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

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

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

the gardner method for symmetries the gardner method traditionally used to generate conservation laws of integrable equations is generalized to generate symmetries the method is demonstrated for the kdv camassa holm and sine gordon equations the method involves identifying a generating symmetry which depends upon a parameter expansion of this symmetry in a formal power series in the parameter then gives the usual infinite hierarchy of symmetries we show that the obtained symmetries commute discuss the relation of the gardner method with lenard recursion both for symmetries and conservation laws and also the connection between the symmetries of continuous integrable equations and their discrete analogues

a simple method for detecting scatterers in a stratified ocean waveguide abstract in this paper we have designed a simple method for the inverse scattering problem of stratified ocean waveguide the simple approach applies the bisection technique in parallel to estimate the boundaries of inhomogeneous media from the received partial data in addition the algorithm only involves the matrix vector operations and possesses the optimal computation complexity in both two and three dimensions in practice it is easy to carry out robust against noise and capable of reconstructing the penetrable obstacles of different locations and shapes we can consider the simple method as a direct and straightforward process to supply satisfactory initial positions for the implementation of any existing more refined but computationally more demanding techniques to achieve accurate reconstructions of physical features of scatterers

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

on the cauchy problem for the integrable modified camassa holm equation with cubic nonlinearity abstract considered in this paper is the modified camassa holm equation with cubic nonlinearity which is integrable and admits the single peaked solitons and multi peakon solutions the short wave limit of this equation is known as the short pulse equation the main investigation is the cauchy problem of the modified camassa holm equation with qualitative properties of its solutions it is firstly shown that the equation is locally well posed in a range of the besov spaces the blow up scenario and the lower bound of the maximal time of existence are then determined a blow up mechanism for solutions with certain initial profiles is described in detail and nonexistence of the smooth traveling wave solutions is also demonstrated

comment on a new integrable equation with cuspons and w m shape peaks solitons j math phys 47 112701 2006 in a recent paper j math phys 47 112701 2006 qiao proposed a new completely integrable wave equation the equation was derived from the two dimensional euler equations and was proven to posses lax pair bi hamiltonian structure and new types of soliton solutions in this comment we show that qiao s equation is a subcase of an integrable equation derived by a method that was proposed by fuchssteiner and fokas physica d 4 47 1981 in the early 1980s we also discuss the existence of the new types of soliton solutions

dirty paper coding versus tdma for mimo broadcast channels we compare the capacity of dirty paper coding dpc to that of time division multiple access tdma for a multiple antenna multiple input multiple output mimo gaussian broadcast channel bc we find that the sum rate capacity achievable using dpc of the multiple antenna bc is at most min m k times the largest single user capacity i e the tdma sum rate in the system where m is the number of transmit antennas and k is the number of receivers this result is independent of the number of receive antennas and the channel gain matrix and is valid at all signal to noise ratios snrs we investigate the tightness of this bound in a time varying channel assuming perfect channel knowledge at receivers and transmitters where the channel experiences uncorrelated rayleigh fading and in some situations we find that the dirty paper gain is upper bounded by the ratio of transmit to receive antennas we also show that min m k upper bounds the sum rate gain of successive decoding over tdma for the uplink channel where m is the number of receive antennas at the base station and k is the number of transmitters

darboux transformation and multi soliton solutions of the camassa holm equation and modified camassa holm equation in this paper we propose a new approach to calculate multi soliton solutions of camassa holm ch equation and modified camassa holm mch equation with the aid of darboux transformation dt the new approach simplifies the approach presented by li and zhang proc r soc london ser a 460 2617 2627 2004 we first map the ch and mch equation to a negative order kdv nkdv equation by a reciprocal transformation then we proceed to apply the dt to solve the nkdv equation in the usual way finally we invert the reciprocal transformation to recover the solutions of the ch equation and mch equation

