback in this letter we derive the exact analytical expressions for the ergodic sum rate of mimo broadcast channels with rub the analysis is facilitated by the development of the complete statistical characterization of ordered beam sinrs for a user which can find their application in many related problems

existence of optimal stochastic controls and global solutions of forward backward stochastic differential equations we consider an optimal stochastic control problem assuming lipschitz conditions and allowing degeneracy of the diffusion coefficient under some structural constraint on the state equation we formulate the problem in the strong form i e we fix the probability space we relate the value function and the feedback law to a forward backward stochastic differential system we prove existence and uniqueness of a global solution to the latter and deduce existence and in some cases uniqueness of an optimal control to solve the coupled forward backward system we use a priori estimates which follow from its control theoretic interpretation

hardy space estimates of hausdorff operators on the heisenberg group abstract this is a continuation of a series of works about hausdorff operator on hardy spaces in the setting of the heisenberg group in this paper we obtain the boundedness from lebesgue spaces to hardy spaces for fractional hausdorff operators and their compositions with riesz transforms we also establish the boundedness for two kinds of special hausdorff operators the hausdorff poisson operator and the hausdorff gauss operator on hardy spaces

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

exponential stability for second order neutral stochastic differential equations with impulses in this paper we investigate the problem on the exponential stability of mild solution for the second order neutral stochastic partial differential equations with impulses by utilising the cosine function theory a set of novel sufficient conditions is derived by establishing an impulsive integral inequality as a final point an example is given to illustrate the effectiveness of the obtained theory

successive refinement for the wyner ziv problem and layered code design we examine successive refinement for the wyner ziv problem described in a recent paper by steinberg and merhav where the authors showed that if the side information for all stages is identical then the jointly gaussian source with squared error distortion measure is successively refinable we first extend this result to the case where the difference between the source and the side information is gaussian and independent of the side information as a byproduct we give an alternative proof that the wyner ziv problem for these sources has no rate loss a result that was recently shown by pradhan et al through invoking the duality between the gaussian wyner ziv problem and the costa problem we then perform layered wyner ziv code design for this general type of source based on nested scalar quantization bit plane coding and low density parity check ldpc code based slepian wolf coding source coding with side information we show that density evolution can be used to analyze the slepian wolf code performance provided that certain symmetry conditions which have been dubbed dual symmetry are satisfied by the hypothetical channel between the source and the side information we also show that the dual symmetry condition is indeed satisfied by the hypothetical channel in our slepian wolf coding setup this justifies the use of density evolution in our ldpc code based slepian wolf code design for wyner ziv coding for the jointly gaussian source our layered coder performs 1 29 to 3 45 db from the wyner ziv bound for rates ranging from 0 47 to 4 68 bits per sample when the side information is laplacian and the source equals the side information plus an independent gaussian noise term our layered coder performs 1 33 to 3 90 db from the wyner ziv bound for rates ranging from 0 48 to 4 64 bits per sample

second order hamilton jacobi equations in infinite dimensions some second order hamilton jacobi equations connected to stochastic optimal control problems for infinite dimensional systems driven by a white noise are studied a direct method to prove existence and uniqueness of mild solutions is developed then this solution is identified as the value function of the related stochastic control problem and a feedback formula for optimal controls is derived

lattice strategies for the dirty multiple access channel in costa s dirty paper channel gaussian random binning is able to eliminate the effect of interference which is known at the transmitter and thus achieve capacity we examine a generalization of the dirty paper problem to a multiple access channel mac setup where structured lattice based binning seems to be necessary to achieve capacity in the dirty mac two additive interference signals are present one known to each transmitter but none to the receiver the achievable rates using costa s gaussian binning vanish if both interference signals are strong in contrast it is shown that lattice strategies lattice precoding can achieve positive rates independent of the interference power furthermore in some cases which depend on the noise variance and power constraints high dimensional lattice strategies are in fact optimal in particular they are optimal in the limit of high snr where the capacity region of the dirty mac with strong interference approaches that of a clean mac whose power is governed by the minimum of the users powers rather than their sum the rate gap at high snr between lattice strategies and optimum rather than gaussian random binning is conjectured to be 1 2 log2 e 6 0 254 bit thus the doubly dirty mac is another instance of a network setting like the korner marton problem where linear structured coding is potentially better than random binning

