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

modulated lattice vector quantization how to make quantization index modulation an efficient variable rate source coder the design of a variable rate joint watermarking and compression jwc scheme is examined in this paper the proposed approach called modulated lattice vector quantization mlvq is based on dither modulation quantization index modulation dm qim which allows for embedding information while maintaining good coding performance in the first part we propose a specific indexing method to make mlvq with a multidimensional codebook feasible furthermore a quantization parameter estimation was designed to ensure the invertibility of the embedding the limitations of the compression performance of jwc schemes are studied in the second part we show the existence of a coding rate lower bound which depends mainly on the codebook characteristics and dramatically decreases coding performance to circumvent this drawback two improved mlvq schemes are proposed in the first one called arbitrary mlvq the embedding is performed on part of the signal to ensure a low embedding coding ratio in the second one called deadzone mlvq the coding efficiency is further improved by maintaining the sparsity of the quantized host signal it consists in excluding the sparse signal components from the embedding process then thresholding them these schemes both applying wavelet coding demonstrate their efficiency as variable rate coders

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

toward a practical scheme for binary broadcast channels with varying channel quality using dirty paper coding we consider practical schemes for binary dirty paper channels and broadcast channels bcs with two receivers and varying channel quality with the bc application in mind this paper proposes a new design for binary dirty paper coding dpc by exploiting the concept of coset binning the complexity of the system is greatly reduced when compared to the existing works some design challenges of the coset binning approach are identified and addressed the proposed binary dpc system achieves similar performance to the state of the art superposition coding based system while demonstrating significant advantages in terms of complexity and flexibility of system design for binary bcs achieving the capacity generally requires the superposition of a normal channel code and a carefully designed channel code with non uniform bit distribution the non uniform bit distribution is chosen according to the channel conditions therefore to achieve the capacity for binary bcs with varying channel quality it is necessary to use quantization codes of different rates which significantly increases the implementation complexity in this paper we also propose a broadcast scheme that generalizes the concept of binary dpc which we term soft dpc by combining soft dpc with time sharing we achieve a large percentage of the capacity for a wide range of channel quality with little complexity overhead our scheme uses only one fixed pair of codes for users 1 and 2 and a single quantization code which possesses many practical advantages over traditional time sharing and superposition coding solutions and provides strictly better performance

wyner ziv coding over broadcast channels hybrid digital analog schemes a new hybrid digital analog scheme is proposed for lossy transmission of a gaussian source over a bandwidth matched gaussian broadcast channel with source side information available at each receiver the proposed scheme combines two schemes that were previously shown to achieve optimal point to point distortion power tradeoff simultaneously at all receivers under two distinct conditions stated in terms of channel and side information quality parameters for the two receiver case the combined scheme is shown to achieve the same kind of optimality for the entire region in the parameter space sandwiched between those two conditions crucial to this result is a new degree of freedom discovered in designing point to point hybrid digital analog schemes with side information when superimposed with analog transmission the proposed scheme outperforms all previously known schemes even outside the optimality region in the parameter space

on gaussian mimo bc mac duality with multiple transmit covariance constraints owing to the special structure of the gaussian multiple input multiple output mimo broadcast channel bc the associated capacity region computation and beamforming optimization problems are typically non convex and thus cannot be solved directly one feasible approach is to consider the respective dual multiple access channel mac problems which are easier to deal with due to their convexity properties the conventional bc mac duality has been established via bc mac signal transformation and is applicable only for the case in which the mimo bc is subject to a single transmit sum power constraint an alternative approach is based on minimax duality which can be applied to the case of the sum power constraint or per antenna power constraint in this paper the conventional bc mac duality is extended to the general linear transmit covariance constraint ltcc case which includes sum power and per antenna power constraints as special cases the obtained general bc mac duality is applied to solve the capacity region computation for the mimo bc and beamforming optimization for the multiple input single output miso bc respectively with multiple ltccs the relationship between this new general bc mac duality and the minimax duality is also discussed and it is shown that the general bc mac duality leads to simpler problem formulations moreover the general bc mac duality is extended to deal with the case of nonlinear transmit covariance constraints in the mimo bc

