on optimal gaussian signaling in mimo relay channels with partial decode and forward for gaussian multiple input multiple output mimo relay channels with partial decode and forward the optimal type of input distribution is still an open question in general recent research has revealed that in some other scenarios with unknown optimal input distributions e g interference channels improper i e noncircular gaussian distributions can outperform proper circular gaussian distributions in this paper we show that this is not the case for partial decode and forward in the gaussian mimo relay channel with gaussian transmit signals i e we show that a proper gaussian input distribution is the optimal one among all gaussian distributions in order to prove this property an innovation covariance matrix is introduced and a decomposition is performed by considering the optimization over this matrix as an outer problem a key point for showing optimality of proper signals then is a reformulation that reveals that one of the subproblems is equivalent to a sum rate maximization in a two user mimo broadcast channel under a sum covariance constraint for which the optimality of proper signals can be shown

lattice codes for the gaussian relay channel decode and forward and compress and forward lattice codes are known to achieve capacity in the gaussian point to point channel achieving the same rates as i i d random gaussian codebooks lattice codes are also known to outperform random codes for certain channel models that are able to exploit their linearity in this paper we show that lattice codes may be used to achieve the same performance as known i i d gaussian random coding techniques for the gaussian relay channel and show several examples of how this may be combined with the linearity of lattices codes in multisource relay networks in particular we present a nested lattice list decoding technique in which lattice codes are shown to achieve the decode and forward df rate of single source single destination gaussian relay channels with one or more relays we next present two examples of how this df scheme may be combined with the linearity of lattice codes to achieve new rate regions which for some channel conditions outperform analogous known gaussian random coding techniques in multisource relay channels that is we derive a new achievable rate region for the two way relay channel with direct links and compare it to existing schemes and derive a new achievable rate region for the multiple access relay channel we furthermore present a lattice compress and forward cf scheme for the gaussian relay channel which exploits a lattice wyner ziv binning scheme and achieves the same rate as the cover el gamal cf rate evaluated for gaussian random codes these results suggest that structured lattice codes may be used to mimic and sometimes outperform random gaussian codes in general gaussian networks

joint optimization of the transmit covariance and relay precoder in general gaussian amplify and forward relay channels the maximum data rate that can be achieved by the strictly causal full duplex amplify and forward af scheme in general gaussian relay channels is achieved by gaussian codebooks and can be cast as the solution of an optimization problem of the input transmit covariance and relay precoder this problem possesses an intricate nonconvex structure and is hence difficult to solve to circumvent this difficulty the relay precoder is assumed to be given and then the karush kuhn tucker conditions are used to obtain closed form expressions for the optimal input covariance corresponding to that precoder these expressions are used to show that subdiagonal precoders suffice to attain the maximum achievable rate of the af scheme at any source transmit power in addition to significantly reducing the effort expended in searching for the optimal relay precoder this observation enables us to find the optimal precoders at low and high source transmit powers for asymptotically low transmit powers the optimal relaying mechanism is shown to possess an interlacing structure thereby resembling half duplex operation in contrast for asymptotically high transmit powers it is optimal for the relay to be silent the asymptotic analysis enables us to develop an explicit formulation for a suboptimal precoder that at intermediate source transmit powers are shown numerically to outperform asymptotically optimal precoders

some estimates for harmonic mappings with given boundary function abstract let w z p f z h z g z be a bounded harmonic mapping defined in the unit disk d with the boundary function f where h z n 1 a n z n and g z n 1 b n z n are analytic in d in this paper using the boundary condition of f we improve the estimate for a n b n in addition if f is a sense preserving homeomorphism of the unit circle onto the boundary of a bounded convex domain then we obtain the sufficient and necessary conditions on f such that w z p f z is a bi lipschitz harmonic mapping which in particular is a quasiconformal mapping

the capacity of the semideterministic relay channel corresp the capacity of the class of relay channels with sender x 1 a relay sender x 2 a relay receiver y 1 f x 1 x 2 and ultimate receiver y is proved to be c max min p x 1 x 2 i x 1 x 2 y h y 1 x 2 i x 1 y x 2 y 1

distributed source coding using abelian group codes a new achievable rate distortion region a distributed source coding problem with a joint distortion criterion that depends on the sources and the reconstruction is considered in this work while the prevalent trend in information theory has been to prove achievability results using shannon s random coding arguments using structured random codes offer rate gains over unstructured random codes for many problems motivated by this a new achievable rate distortion region an inner bound to the performance limit is presented for this problem for discrete memoryless sources based on good structured random nested codes built over abelian groups for certain sources and distortion functions the new rate region is shown to be strictly bigger than the berger tung rate region which has been the best known achievable rate region for this problem till now this is done using numerical plots achievable rates for single user source coding using abelian group codes are also obtained as a corollary of the main coding theorem it is shown that nested linear codes achieve the shannon rate distortion function in the arbitrary discrete memoryless case

numerical conformal mapping methods based on faber series methods are presented for approximating the conformal map from the interior of various regions to the interior of simply connected target regions with a smooth boundary the methods for the disk due to fornberg 1980 and the ellipse due to delillo and elcrat 1993 are reformulated so that they may be extended to other new computational regions the case of a cross shaped region is introduced and developed these methods are used to circumvent the severe ill conditioning due to the crowding phenomenon suffered by conformal maps from the unit disk to target regions with elongated sections while preserving the fast fourier methods available on the disk the methods are based on expanding the mapping function in the faber series for the regions all of these methods proceed by approximating the boundary correspondence of the map with a newton like iteration at each newton step a system of linear equations is solved using the conjugate gradient method the matrix vector multiplication in this inner iteration can be implemented with fast fourier transforms at a cost of o n log n it is shown that the linear systems are discretizations of the identity plus a compact operator and so the conjugate gradient method converges superlinearly several computational examples are given along with a discussion of the accuracy of the methods