reconstruction of an impedance cylinder at oblique incidence from the far field data consider scattering of obliquely incident plane electromagnetic waves by an impedance cylinder embedded in a homogeneous background medium under some assumptions the direct scattering problem is governed by a coupled system of the two dimensional helmholtz equations for x 3 components of the electric field and the magnetic field in this paper we study a corresponding inverse scattering problem which is to reconstruct an unknown scattering object from measurement data of the x 3 component of only the electric field a reconstruction scheme called the linear sampling method is established with rigorous mathematical analysis due to the coupled oblique derivative boundary condition some new characteristics appear in our analysis numerical examples are also presented to illustrate the feasibility of the reconstruction algorithm

integrable peakon equations with cubic nonlinearity we present a new integrable partial differential equation found by vladimir novikov like the camassa holm and degasperis procesi equations this new equation admits peaked soliton peakon solutions but it has nonlinear terms that are cubic rather than quadratic we give a matrix lax pair for v novikov s equation and show how it is related by a reciprocal transformation to a negative flow in the sawada kotera hierarchy infinitely many conserved quantities are found as well as a bi hamiltonian structure the latter is used to obtain the hamiltonian form of the finite dimensional system for the interaction of n peakons and the two body dynamics n 2 is explicitly integrated finally all of this is compared with some analogous results for another cubic peakon equation derived by zhijun qiao

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 new integrable equation with cuspons and w m shape peaks solitons in this paper we propose a new completely integrable wave equation mt mx u2 ux2 2m2ux 0 m u uxx the equation is derived from the two dimensional euler equation and is proven to have lax pair and bi hamiltonian structures this equation possesses new cusp solitons cuspons instead of regular peakons ce x ct with speed c through investigating the equation we develop a new kind of soliton solutions w m shape peaks solitons there exist no smooth solitons for this integrable water wave equation

classification of integrable equations on quad graphs the consistency approach a classification of discrete integrable systems on quad graphs i e on surface cell decompositions with quadrilateral faces is given the notion of integrability laid in the basis of the classification is the three dimensional consistency this property yields among other features the existence of the discrete zero curvature representation with a spectral parameter for all integrable systems of the obtained exhaustive list the so called three leg forms are found this establishes lagrangian and symplectic structures for these systems and the connection to discrete systems of the toda type on arbitrary graphs generalizations of these ideas to the three dimensional integrable systems and to the quantum context are also discussed

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

zero curvature formulations of dual hierarchies zero curvature formulations are given for the dual hierarchies of standard soliton equation hierarchies recently introduced by olver and rosenau including the physically interesting fuchssteiner fokas camassa holm hierarchy

tri hamiltonian duality between solitons and solitary wave solutions having compact support a simple scaling argument shows that most integrable evolutionary systems which are known to admit a bi hamiltonian structure are in fact governed by a compatible trio of hamiltonian structures we demonstrate how their recombination leads to integrable hierarchies endowed with nonlinear dispersion that supports compactons solitary wave solutions having compact support or cusped and or peaked solitons a general algorithm for effecting this duality between classical solitons and their nonsmooth counterparts is illustrated by the construction of dual versions of the modified korteweg de vries equation the nonlinear schr odinger equation the integrable boussinesq system used to model the two way propagation of shallow water waves and the ito system of coupled nonlinear wave equations these hierarchies include a remarkable variety of interesting integrable nonlinear differential equations textcopyright 1996 the american physical society

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

loop soliton interaction in an integrable nonlinear telegraphy model reciprocal and backlund transformations an integrable telegraphy equation linked in turn to the geometry of pseudospherical surfaces and a class of model nonlinear elastic stress strain laws descriptive of ideally hard material response is investigated a constant coefficient ideal formalism is introduced which leads to a reciprocal transformation between this nonlinear telegraphy equation and a system compatible with the classical sine gordon equation a backlund transformation is then constructed which is used to analyse two loop soliton interaction the latter exhibits a novel exchange particle phenomenon

on a class of physically important integrable equations abstract a methodology introduced by fuchssteiner and the author is used to derive a class of physically important integrable evolution equations among these equations are integrable generalizations of the korteweg devries kdv of the modified kdv of the nonlinear schrodinger nls and of the sine gordon equations the modeling of water waves as well as general asymptotic considerations are used to illustrate the occurrence of the generalized modified kdv and nls equations respectively