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

joint wyner ziv dirty paper coding by modulo lattice modulation the combination of source coding with decoder side information the wyner ziv problem and channel coding with encoder side information the gel fand pinsker problem can be optimally solved using the separation principle in this work we show an alternative scheme for the quadratic gaussian case which merges source and channel coding this scheme achieves the optimal performance by applying a modulo lattice modulation to the analog source thus it saves the complexity of quantization and channel decoding and remains with the task of ldquoshapingrdquo only furthermore for high signal to noise ratio snr the scheme approaches the optimal performance using an snr independent encoder thus it proves for this special case the feasibility of universal joint source channel coding

linear growth harmonic functions on a complete manifold soit m une variete de riemann a n dimensions a courbure de ricci non negative on suppose que le volume des boules geodesiques de rayon r centrees en un point x m satisfait v b x r o r h alors la dimension de l espace des fonctions harmoniques a croissance lineaire sur m doit etre k

superposition signaling in broadcast interference networks it is known that superposition signaling in gaussian interference networks is capable of improving the achievable rate region however the problem of maximizing the rate gain offered by superposition signaling is computationally prohibitive even in the simplest case of two user single input single output interference networks this paper examines superposition signaling for the general multiple input multiple output broadcast gaussian interference networks the problem of maximizing either the sum rate or the minimal user s rate under superposition signaling and dirty paper coding is solved by a computationally efficient path following procedure which requires only a convex quadratic program for each iteration but ensures convergence at least to a locally optimal solution numerical results demonstrate the substantial performance advantage of the proposed approach

on the equivalence of the entropic curvature dimension condition and bochner s inequality on metric measure spaces we prove the equivalence of the curvature dimension bounds of lott sturm villani via entropy and optimal transport and of bakry emery via energy and gamma 2 calculus in complete generality for infinitesimally hilbertian metric measure spaces in particular we establish the full bochner inequality on such metric measure spaces moreover we deduce new contraction bounds for the heat flow on riemannian manifolds and on mms in terms of the l 2 wasserstein distance

practical dirty paper coding with sum codes in this paper we present a practical method to construct dirty paper coding dpc schemes using sum codes unlike the commonly used approach to dpc where the coding scheme involves concatenation of a channel code and a quantization code the proposed method embodies a unified approach that emulates the binning method used in the proof of the dpc result auxiliary bits are used to create the desired number of code vectors in each bin sum codes are obtained when information sequences augmented with auxiliary bits are encoded using linear block codes sum code based dpc schemes can be implemented using any linear block code and entail a relatively small increase in decoder complexity when compared to standard communication schemes they can also lead to significant reduction in transmit power in comparison to standard schemes

capacity region of cooperative multiple access channel with states we consider a two user state dependent multiaccess channel in which the states of the channel are known noncausally to one of the encoders and only strictly causally to the other encoder both encoders transmit a common message and in addition the encoder that knows the states noncausally transmits an individual message we find explicit characterizations of the capacity region of this communication model in both discrete memoryless and memoryless gaussian cases in particular the capacity region analysis demonstrates the utility of the knowledge of the states only strictly causally at the encoder that sends only the common message in general more specifically in the discrete memoryless setting we show that such a knowledge is beneficial and increases the capacity region in general in the gaussian setting we show that such a knowledge does not help and the capacity is same as if the states were completely unknown at the encoder that sends only the common message furthermore we also study the special case in which the two encoders transmit only the common message and show that the knowledge of the states only strictly causally at the encoder that sends only the common message is not beneficial in this case in both discrete memoryless and memoryless gaussian settings the analysis also reveals optimal ways of exploiting the knowledge of the state only strictly causally at the encoder that sends only the common message when such a knowledge is beneficial the encoders collaborate to convey to the decoder a lossy version of the state in addition to transmitting the information messages through a generalized gel fand pinsker binning particularly important in this problem are the questions of 1 optimal ways of performing the state compression and 2 whether or not the compression indices should be decoded uniquely by developing two optimal coding schemes that perform this state compression differently we show that when used as parts of appropriately tuned encoding and decoding processes both compression a la noisy network coding by lim or the quantize map and forward by avestimeher i e with no binning and compression using wyner ziv binning are optimal the scheme that uses wyner ziv binning shares elements with cover and el gamal original compress and forward but differs from it mainly in that backward decoding is employed instead of forward decoding and the compression indices are not decoded uniquely finally by exploring the properties of our outer bound we show that although not required in general the compression indices can in fact be decoded uniquely essentially without altering the capacity region but at the expense of larger alphabets sizes for the auxiliary random variables