nested lattice codes for gaussian relay networks with interference in this paper we consider a class of single source multicast relay networks we assume that all outgoing channels of a node in the network to its neighbors are orthogonal while the incoming signals from its neighbors can interfere with each other we first focus on gaussian relay networks with interference and find an achievable rate using a lattice coding scheme we show that the achievable rate of our scheme is within a constant bit gap from the information theoretic cut set bound where the constant depends only on the network topology but not on the transmit power noise variance and channel gains this is similar to a recent result by avestimehr diggavi and tse who showed an approximate capacity characterization for general gaussian relay networks however our achievability uses a structured code instead of a random one using the idea used in the gaussian case we also consider a linear finite field symmetric network with interference and characterize its capacity using a linear coding scheme

numerical techniques for conformal mapping onto a rectangle abstract this paper is concerned with the problem of determining approximations to the function f which maps conformally a simply connected domain onto a rectangle r so that four specified points on are mapped respectively onto the four vertices of r in particular we study the following two classes of methods for the mapping of domains of the form z x iy 00 1 x 2 x i methods which approximate f r by f s f where f is an approximation to the conformal map of onto the unit disc and s is a simple schwarz christoffel transformation ii methods based on approximating the conformal map of a certain symmetric doubly connected domain onto a circular annulus

linear non regenerative multicarrier mimo relay communications based on mmse criterion in this letter we propose linear non regenerative multicarrier multiple input multiple output mimo relay technique that aims to minimize the mean squared error mse of the signal waveform estimation at the destination we generalize the existing result on the structure of the optimal relay amplifying matrix by considering the direct source destination link to minimize the mse a power loading algorithm is developed which has a significantly reduced computational complexity compared with existing techniques

the accuracy of numerical conformal mapping methods a survey of examples and results this paper shows how the geometry of the region affects the conditioning and the accuracy of numerical conformal mapping methods for simply connected regions especially fourier series methods both explicit examples of popular test cases and more general estimates are discussed the severe ill conditioning that is known as the crowding phenomenon is discussed and its effect on a conformally transplanted boundary value problem is illustrated remarks on various numerical methods are included

on the quasi isometries of harmonic quasiconformal mappings abstract we prove versions of the ahlfors schwarz lemma for quasiconformal euclidean harmonic functions and harmonic mappings with respect to the poincare metric

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

a schwarz pick inequality for harmonic quasiconformal mappings and its applications abstract the main result of this paper is the sharp generalized schwarz pick inequality for euclidean harmonic quasiconformal mappings with convex ranges which generalizes a result given by mateljevic as its applications we obtain the property of quasi isometry with respect to the poincare distance and an analogue of the koebe theorem for this class of mappings

extremal distance harmonic measure and numerical conformal mapping abstract delillo t k and j a pfaltzgraff extremal distance harmonic measure and numerical conformal mapping journal of computational and applied mathematics 46 1993 103 113 estimates of extremal distance and harmonic measure are used to show how the geometric properties of a simply connected domain influence the boundary distortion of a conformal map from the unit disk to the domain numerical examples and remarks on the conditioning of numerical conformal mapping methods are included a sharp estimate is given of the exponential ill conditioning known as the crowding phenomenon which occurs for slender regions

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

joint physical layer coding and network coding for bidirectional relaying we consider a communication system where two transmitters wish to exchange information through a central relay the transmitter and relay nodes exchange data over synchronized average power constrained additive white gaussian noise channels with a real input with signal to noise ratio snr of snr an upper bound on the capacity is 1 2 log 1 snr bits per transmitter per use of the multiple access phase and broadcast phase of the bidirectional relay channel we show that using lattice codes and lattice decoding we can obtain a rate of 1 2 log 1 2 snr bits per transmitter which is essentially optimal at high snr the main idea is to decode the sum of the codewords modulo a lattice at the relay followed by a broadcast phase which performs slepian wolf coding we also show that if the two transmitters use identical lattices with minimum angle decoding we can achieve the same rate of 1 2 log 1 2 snr the proposed scheme can be thought of as a joint physical layer network layer code which outperforms other recently proposed analog network coding schemes

gaussian orthogonal relay channels optimal resource allocation and capacity a gaussian orthogonal relay model is investigated where the source transmits to the relay and destination in channel 1 and the relay transmits to the destination in channel 2 with channels 1 and 2 being orthogonalized in the time frequency plane in order to satisfy practical constraints the total available channel resource time and bandwidth is split into the two orthogonal channels and the resource allocation to the two channels is considered to be a design parameter that needs to be optimized the main focus of the analysis is on the case where the source to relay link is better than the source to destination link which is the usual scenario encountered in practice a lower bound on the capacity achievable rate is derived and optimized over the parameter spl theta which represents the fraction of the resource assigned to channel 1 it is shown that the lower bound achieves the max flow min cut upper bound at the optimizing spl theta the common value thus being the capacity of the channel at the optimizing spl theta furthermore it is shown that when the relay to destination signal to noise ratio snr is less than a certain threshold the capacity at the optimizing spl theta is also the maximum capacity of the channel over all possible resource allocation parameters spl theta finally the achievable rates for optimal and equal resource allocations are compared and it is shown that optimizing the resource allocation yields significant performance gains

on the relay channel with receiver transmitter feedback an achievable rate for the discrete memoryless relay channel with receiver transmitter feedback is proposed based on block markov superposition encoding the achievable rate can also be extended to gaussian channels a second achievable rate for the gaussian relay channel based on a schalkwijk kailath type scheme is presented for some channels both achievable rates strictly improve upon all previously known achievable rates for the discrete memoryless relay channel also a converse result is provided