a stochastic model for electrodeposition process with applications in filtering and boundary control electrodeposition is a complex partially observed mass transfer process driven by several surface reactions without exact model in this article the process uncertainties are described by a finite number of wiener processes in a stochastic model applied in the filtering and control problems these problems are solved as a boundary observation control problem based on a finite diffusion model with uncertainties in the domain interior and on the boundaries a mixed boundary problem is considered on an interval with the dirichlet data on one end bulk solution and neumann data on the other end cathode surface the concentration of oxidising species in the domain interior is unattainable for observations but the flux on the boundary electric current can be measured with a limited accuracy sensor error the total flux for the main and side reactions is controlled by the current density on the cathode surface the disturbing effect of the side reactions is modelled as a noise the concentration of speci

causal state communication the problem of state communication over a discrete memoryless channel with discrete memoryless state is studied when the state information is available strictly causally at the encoder it is shown that block markov encoding in which the encoder communicates a description of the state sequence in the previous block by incorporating side information about the state sequence at the decoder yields the minimum state estimation error when the same channel is used to send additional independent information at the expense of a higher channel state estimation error the optimal tradeoff between the rate of the independent information and the state estimation error is characterized via the capacity distortion function it is shown that any optimal tradeoff pair can be achieved via rate splitting these coding theorems are then extended optimally to the case of causal channel state information at the encoder using the shannon strategy

dimension free lp estimates for single riesz transforms via an h joint functional calculus abstract by using an h joint functional calculus for strongly commuting operators we derive a scheme to deduce the l p boundedness of certain d dimensional riesz transforms from the l p boundedness of appropriate one dimensional riesz transforms moreover the l p bounds we obtain are independent of the dimension the scheme is applied to riesz transforms connected with orthogonal expansions and discrete riesz transforms on products of groups with polynomial growth

optimal control problem for stochastic evolution equations in hilbert spaces in this article we consider an optimal control problem in which the controlled state dynamics is governed by a stochastic evolution equation in hilbert spaces and the cost functional has a quadratic growth the existence and uniqueness of the optimal control are obtained by the means of an associated backward stochastic differential equations with a quadratic growth and an unbounded terminal value as an application an optimal control of stochastic partial differential equations with dynamical boundary conditions is also given to illustrate our results

bsde with quadratic growth and unbounded terminal value in this paper we study the existence of solution to bsde with quadratic growth and unbounded terminal value the main idea consists in using a localization procedure together with a priori bounds

backward stochastic differential equations and partial differential equations with quadratic growth we provide existence comparison and stability results for one dimensional backward stochastic differential equations bsdes when the coefficient or generator f t y z is continuous and has a quadratic growth in z and the terminal condition is bounded we also give in this framework the links between the solutions of bsdes set on a diffusion and viscosity or sobolev solutions of the corresponding semilinear partial differential equations

stochastic equations with delay optimal control via bsdes and regular solutions of hamilton jacobi bellman equations we consider an ito stochastic differential equation with delay driven by brownian motion whose solution by an appropriate reformulation defines a markov process x with values in a space of continuous functions mathbf c with generator mathcal l we then consider a backward stochastic differential equation depending on x with unknown processes y z and we study properties of the resulting system in particular we identify the process z as a deterministic functional of x we next prove that the forward backward system provides a suitable solution to a class of parabolic partial differential equations on the space mathbf c driven by mathcal l and we apply this result to prove a characterization of the fair price and the hedging strategy for a financial market with memory effects we also include applications to optimal stochastic control of differential equation with delay in particular we characterize optimal controls as feedback laws in terms of the process x

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