nested linear lattice codes for structured multiterminal binning network information theory promises high gains over simple point to point communication techniques at the cost of higher complexity however lack of structured coding schemes limited the practical application of these concepts so far one of the basic elements of a network code is the binning scheme wyner 1974 1978 and other researchers proposed various forms of coset codes for efficient binning yet these schemes were applicable only for lossless source or noiseless channel network coding to extend the algebraic binning approach to lossy source or noisy channel network coding previous work proposed the idea of nested codes or more specifically nested parity check codes for the binary case and nested lattices in the continuous case these ideas connect network information theory with the rich areas of linear codes and lattice codes and have strong potential for practical applications we review these developments and explore their tight relation to concepts such as combined shaping and precoding coding for memories with defects and digital watermarking we also propose a few novel applications adhering to a unified approach

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

a scale space filtering approach for visual feature extraction this paper presents a new integrated approach for detecting visual features which include corners ends arcs and lines the effect of scale space filtering on visual features is studied in detail as it forms the theoretical basis of our work in this approach the outline of the object is first extracted and it is then smoothed by scale space filtering at different scale levels subsequently the local extreme curvature points extracted from the smoothed curve and end candidates are determined to guide the termination of the filtering process information about the curvature of each point at the largest scale level is used to detect the different kinds of visual features several algorithms are proposed to determine corners ends arcs and lines experimental results show that our approach is robust to translation rotation and scaling of the object as well as noise corruption in addition efficient visual features can also be successfully extracted with this approach

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

rotation invariant watermark embedding based on scale adapted characteristic regions rotation invariance is one of the most challenging issues in robust image watermarking this paper presents two rotation invariant watermark embedding schemes in the non subsampled contourlet transform nsct domain based on the scale adapted local regions watermark synchronization is achieved using the scale space feature point based local characteristic regions the first method embeds a binary watermark sequence by partitioning the local regions in a rotation invariant pattern the second method embeds a binary watermark image in a content based manner and the watermark signal is adaptive to the orientation of the image both methods achieve rotation invariant embedding by only using the rotation normalizing angle thus no interpolation operation is performed extensive simulation results and comparisons show that the proposed schemes can efficiently resist both signal processing attacks and geometric attacks

a feature based robust digital image watermarking scheme a robust digital image watermarking scheme that combines image feature extraction and image normalization is proposed the goal is to resist both geometric distortion and signal processing attacks we adopt a feature extraction method called mexican hat wavelet scale interaction the extracted feature points can survive a variety of attacks and be used as reference points for both watermark embedding and detection the normalized image of an image object is nearly invariant with respect to rotations as a result the watermark detection task can be much simplified when it is applied to the normalized image however because image normalization is sensitive to image local variation we apply image normalization to nonoverlapped image disks separately the disks are centered at the extracted feature points several copies of a 16 bit watermark sequence are embedded in the original image to improve the robustness of watermarks simulation results show that our scheme can survive low quality jpeg compression color reduction sharpening gaussian filtering median filtering row or column removal shearing rotation local warping cropping and linear geometric transformations