log determinant relaxation for approximate inference in discrete markov random fields graphical models are well suited to capture the complex and non gaussian statistical dependencies that arise in many real world signals a fundamental problem common to any signal processing application of a graphical model is that of computing approximate marginal probabilities over subsets of nodes this paper proposes a novel method applicable to discrete valued markov random fields mrfs on arbitrary graphs for approximately solving this marginalization problem the foundation of our method is a reformulation of the marginalization problem as the solution of a low dimensional convex optimization problem over the marginal polytope exactly solving this problem for general graphs is intractable for binary markov random fields we describe how to relax it by using a gaussian bound on the discrete entropy and a semidefinite outer bound on the marginal polytope this combination leads to a log determinant maximization problem that can be solved efficiently by interior point methods thereby providing approximations to the exact marginals we show how a slightly weakened log determinant relaxation can be solved even more efficiently by a dual reformulation when applied to denoising problems in a coupled mixture of gaussian model defined on a binary mrf with cycles we find that the performance of this log determinant relaxation is comparable or superior to the widely used sum product algorithm over a range of experimental conditions

on minimal eigenvalues of a class of tridiagonal matrices it is known that the worst case near far resistance of optimum multiuser detectors for asynchronous gaussian multiple access channels can be expressed in terms of a class of block tridiagonal matrices and the minimal eigenvalues of such a class of block tridiagonal matrices serve as a good measure of the worst case near far resistance in this paper we focus on the two user scenario where each block tridiagonal matrix under consideration is a tridiagonal matrix we derive closed form expressions for the minimal eigenvalues of such a class of tridiagonal matrices in terms of the largest real solution of a trigonometric equation in 0 pi we also obtain lower bounds and upper bounds on the minimal eigenvalues which improve on previously known results in the literature

communication over mimo x channels interference alignment decomposition and performance analysis in a multiple antenna system with two transmitters and two receivers a scenario of data communication known as the x channel is studied in which each receiver receives data from both transmitters in this scenario it is assumed that each transmitter is unaware of the other transmitter s data noncooperative scenario this system can be considered as a combination of two broadcast channels from the transmitters points of view and two multiple access channels from the receivers points of view taking advantage of both perspectives two signaling schemes for such a scenario are developed in these schemes some linear filters are employed at the transmitters and at the receivers which decompose the system into either two noninterfering multiple antenna broadcast subchannels or two noninterfering multiple antenna multiple access subchannels the main objective in the design of the filters is to exploit the structure of the channel matrices to achieve the highest multiplexing gain mg it is shown that the proposed noncooperative signaling schemes outperform other known noncooperative schemes in terms of the achievable mg in particular it is shown that in some specific cases the achieved mg is the same as the mg of the system if full cooperation is provided either between the transmitters or between the receivers in the second part of the paper it is shown that by using mixed design schemes rather than decomposition schemes and taking the statistical properties of the interference terms into account the power offset of the system can be improved the power offset represents the horizontal shift in the curve of the sum rate versus the total power in decibels

lattices which are good for almost everything we define an ensemble of lattices and show that for asymptotically high dimension most of its members are simultaneously good as sphere packings sphere coverings additive white gaussian noise awgn channel codes and mean squared error mse quantization codes these lattices are generated by applying construction a to a random linear code over a prime field of growing size i e by lifting the code to spl ropf sup n

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

practical quantizer design for half duplex estimate and forward relaying we propose a quantizer design method for practical half duplex estimate and forward ef relaying first we identify the regime in which ef relaying yields substantial gains where the snr is low and the relay destination link is strong then we discover design simplifications that reduce complexity with little loss in the above regime for relay quantizer design we first consider mean squared distortion minimization to illustrate the unsuitability of the approach we present an example with awgn links and a bpsk source where the quantizer with worst mean squared distortion in a given set maximizes achievable rate a distortion minimizing quantizer attempts to preserve the received signal at the relay the quantizer should instead preserve source information in information theoretical terms the quantizer should maximize the mutual information between the source transmission and the quantizer output conditioned on the side information at the destination subject to a rate constraint the above conclusion derived from information theoretical principles is then translated to a quantizer design method for the low snr regime using ldpc codes of blocklength 100000 bpsk modulation and quantizers designed using the proposed criterion we observe performance less than a decibel away from the achievable rate at a ber of 10 4

quasiconformal and harmonic mappings between jordan domains let and 1 be jordan domains let 0 1 and let f omega mapsto omega 1 be a harmonic homeomorphism the object of the paper is to prove the following results a if f is q c and 1 c 1 then f is lipschitz b if f is q c 1 c 1 and 1 is convex then f is bi lipschitz and c if is the unit disk 1 is convex and 1 c 1 then f is quasiconformal if and only if its boundary function is bi lipschitz and the hilbert transform of its derivative is in l these extend the results of pavlovic ann acad sci fenn 27 365 372 2002

an efficient implementation of a conformal mapping method based on the szego kernel an implementation based on iterative techniques of a method to compute the riemann mapping function is presented the method has been recently introduced by n kerzman and the author it expresses the szego kernel as the solution of an integral equation of the second kind it is shown how to treat symmetric regions the algorithm is tested on five examples the numerical results show that the method is competitive with respect to accuracy stability and efficiency

schwarz pick estimates for holomorphic mappings from the polydisk to the unit ball abstract in this paper schwarz pick estimates of arbitrary order partial derivatives for holomorphic mappings from the polydisk to the unit ball are presented we generalize the early work on schwarz pick estimates of higher order derivatives for bounded holomorphic functions on the unit disk and the polydisk