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

three circles theorems for harmonic functions we proved two three circles theorems for harmonic functions on manifolds in integral sense as one application on manifold with nonnegative ricci curvature whose tangent cone at infinity is the unique metric cone with unique conic measure we showed the existence of nonconstant harmonic functions with polynomial growth this existence result recovered and generalized the former result of ding and led to a complete answer of ni s conjecture furthermore in similar context combining the techniques of estimating the frequency of harmonic functions with polynomial growth which were developed by colding and minicozzi we confirmed their conjecture about the uniform bound of frequency

sharp holder continuity of tangent cones for spaces with a lower ricci curvature bound and applications we prove a new estimate on manifolds with a lower ricci bound which asserts that the geometry of balls centered on a minimizing geodesic can change in at most a holder continuous way along the geodesic we give examples that show that the holder exponent along with essentially all the other consequences that follow from this estimate are sharp among the applications is that the regular set is convex for any non collapsed limit of einstein metrics in the general case of a potentially collapsed limit of manifolds with just a lower ricci curvature bound we show that the regular set is weakly convex and a e convex we also show two conjectures of cheeger colding one of these asserts that the isometry group of any even collapsed limit of manifolds with a uniform lower ricci curvature bound is a lie group the other asserts that the dimension of any limit space is the same everywhere

image watermarking an evolution to content based approaches the paper is focused on the evolution of the watermarking schemes from pixel based approaches to content based methods firstly the field of watermarking is presented its implication in the real word is outlined the second section gives a brief overview of different approaches in the spatial and the frequential domain we then present different content based approaches used to improve the invisibility or the synchronisation of the mark the last section describes our content based scheme the synchronisation of the mark after image processing lies in the use of feature point detectors the image is decomposed into a set of triangles and each triangle is individually marked c 2001 pattern recognition society published by elsevier science ltd all rights reserved

large time behavior of the heat kernel in this paper we study the large time behavior of the heat kernel on complete riemannian manifolds with nonnegative ricci curvature which was studied by p li with additional maximum volume growth assumption following y ding s original strategy by blowing down the metric using cheeger and colding s theory about limit spaces of gromov hausdorff convergence combining with the gaussian upper bound of heat kernel on limit spaces we succeed in reducing the limit behavior of the heat kernel on manifold to the values of heat kernels on tangent cones at infinity of manifold with renormalized measure as one application we get the consistent large time limit of heat kernel in more general context which generalizes the former result of p li furthermore by choosing different sequences to blow down the suitable metric we show the first example manifold whose heat kernel has inconsistent limit behavior which answers an open question posed by p li negatively

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

circularly symmetric watermark embedding in 2 d dft domain in this paper a method for digital image watermarking is described that is resistant to geometric transformations a private key which allows a very large number of watermarks determines the watermark which is embedded on a ring in the dft domain the watermark possesses circular symmetry correlation is used for watermark detection the original image is not required in detection the proposed method is resistant to jpeg compression filtering noise addition scaling translation cropping rotation printing and rescanning experimental results prove the robustness of this method against the aforementioned 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

on uniqueness of tangent cones for einstein manifolds we show that for any ricci flat manifold with euclidean volume growth the tangent cone at infinity is unique if one tangent cone has a smooth cross section similarly for any noncollapsing limit of einstein manifolds with uniformly bounded einstein constants we show that local tangent cones are unique if one tangent cone has a smooth cross section

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

sobolev spaces on warped products abstract we study the structure of sobolev spaces on the cartesian warped products of a given metric measure space and an interval our main results are the characterization of the sobolev spaces in such products the proof that under natural assumptions the warped products possess the sobolev to lipschitz property which is key for geometric applications the results of this paper have been needed in the recent proof of the volume cone to metric cone property of rcd spaces obtained by the first author and de philippis

a comparison of time sharing dpc and beamforming for mimo broadcast channels with many users in this letter we derive the scaling laws of the sum rate for fading multiple input multiple output gaussian broadcast channels using time sharing to the strongest user dirty paper coding dpc and beamforming when the number of users receivers n is large throughout the letter we assume a fix average transmit power and consider a block fading rayleigh channel first we show that for a system with m transmit antennas and users equipped with n antennas the sum rate scales like mloglognn for dpc and beamforming when m is fixed and for any n either growing to infinity or not on the other hand when both m and n are fixed the sum rate of time sharing to the strongest user scales like min m n loglogn therefore the asymptotic gain of dpc over time sharing for the sum rate is m min m n when m and n are fixed it is also shown that if m grows as logn the sum rate of dpc and beamforming will grow linearly in m but with different constant multiplicative factors in this region the sum rate capacity of time sharing scales like nloglogn

riemannian ricci curvature lower bounds in metric measure spaces with finite measure in prior work 4 of the first two authors with savare a new riemannian notion of lower bound for ricci curvature in the class of metric measure spaces x d m was introduced and the corresponding class of spaces denoted by rcd k this notion relates the cd k n theory of sturm and lott villani in the case n to the bakry emery approach in 4 the rcd k property is defined in three equivalent ways and several properties of rcd k spaces including the regularization properties of the heat flow the connections with the theory of dirichlet forms and the stability under tensor products are provided in 4 only finite reference measures m have been considered the goal of this paper is twofold on one side we extend these results to general finite spaces on the other we remove a technical assumption appeared in 4 concerning a strengthening of the cd k condition this more general class of spaces includes euclidean spaces endowed with lebesgue measure complete noncompact riemannian manifolds with bounded geometry and the pointed metric measure limits of manifolds with lower ricci curvature bounds

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

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

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

calculus and heat flow in metric measure spaces and applications to spaces with ricci bounds from below this paper is devoted to a deeper understanding of the heat flow and to the refinement of calculus tools on metric measure spaces x mathsf d mathfrak m our main results are a general study of the relations between the hopf lax semigroup and hamilton jacobi equation in metric spaces x d the equivalence of the heat flow in l 2 x mathfrak m generated by a suitable dirichlet energy and the wasserstein gradient flow of the relative entropy functional mathrm ent mathfrak m in the space of probability measures open image in new window the proof of density in energy of lipschitz functions in the sobolev space w 1 2 x mathsf d mathfrak m a fine and very general analysis of the differentiability properties of a large class of kantorovich potentials in connection with the optimal transport problem is the fourth achievement of the paper our results apply in particular to spaces satisfying ricci curvature bounds in the sense of lott and villani ann math 169 903 991 2009 and sturm acta math 196 65 131 2006 and acta math 196 133 177 2006 and require neither the doubling property nor the validity of the local poincare inequality

local spectral convergence in rcd k n spaces abstract in this paper we give necessary and sufficient conditions for the validity of the local spectral convergence in balls in the setting of rcd spaces

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

metric measure spaces with riemannian ricci curvature bounded from below in this paper we introduce a synthetic notion of riemannian ricci bounds from below for metric measure spaces x d m which is stable under measured gromov hausdorff convergence and rules out finsler geometries it can be given in terms of an enforcement of the lott sturm and villani geodesic convexity condition for the entropy coupled with the linearity of the heat flow besides stability it enjoys the same tensorization global to local and local to global properties in these spaces which we call rcd k spaces we prove that the heat flow which can be equivalently characterized either as the flow associated to the dirichlet form or as the wasserstein gradient flow of the entropy satisfies wasserstein contraction estimates and several regularity properties in particular bakry emery estimates and the l lip feller regularization we also prove that the distance induced by the dirichlet form coincides with d that the local energy measure has density given by the square of cheeger s relaxed slope and as a consequence that the underlying brownian motion has continuous paths all these results are obtained independently of poincare and doubling assumptions on the metric measure structure and therefore apply also to spaces which are not locally compact as the infinite dimensional ones