on the reliability function of the discrete memoryless relay channel bounds on the reliability function for the discrete memoryless relay channel are derived using the method of types two achievable error exponents are derived based on partial decode forward and compress forward which are well known superposition block markov coding schemes the derivations require combinations of the techniques involved in the proofs of csiszar korner marton s packing lemma for the error exponent of channel coding and marton s type covering lemma for the error exponent of source coding with a fidelity criterion the decode forward error exponent is evaluated on sato s relay channel from this example it is noted that to obtain the fastest possible decay in the error probability for a fixed effective coding rate one ought to optimize the number of blocks in the block markov coding scheme assuming the blocklength within each block is large an upper bound on the reliability function is also derived using ideas from haroutunian s lower bound on the error probability for point to point channel coding with feedback

ergodic interference alignment this paper develops a new communication strategy ergodic interference alignment for the k user interference channel with time varying fading at any particular time each receiver will see a superposition of the transmitted signals plus noise the standard approach to such a scenario results in each transmitter receiver pair achieving a rate proportional to 1 k its interference free ergodic capacity however given two well chosen time indices the channel coefficients from interfering users can be made to exactly cancel by adding up these two observations each receiver can obtain its desired signal without any interference if the channel gains have independent uniform phases this technique allows each user to achieve at least 1 2 its interference free ergodic capacity at any signal to noise ratio prior interference alignment techniques were only able to attain this performance as the signal to noise ratio tended to infinity extensions are given for the case where each receiver wants a message from more than one transmitter as well as the x channel case with two receivers where each transmitter has an independent message for each receiver finally it is shown how to generalize this strategy beyond gaussian channel models for a class of finite field interference channels this approach yields the ergodic capacity region

data processing bounds for scalar lossy source codes with side information at the decoder in this paper we introduce new lower bounds on the distortion of scalar fixed rate codes for lossy compression with side information available at the receiver these bounds are derived by presenting the relevant random variables as a markov chain and applying generalized data processing inequalities a la ziv and zakai we show that by replacing the logarithmic function with other functions in the data processing theorem we formulate we obtain new lower bounds on the distortion of scalar coding with side information at the decoder the usefulness of these results is demonstrated for uniform sources and the convex function q t t1 1 the bounds in this case are shown to be better than one can obtain from the wyner ziv rate distortion function

representation of conformal maps by rational functions the traditional view in numerical conformal mapping is that once the boundary correspondence function has been found the map and its inverse can be evaluated by contour integrals we propose that it is much simpler and 10 1000 times faster to represent the maps by rational functions computed by the aaa algorithm to justify this claim first we prove a theorem establishing root exponential convergence of rational approximations near corners in a conformal map generalizing a result of d j newman in 1964 this leads to the new algorithm for approximating conformal maps of polygons then we turn to smooth domains and prove a sequence of four theorems establishing that in any conformal map of the unit circle onto a region with a long and slender part there must be a singularity or loss of univalence exponentially close to the boundary and polynomial approximations cannot be accurate unless of exponentially high degree this motivates the application of the new algorithm to smooth domains where it is again found to be highly effective

diversity analysis of randomized linear dispersion codes in a half duplex amplify and forward multiple relay system a point to point multiple relay communication system with half duplex constraints is considered the relays operate under the amplify and forward paradigm and implement a linear dispersion distributed space time code with randomized dispersion matrices of independent and identically distributed entries the large signal to noise ratio behavior of the asymptotically large deterministic system is studied for both the optimum maximum likelihood receiver and the linear minimum mean squared error lmmse receiver the diversity order of the system is shown to have a strong dependence on the aspect ratio of the linear dispersion matrices more specifically when the linear dispersion matrices are sufficiently tall both receivers achieve the maximum diversity order i e the total number of relays plus one conversely when the linear dispersion matrices are fat in the sense that relays linearly compress the information received from the source the optimum receiver is shown to achieve an asymptotic diversity order of two whereas the lmmse receiver is totally unable to exploit the available spatial diversity

the approximate capacity of the many to one and one to many gaussian interference channels recently etkin tse and wang found the capacity region of the two user gaussian interference channel to within 1 bit s hz a natural goal is to apply this approach to the gaussian interference channel with an arbitrary number of users we make progress towards this goal by finding the capacity region of the many to one and one to many gaussian interference channels to within a constant number of bits the result makes use of a deterministic model to provide insight into the gaussian channel the deterministic model makes explicit the dimension of signal level a central theme emerges the use of lattice codes for alignment of interfering signals on the signal level

bounds on capacity and minimum energy per bit for awgn relay channels upper and lower bounds on the capacity and minimum energy per bit for general additive white gaussian noise awgn and frequency division awgn fd awgn relay channel models are established first the max flow min cut bound and the generalized block markov coding scheme are used to derive upper and lower bounds on capacity these bounds are never tight for the general awgn model and are tight only under certain conditions for the fd awgn model two coding schemes that do not require the relay to decode any part of the message are then investigated first it is shown that the side information coding scheme can outperform the block markov coding scheme it is also shown that the achievable rate of the side information coding scheme can be improved via time sharing in the second scheme the relaying functions are restricted to be linear the problem is reduced to a single letter nonconvex optimization problem for the fd awgn model the paper also establishes a relationship between the minimum energy per bit and capacity of the awgn relay channel this relationship together with the lower and upper bounds on capacity are used to establish corresponding lower and upper bounds on the minimum energy per bit that do not differ by more than a factor of 1 45 for the fd awgn relay channel model and 1 7 for the general awgn model