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

on the loss of single letter characterization the dirty multiple access channel for general memoryless systems the existing information theoretic solutions have a ldquosingle letterrdquo form this reflects the fact that optimum performance can be approached by a random code or a random binning scheme generated using independent and identically distributed copies of some scalar distribution is that the form of the solution of any information theoretic problem in fact some counter examples are known the most famous one is the ldquotwo help onerdquo problem korner and marton showed that if we want to decode the modulo two sum of two correlated binary sources from their independent encodings then linear coding is better than random coding in this paper we provide another counter example the ldquodoubly dirtyrdquo multiple access channel mac like the korner marton problem this is a multiterminal scenario where side information is distributed among several terminals each transmitter knows part of the channel interference while the receiver only observes the channel output we give an explicit solution for the capacity region of the binary doubly dirty mac demonstrate how this region can be approached using a linear coding scheme and prove that the ldquobest known single letter regionrdquo is strictly contained in it we also state a conjecture regarding the capacity loss of single letter characterization in the gaussian case

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

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

scale invariant image recognition based on higher order autocorrelation features we propose a framework and a complete implementation of a translation and scale invariant image recognition system for natural indoor scenes the system employs higher order autocorrelation features of scale space data which permit linear classification an optimal linear classification method is presented which is able to cope with a large number of classes represented by many as well as very few samples in the course of the analysis of our system we examine which numerical methods for feature transformation and classification show sufficient stability to fulfill these demands the implementation has been extensively tested we present the results of our own application and several classification benchmarks

cheeger harmonic functions in metric measure spaces revisited let x d be a complete metric measure space with a locally doubling measure that supports a local weak l2 poincare inequality by assuming a heat semigroup type curvature condition we prove that cheeger harmonic functions are lipschitz continuous on x d gradient estimates for cheeger harmonic functions and solutions to a class of non linear poisson type equations are presented

rotation scale and translation resilient watermarking for images many electronic watermarks for still images and video content are sensitive to geometric distortions for example simple rotation scaling and or translation rst of an image can prevent blind detection of a public watermark in this paper we propose a watermarking algorithm that is robust to rst distortions the watermark is embedded into a one dimensional 1 d signal obtained by taking the fourier transform of the image resampling the fourier magnitudes into log polar coordinates and then summing a function of those magnitudes along the log radius axis rotation of the image results in a cyclical shift of the extracted signal scaling of the image results in amplification of the extracted signal and translation of the image has no effect on the extracted signal we can therefore compensate for rotation with a simple search and compensate for scaling by using the correlation coefficient as the detection measure false positive results on a database of 10 000 images are reported robustness results on a database of 2000 images are described it is shown that the watermark is robust to rotation scale and translation in addition we describe tests examining the watermarks resistance to cropping and jpeg compression

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

local grayvalue invariants for image retrieval this paper addresses the problem of retrieving images from large image databases the method is based on local grayvalue invariants which are computed at automatically detected interest points a voting algorithm and semilocal constraints make retrieval possible indexing allows for efficient retrieval from a database of more than 1 000 images experimental results show correct retrieval in the case of partial visibility similarity transformations extraneous features and small perspective deformations

weighted sum rate optimization for downlink multiuser mimo coordinated base station systems centralized and distributed algorithms this paper considers the joint linear transceiver design problem for the downlink multiuser multiple input multiple output mimo systems with coordinated base stations bss we consider maximization of the weighted sum rate with per bs antenna power constraint problem we propose novel centralized and computationally efficient distributed iterative algorithms that achieve local optimum to the latter problem these algorithms are described as follows first by introducing additional optimization variables we reformulate the original problem into a new problem second for the given precoder matrices of all users the optimal receivers are computed using minimum mean square error mmse method and the optimal introduced variables are obtained in closed form expressions third by keeping the introduced variables and receivers constant the precoder matrices of all users are optimized by using second order cone programming socp and matrix fractional minimization approaches for the centralized and distributed algorithms respectively finally the second and third steps are repeated until these algorithms converge we have shown that the proposed algorithms are guaranteed to converge we also show that the proposed algorithms require less computational cost than that of the existing linear algorithm all simulation results demonstrate that our distributed algorithm achieves the same performance as that of the centralized algorithm moreover the proposed algorithms outperform the existing linear algorithm in particular when each of the users has single antenna we have observed that the proposed algorithms achieve the global optimum

information embedding and the triple role of control we consider the problem of information embedding where the encoder modifies a white gaussian host signal in a power constrained manner to encode a message and the decoder recovers both the embedded message and the modified host signal this partially extends the recent work of sumszyk and steinberg to the continuous alphabet gaussian setting through a control theoretic lens we observe that the problem is a minimalist example of what is called the triple role of control actions we show that a dirty paper coding strategy achieves the optimal rate for perfect recovery of the modified host and the message for any message rate for imperfect recovery of the modified host by deriving bounds on the minimum mean square error mmse in recovering the modified host signal we show that dirty paper coding based strategies are guaranteed to attain within a uniform constant factor of 16 of the optimal weighted sum of power required in host signal modification and the mmse in the modified host signal reconstruction for all weights and all message rates when specialized to the zero rate case our results provide the tightest known lower bounds on the asymptotic costs for the vector version of a famous open problem in decentralized control the witsenhausen counterexample numerically this tighter bound helps us characterize the asymptotically optimal costs for the vector witsenhausen problem to within a factor of 1 3 for all problem parameters improving on the earlier best known bound of 2

on the geometry of metric measure spaces ii we introduce a curvature dimension condition cd k n for metric measure spaces it is more restrictive than the curvature bound underline text curv left m text d m right k introduced in sturm k t 2006 on the geometry of metric measure spaces i acta math 196 65 131 which is recovered as the borderline case cd k the additional real parameter n plays the role of a generalized upper bound for the dimension for riemannian manifolds cd k n is equivalent to text ric m left xi xi right k left xi right 2 and dim m n the curvature dimension condition cd k n is stable under convergence for any triple of real numbers k n l the family of normalized metric measure spaces m d m with cd k n and diameter l is compact condition cd k n implies sharp version of the brunn minkowski inequality of the bishop gromov volume comparison theorem and of the bonnet myers theorem moreover it implies the doubling property and local scale invariant poincare inequalities on balls in particular it allows to construct canonical dirichlet forms with gaussian upper and lower bounds for the corresponding heat kernels

rank constrained separable semidefinite programming with applications to optimal beamforming consider a downlink communication system where multiantenna base stations transmit independent data streams to decentralized single antenna users over a common frequency band the goal of the base stations is to jointly adjust the beamforming vectors to minimize the transmission powers while ensuring the signal to interference noise ratio requirement of each user within the system at the same time it may be necessary to keep the interference generated on other coexisting systems under a certain tolerable level in addition one may want to include general individual shaping constraints on the beamforming vectors this beamforming problem is a separable homogeneous quadratically constrained quadratic program and it is difficult to solve in general in this paper we give conditions under which strong duality holds and propose efficient algorithms for the optimal beamforming problem first we study rank constrained solutions of general separable semidefinite programs sdps and propose rank reduction procedures to achieve a lower rank solution then we show that the sdp relaxation of three classes of optimal beamforming problem always has a rank one solution which can be obtained by invoking the rank reduction procedures

sum rate analysis of multiuser mimo system with zero forcing transmit beamforming in this letter we present the exact sum rate analysis of the multiuser multiple input multiple output mimo systems with zero forcing transmit beamforming zfbf we develop the analytical expressions of the ergodic sum rate for two low complexity user selection strategies for the dual transmit antenna scenario based on the analytical results we examine the parameter optimization problem to properly trade off between channel power gain and directional gain in term of maximizing the ergodic sum rate