low delay prediction and transform based wyner ziv coding this paper studies low delay wyner ziv coding i e lossy source coding with side information at the decoder with emphasis on the extreme of zero delay to achieve zero delay a scalar quantizer is followed by scalar coding of quantization indices in the fixed length coding scenario under high resolution assumptions and appropriately defined decodability constraints the optimal quantization level density is conjectured to be periodic this conjecture which is provable when the correlation is high allows for a precise analysis of the rate distortion tradeoff the performance of variable length coding with periodic quantization is also characterized the results are then incorporated in predictive wyner ziv coding for gaussian sources with memory and optimal prediction filters are numerically designed so as to strike a balance between maximally exploiting both temporal and spatial correlation and limiting the propagation of distortion due to occasional decoding errors finally the zero delay schemes are also employed in transform coding with small block lengths where the gaussian source and side information are transformed separately with the premise that corresponding transform coefficient pairs exhibit good spatial correlation and minimal temporal correlation for the specific source side information pairs studied it is shown that transform coding even with a small block length outperforms predictive coding performances of both predictive and transform coding are also compared with the asymptotic rate distortion bounds

boundary schwarz lemma for pluriharmonic mappings between unit balls abstract in this paper we get a schwarz lemma for pluriharmonic mappings between the unit balls of any dimensions which generalizes classical schwarz lemma for bounded harmonic functions to higher dimensions as an application of the schwarz lemma obtained a boundary schwarz lemma is established for pluriharmonic mappings between unit balls with any dimensions

a joint time invariant filtering approach to the linear gaussian relay problem in this paper the linear gaussian relay problem is considered under the linear time invariant lti model the rate maximization problem in the linear gaussian relay channel is formulated in the frequency domain based on the toeplitz distribution theorem under the further assumption of realizable input spectra the rate maximization problem is converted to the problem of joint source and relay filter design with two power constraints one at the source and the other at the relay and a practical solution to this problem is proposed based on the adaptive projected sub gradient method numerical results show that the proposed method yields a considerable gain over the instantaneous amplify and forward af scheme in inter symbol interference isi channels also the optimality of the af scheme within the class of one tap relay filters is established in flat fading channels

gradient of mutual information in linear vector gaussian channels this paper considers a general linear vector gaussian channel with arbitrary signaling and pursues two closely related goals i closed form expressions for the gradient of the mutual information with respect to arbitrary parameters of the system and ii fundamental connections between information theory and estimation theory generalizing the fundamental relationship recently unveiled by guo shamai and verdu spl acute we show that the gradient of the mutual information with respect to the channel matrix is equal to the product of the channel matrix and the error covariance matrix of the best estimate of the input given the output gradients and derivatives with respect to other parameters are then found via the differentiation chain rule

wyner ziv coding based on tcq and ldpc codes this paper considers trellis coded quantization tcq and low density parity check ldpc codes for the quadratic gaussian wyner ziv coding problem after tcq of the source x ldpc codes are used to implement slepian wolf coding of the quantized source q x with side information y at the decoder assuming 256 state tcq and ideal slepian wolf coding in the sense of achieving the theoretical limit h q x y we experimentally show that slepian wolf coded tcq performs 0 2 db away from the wyner ziv distortion rate function dwz r at high rate this result mirrors that of entropy constrained tcq in classic source coding of gaussian sources furthermore using 8 192 state tcq and assuming ideal slepian wolf coding our simulations show that slepian wolf coded tcq performs only 0 1 db away from dwz r at high rate these results establish the practical performance limit of slepian wolf coded tcq for quadratic gaussian wyner ziv coding practical designs give performance very close to the theoretical limit for example with 8 192 state tcq irregular ldpc codes for slepian wolf coding and optimal non linear estimation at the decoder our performance gap to dwz r is 0 20 db 0 22 db 0 30 db and 0 93 db at 3 83 bit per sample b s 1 83 b s 1 53 b s and 1 05 b s respectively when 256 state 4 d trellis coded vector quantization instead of tcq is employed the performance gap to dwz r is 0 51 db 0 51 db 0 54 db and 0 80 db at 2 04 b s 1 38 b s 1 0 b s and 0 5 b s respectively

quasiconformal harmonic mappings and the curvature of the boundary abstract we estimate the jacobian of harmonic mapping of the unit disk onto a smooth and convex jordan domain via the boundary function and the boundary curvature of the image domain by using this result we make some asymptotically sharp estimates of constant of quasiconformality for harmonic diffeomorphisms between the unit disk and the convex domains via their boundary mappings

compute and forward harnessing interference through structured codes interference is usually viewed as an obstacle to communication in wireless networks this paper proposes a new strategy compute and forward that exploits interference to obtain significantly higher rates between users in a network the key idea is that relays should decode linear functions of transmitted messages according to their observed channel coefficients rather than ignoring the interference as noise after decoding these linear equations the relays simply send them towards the destinations which given enough equations can recover their desired messages the underlying codes are based on nested lattices whose algebraic structure ensures that integer combinations of codewords can be decoded reliably encoders map messages from a finite field to a lattice and decoders recover equations of lattice points which are then mapped back to equations over the finite field this scheme is applicable even if the transmitters lack channel state information

lattices for distributed source coding jointly gaussian sources and reconstruction of a linear function consider a pair of correlated gaussian sources x 1 x 2 two separate encoders observe the two components and communicate compressed versions of their observations to a common decoder the decoder is interested in reconstructing a linear combination of x 1 and x 2 to within a mean square distortion of d we obtain an inner bound to the optimal rate distortion region for this problem a portion of this inner bound is achieved by a scheme that reconstructs the linear function directly rather than reconstructing the individual components x 1 and x 2 first this results in a better rate region for certain parameter values our coding scheme relies on lattice coding techniques in contrast to more prevalent random coding arguments used to demonstrate achievable rate regions in information theory we then consider the case of linear reconstruction of k sources and provide an inner bound to the optimal rate distortion region some parts of the inner bound are achieved using the following coding structure lattice vector quantization followed by ldquocorrelatedrdquo lattice structured binning

lattice quantization with side information codes asymptotics and applications in sensor networks in this paper we consider the problem of rate distortion with side information available only at the decoder for the case of jointly gaussian source x and side information y and mean squared error distortion wyner proved in 1976 that the rate distortion function for this problem is identical to the conditional rate distortion function r x y assuming the side information y is available at the encoder in this paper we construct a structured class of asymptotically optimal quantizers for this problem under the assumption of high correlation between source x and side information y we show there exist quantizers within our class whose performance comes arbitrarily close to wyner s bound as an application illustrating the relevance of the high correlation asymptotics we also explore the use of these quantizers in the context of a problem of data compression for sensor networks in a setup involving a large number of devices collecting highly correlated measurements within a confined area an important feature of our formulation is that although the per node throughput of the network tends to zero as network size increases so does the amount of information generated by each transmitter this is a situation likely to be encountered often in practice which allows us to cast under new and more optimistic light some negative results on the transport capacity of large scale wireless networks

a fornberg like conformal mapping method for slender regions abstract a method is presented for approximating the conformal map from the interior of an ellipse to the interior of a simply connected target region the map is represented as a truncated chebyshev series conditions that the mapping function be conformal are transplanted from the ellipse to an annulus with the joukowski map the resulting conditions on the laurent coefficients then give a system of equations for the newton update of the approximate boundary correspondence this system is a generalization of fornberg s system for maps from the disk and is solved similarly in o n log n operations by the conjugate gradient method our numerical experiments demonstrate that the maps from the ellipse to a slender target region of similar aspect ratio can be constructed with far fewer mesh points than are required for maps from the disk thus circumventing the ill conditioning due to crowding in these cases

state dependent relay channel achievable rate and capacity of a semideterministic class this paper considers the problem of communicating over a relay channel with state when noncausal state information is partially available at the nodes we first establish a lower bound on the achievable rates based on noisy network coding and gelfand pinsker coding and show that it provides an alternative characterization of a previously known bound we then introduce the class of state decoupled relay channels and show that our lower bound is tight for a subclass of semideterministic channels we also compute the capacity for two specific examples of this subclass a channel with multiplicative binary fading and a channel with additive gaussian interference these examples are not special cases of previous classes of semideterministic relay channels with known capacity

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

study of gaussian relay channels with correlated noises in this paper we consider the full duplex and half duplex gaussian relay channels where the noises at the relay and destination are arbitrarily correlated we first derive the capacity upper bound and the achievable rates with three existing schemes decode and forward df compress and forward cf and amplify and forward af we present two capacity results under specific noise correlation coefficients one being achieved by df and the other being achieved by direct link transmission or a special case of cf the channel for the former capacity result is equivalent to the traditional gaussian degraded relay channel and the latter corresponds to the gaussian reversely degraded relay channel for cf and af schemes we show that their achievable rates are strictly decreasing functions of the correlation coefficient when the correlation coefficient is negative moreover when the noise correlation coefficient is positive the cf achievable rate may also outperform the independent noise case if the noise correlation coefficient is within a certain range through numerical comparisons under different channel settings we observe that although df completely disregards the noise correlation while the other two can potentially exploit such extra information none of the three relay schemes always outperforms the others over different correlation coefficients moreover the exploitation of noise correlation by cf and af accrues more benefit when the source relay link is weak this paper also considers the optimal power allocation problem under the correlated noise channel setting with individual power constraints at the relay and the source it is shown that the relay should use all its available power to maximize the achievable rates under any correlation coefficient with a total power constraint across the source and the relay the achievable rates are proved to be concave functions over the power allocation factor for af and cf under full duplex mode where the closed form power allocation strategy is derived

analysis of the generalized df cf for gaussian relay channels decode or compress we consider a three node quasi static communication system with a full duplex relay the goal is to determine the relaying mode that enables rate efficient communication under given channel conditions to achieve this goal we consider a generalized scheme that subsumes the decode and forward df and compress and forward cf schemes as special cases the generalized scheme is considered when the source and relay signals are synthesized from commonly used gaussian codebooks which are shown to be capacity achieving in two asymptotic cases perfect relay destination link and broken source destination link studying the generalized df cf scheme it is shown that for two non asymptotic cases in which the signal to noise ratios snrs of the links satisfy certain conditions this scheme reduces to either df or cf for another set of non asymptotic snrs the generalized scheme is shown to yield strictly higher rates than both df and cf despite the complexity of the generalized scheme its rate advantage over df and cf is shown to be upper bounded by 0 5 bits per channel use this indicates that the practical benefit of the analysis of this scheme is to enable selecting the relaying mode that suits a given channel realization numerical results show that under rayleigh fading conditions this selection yields significant gains over fixed df and cf

on instantaneous relaying the gaussian three node relay channel with orthogonal receive components i e the transmitted signals from the source and the relay do not interfere with each other is investigated for such channels linear relaying is a suboptimal strategy in general this is because a linear scheme merely repeats the received noisy signal and does not utilize the available degrees of freedom efficiently at this background nonlinear symbol wise as opposed to block wise relaying strategies are developed to compensate for the shortcomings of the linear strategy optimal strategies are presented for two special cases of the general scenario and it is shown that memoryless relaying can achieve the capacity furthermore for the general gaussian relay channel a parametric piecewise linear pl mapping is proposed and analyzed the achievable rates obtained by the pl mapping are computed numerically and optimized for a certain number of design parameters it is concluded that optimized pl relaying always outperforms conventional instantaneous linear relaying amplify and forward it is also illustrated that the proposed pl relaying scheme can improve on sophisticated block markov encoding i e decode and forward when the source relay link is ill conditioned relative to other links furthermore pl relaying can work at rates close to those achieved by side information encoding i e compress and forward but at a much lower complexity