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

region based image watermarking we introduce a novel method for embedding and detecting a chaotic watermark in the digital spatial image domain based on segmenting the image and locating regions that are robust to several image manipulations the robustness of the method is confirmed by experimental results that display the immunity of the embedded watermark to several kinds of attacks such as compression filtering scaling cropping and rotation

ricci curvature for metric measure spaces via optimal transport we dene a notion of a measured length space x having nonnegative n ricci curvature for n 2 1 1 or having1 ricci curvature bounded below byk fork2 r the denitions are in terms of the displacement convexity of certain functions on the associated wasserstein metric space p2 x of probability measures we show that these properties are preserved under measured gromov hausdor limits we give geometric and analytic consequences this paper has dual goals one goal is to extend results about optimal transport from the setting of smooth riemannian manifolds to the setting of length spaces a second goal is to use optimal transport to give a notion for a measured length space to have ricci curvature bounded below we refer to 11 and 44 for background material on length spaces and optimal transport respectively further bibliographic notes on optimal transport are in appendix f in the present introduction we motivate the questions that we address and we state the main results to start on the geometric side there are various reasons to try to extend notions of curvature from smooth riemannian manifolds to more general spaces a fairly general setting is that of length spaces meaning metric spaces x d in which the distance between two points equals the inmum of the lengths of curves joining the points in the rest of this introduction we assume that x is a compact length space alexandrov gave a good notion of a length space having curvature bounded below by k with k a real number in terms of the geodesic triangles in x in the case of a riemannian manifold m with the induced length structure one recovers the riemannian notion of having sectional curvature bounded below by k length spaces with alexandrov curvature bounded below by k behave nicely with respect to the gromovhausdor topology on compact metric spaces modulo isometries they form

lower bounds on ricci curvature and the almost rigidity of warped products the basic rigidity theorems for manifolds of nonnegative or positive ricci curvature are the volume cone implies metric cone theorem the maximal diameter theorem cg and the splitting theorem cg each asserts that if a certain geometric quantity volume or diameter is as large as possible relative to the pertinent lower bound on ricci curvature then the metric on the manifold in question is a warped product metric of a particular type in this paper we provide quantitative generalizations of the above mentioned results among the applications are the splitting theorem for gromovhausdorff limit spaces x where mn x ricmn i see fy other applications include the assertion that for complete manifolds m with ricmf 0 and euclidean volume growth all tangent cones at infinity are metric cones compare bkn ct p1 via resealing arguments there are also strong consequences for the local structure of manifolds whose ricci curvature satisfies a fixed lower bound and for their gromov hausdorff limits some of these are announced in ccol for a more detailed discussion see cco2 cco3 cco4 our work further develops and significantly extends techniques which were introduced in col co2 and significantly extended in co3 in order to prove certain stability conjectures of anderson cheeger gromov and perelman the results of col co3 were announced in co4 we briefly review some of those results let dgh denote the gromov hausdorff distance between metric spaces see glp let s denote the unit sphere and recall that s is the unique complete

localization and tensorization properties of the curvature dimension condition for metric measure spaces abstract this is an addendum to the paper k bacher k t sturm localization and tensorization properties of the curvature dimension condition for metric measure spaces j funct anal 259 2010 28 56 we prove the tensorization property for the curvature dimension condition add some detailed calculations including explicit dependence of constants and comment on assumptions and conjectures concerning the local to global statement in bacher and sturm 2010 1 and villani 2009 6 respectively

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

localized image watermarking based on feature points of scale space representation this paper proposes a novel method for content based watermarking based on feature points of an image at each feature point the watermark is embedded after scale normalization according to the local characteristic scale characteristic scale is the maximum scale of the scale space representation of an image at the feature point by binding watermarking with the local characteristics of an image resilience against affine transformations can be obtained easily experimental results show that the proposed method is robust against various image processing steps including affine transformations cropping filtering and jpeg compression