a conformal map formula for difficult cases abstract a simple approximate formula is derived for the boundary map function of a conformal map which provides a remarkably good fit for mappings to regions with highly distorted boundaries the approximation follows from the reduction of a nonlocal integral equation for the map function to a local equation based on the nature of the crowding associated with distorted regions numerical examples are given

convergence proofs and error estimates for an iterative method for conformal mapping the iterative method as introduced in 8 and 9 for the determination of the conformal mapping of the unit disc onto a domaing is here described explicitly in terms of the operatork which assigns to a periodic functionu its periodic conjugate functionk u it is shown that whenever the boundary curve ofg is parametrized by a function with lipschitz continuous derivative dot eta ne 0 then the method converges locally in the sobolev spacew of 2 periodic absolutely continuous functions with square integrable derivative if is in a holder classc 2 the order of convergence is at least 1 if is inc l 1 withl 1 0 1 then the iteration converges inc l for analytic boundary curves the convergence takes place in a space of analytic functions for the numerical implementation of the method the operatork can be approximated by wittich s method which can be applied very effectively using fast fourier transform the sobolev norm of the numerical error can be estimated in terms of the numbern of grid points it iso n 1 l if is inc l 1 ando exp n 2 if is an analytic curve the number in the latter formula is bounded by logr wherer is the radius of the largest circle into which can be extended analytically such that z 0 for z r the results of some test calculations are reported

slepian wolf coded nested lattice quantization for wyner ziv coding high rate performance analysis and code design nested lattice quantization provides a practical scheme for wyner ziv coding this paper examines the high rate performance of nested lattice quantizers and gives the theoretical performance for general continuous sources in the quadratic gaussian case as the rate increases we observe an increasing gap between the performance of finite dimensional nested lattice quantizers and the wyner ziv distortion rate function we argue that this is because the boundary gain decreases as the rate of the nested lattice quantizers increases to increase the boundary gain and ultimately boost the overall performance a new practical wyner ziv coding scheme called slepian wolf coded nested lattice quantization swc nq is proposed where slepian wolf coding is applied to the quantization indices of the source for the purpose of compression with side information at the decoder theoretical analysis shows that for the quadratic gaussian case and at high rate swc nq performs the same as conventional entropy coded lattice quantization with the side information available at both the encoder and the decoder furthermore a nonlinear minimum mean square error mse estimator is introduced at the decoder which is theoretically proven to degenerate to the linear minimum mse estimator at high rate and experimentally shown to outperform the linear estimator at low rate practical designs of one and two dimensional nested lattice quantizers together with multilevel low density parity check ldpc codes for slepian wolf coding give performance close to the theoretical limits of swc nq

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

a domain decomposition method for approximating the conformal modules of long quadrilaterals this paper is concerned with the study of a domain decomposition method for approximating the conformal modules of long quadrilaterals the method has been studied already by us and also by d gaier and w k hayman but only in connection with a special class of quadrilaterals viz quadrilaterals where a the defining domain is bounded by two parallel straight lines and two jordan arcs and b the four specified boundary points are the four corners where the arcs meet the straight lines our main purpose here is to explain how the method may be extended to a wider class of quadrilaterals than that indicated above

distributed source channel coding based on real field bch codes we use real number codes to compress statistically dependent sources and establish a new framework for distributed lossy source coding in which we compress sources before rather than after quantization this change in the order of binning and quantization blocks makes it possible to model the correlation between continuous valued sources more realistically and compensate for the quantization error partially we then focus on the asymmetric case i e lossy source coding with side information at the decoder the encoding and decoding procedures are described in detail for a class of real number codes called discrete fourier transform dft codes both for the syndrome and parity based approaches we leverage subspace based decoding to improve the decoding and by extending it we are able to perform distributed source coding in a rate adaptive fashion to further improve the decoding performance when the statistical dependency between sources is unknown we also extend the parity based approach to the case where the transmission channel is noisy and thus we perform distributed joint source channel coding in this context the proposed system is well suited for low delay communications as the mean squared reconstruction error mse is shown to be reasonably low for very short block length

the distributed karhunen loeve transform the karhunen loeve transform klt is a key element of many signal processing and communication tasks many recent applications involve distributed signal processing where it is not generally possible to apply the klt to the entire signal rather the klt must be approximated in a distributed fashion this paper investigates such distributed approaches to the klt where several distributed terminals observe disjoint subsets of a random vector we introduce several versions of the distributed klt first a local klt is introduced which is the optimal solution for a given terminal assuming all else is fixed this local klt is different and in general improves upon the marginal klt which simply ignores other terminals both optimal approximation and compression using this local klt are derived two important special cases are studied in detail namely the partial observation klt which has access to a subset of variables but aims at reconstructing them all and the conditional klt which has access to side information at the decoder we focus on the jointly gaussian case with known correlation structure and on approximation and compression problems then the distributed klt is addressed by considering local klts in turn at the various terminals leading to an iterative algorithm which is locally convergent sometimes reaching a global optimum depending on the overall correlation structure for compression it is shown that the classical distributed source coding techniques admit a natural transform coding interpretation the transform being the distributed klt examples throughout illustrate the performance of the proposed distributed klt this distributed transform has potential applications in sensor networks distributed image databases hyper spectral imagery and data fusion

on channel capacity per unit cost memoryless communication channels with arbitrary alphabets where each input symbol is assigned a cost are considered the maximum number of bits that can be transmitted reliably through the channel per unit cost is studied it is shown that if the input alphabet contains a zero cost symbol then the capacity per unit cost admits a simple expression as the maximum normalized divergence between two conditional output distributions the direct part of this coding theorem admits a constructive proof via stein s lemma on the asymptotic error probability of binary hypothesis tests single user multiple access and interference channels are studied

capacity of a class of multicast tree networks in this paper we characterize the capacity of a new class of discrete memoryless multicast networks having a tree topology for achievability a novel coding scheme is constructed where some relays employ a combination of decode and forward and compress and forward and the other relays perform a random binning such that codebook constructions and relay operations are independent for each node and do not depend on the network topology for converse a new technique of iteratively manipulating inequalities exploiting the tree topology is used this class of multicast tree networks includes the class of diamond networks studied by kang and ulukus as a special case

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

achieving 1 2 log 1 snr on the awgn channel with lattice encoding and decoding we address an open question regarding whether a lattice code with lattice decoding as opposed to maximum likelihood ml decoding can achieve the additive white gaussian noise awgn channel capacity we first demonstrate how minimum mean square error mmse scaling along with dithering lattice randomization techniques can transform the power constrained awgn channel into a modulo lattice additive noise channel whose effective noise is reduced by a factor of spl radic 1 snr snr for the resulting channel a uniform input maximizes mutual information which in the limit of large lattice dimension becomes 1 2 log 1 snr i e the full capacity of the original power constrained awgn channel we then show that capacity may also be achieved using nested lattice codes the coarse lattice serving for shaping via the modulo lattice transformation the fine lattice for channel coding we show that such pairs exist for any desired nesting ratio i e for any signal to noise ratio snr furthermore for the modulo lattice additive noise channel lattice decoding is optimal finally we show that the error exponent of the proposed scheme is lower bounded by the poltyrev exponent

filter and forward relay design for mimo ofdm systems in this paper the filter and forward ff relay design for multiple input multiple output mimo orthogonal frequency division multiplexing ofdm systems is investigated due to the considered mimo structure the ff relay design is investigated in the framework of joint design together with the linear mimo transceiver as the design criterion first the minimization of weighted sum mean square error mse is considered the joint design in this case is approached based on alternating optimization that iterates between the optimal design of the ff relay for given mimo precoding and decoding matrices and the optimal design of mimo precoding and decoding matrices for a given ff relay filter second a more advanced problem of joint design for rate maximization is considered the second problem is approached based on the obtained result regarding the first problem of weighted sum mse minimization and the existing result regarding the relationship between weighted mse minimization and rate maximization numerical results show the effectiveness of the proposed ff relay design method and significant performance improvement by the proposed ff relay over widely considered simple af relays for mimo ofdm systems

asymptotic analysis of amplify and forward relaying in a parallel mimo relay network this paper studies the setup of a parallel mimo relay network in which k relays each equipped with n antennas assist in transmitting data between a source and a destination each equipped with m antennas m n in the half duplex mode it is assumed that there is no direct source destination link and the communication is performed in two hops an amplify and forward relaying scheme called incremental cooperative beamforming scheme icbs is introduced and shown to achieve the capacity of the network in the asymptotic case of k with a gap scaling of at most log k 4 k this result is shown to hold as long as the power of each relay is significantly larger than log3 k log log k k in addition in the case that the source power is equal to the relays power and both tend to infinity the proposed scheme is shown to achieve the full multiplexing gain regardless of the number of relays simulation results confirm the validity of analytical arguments

the approximate sum capacity of the symmetric gaussian k user interference channel interference alignment has emerged as a powerful tool in the analysis of multiuser networks despite considerable recent progress the capacity region of the gaussian k user interference channel is still unknown in general in part due to the challenges associated with alignment on the signal scale using lattice codes this paper develops a new framework for lattice interference alignment based on the compute and forward approach within this framework each receiver decodes by first recovering two or more linear combinations of the transmitted codewords with integer valued coefficients and then solving these linear combinations for its desired codeword for the special case of symmetric channel gains this framework is used to derive the approximate sum capacity of the gaussian interference channel up to an explicitly defined outage set of the channel gains the key contributions are the capacity lower bounds for the weak through strong interference regimes where each receiver should jointly decode its own codeword along with part of the interfering codewords as part of the analysis it is shown that decoding k linear combinations of the codewords can approach the sum capacity of the k user gaussian multiple access channel up to a gap of no more than k 2 log k bits

averaging bounds for lattices and linear codes general random coding theorems for lattices are derived from the minkowski hlawka theorem and their close relation to standard averaging arguments for linear codes over finite fields is pointed out a new version of the minkowski hlawka theorem itself is obtained as the limit for p spl rarr spl infin of a simple lemma for linear codes over gf p used with p level amplitude modulation the relation between the combinatorial packing of solid bodies and the information theoretic soft packing with arbitrarily small but positive overlap is illuminated the soft packing results are new when specialized to the additive white gaussian noise channel they reduce to a version of the de buda poltyrev result that spherically shaped lattice codes and a decoder that is unaware of the shaping can achieve the rate 1 2 log sub 2 p n

a schwarz lemma at the boundary using the julia wolff caratheodory type condition on finite dimensional irreducible bounded symmetric domains abstract in this paper we prove a schwarz lemma at the boundary for holomorphic self mappings f of finite dimensional irreducible bounded symmetric domains without assuming the boundary regularity of f our result generalizes the previous results obtained for holomorphic self mappings f of the euclidean unit ball or of the classical cartan domains of type i and of type ii which are smooth up to the boundary