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

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

detecting buried wave penetrable scatterers in a two layered medium abstract in a two layered medium we prove that a buried inhomogeneous scatterer is uniquely determined from the wave field data measured in the upper half space with respect to many incident point sources moreover we extend the multilevel sampling method in liu and zou 2013 to numerically reconstruct the buried scatterer applying only few incident fields and partial scattered data the extended recovery scheme only involves matrix vector operations and does not need to solve any large scale ill posed linear systems or any optimization process it is feasible to deal with the scatterers of different features and easy to implement highly tolerant to noise and computationally quite cheap we can regard it as an effective yet simple computational method to provide a reliable initial guess for the implementation in existing more accurate and refined optimization type reconstruction algorithms

a multilevel sampling method for detecting sources in a stratified ocean waveguide in the reconstruction process of sound waves in a 3d stratified waveguide a key technique is to effectively reduce the huge computational demand in this work we propose an efficient and simple multilevel reconstruction method to locate the accurate position of a point source in a stratified ocean the proposed method can be viewed as a direct sampling method since no solutions of optimizations or linear systems are involved the novel method exhibits several strengths fast convergence robustness against noise advantages in computational complexity and applicability for a very small number of receivers

reconstruction of a small inclusion in a two dimensional open waveguide we consider wave propagation in a perturbed open waveguide we provide a new asymptotic expansion for the scattered wave when the inclusion is of small diameter we design a music multiple signal classification type of algorithm for locating the inclusion and illustrate its viability in numerical examples

n loop solitons and their link with the complex harry dym equation n loop solitons are constructed by means of n cusp soliton solutions of the harry dym equation the proposed approach is based on a novel link between the loop soliton equation and the complex harry dym equation considered on a special curve

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

orbital stability of the train of peakons for an integrable modified camassa holm equation abstract in this paper we consider the modified camassa holm equation with cubic nonlinearity which is integrable and admits the single peakons and multi peakons using energy argument and combining the method of the orbital stability of a single peakon with monotonicity of the local energy norm we prove that the sum of n sufficiently decoupled peakons is orbitally stable in the energy space

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

backlund transformation and smooth multisoliton solutions for a modified camassa holm equation with cubic nonlinearity we present a compact parametric representation of the smooth bright multisoliton solutions for the modified camassa holm mch equation with cubic nonlinearity we first transform the mch equation to an associated mch equation through a reciprocal transformation and then find a novel backlund transformation between solutions of the associated mch equation and a model equation for shallow water waves sww introduced by ablowitz et al we combine this result with the expressions of the multisoliton solutions for the sww and modified korteweg de vries equations to obtain the multisoliton solutions of the mch equation subsequently we investigate the properties of the one and two soliton solutions as well as the general multisoliton solutions we show that the smoothness of the solutions is assured only if the amplitude parameters of solitons satisfy certain conditions we also find that at a critical value of the parameter beyond which the solution becomes singular the soliton solution exhibits a different feature from that of the peakon solution of the ch equation then by performing an asymptotic analysis for large time we obtain the formula for the phase shift and confirm the solitonic nature of the multisoliton solutions finally we use the backlund transformation to derive an infinite number of conservation laws of the mch equation

smooth and singular multisoliton solutions of a modified camassa holm equation with cubic nonlinearity and linear dispersion we develop a direct method for solving a modified camassa holm equation with cubic nonlinearity and linear dispersion under the rapidly decreasing boundary condition we obtain a compact parametric representation for the multisoliton solutions and investigate their properties we show that the introduction of a linear dispersive term exhibits various new features in the structure of solutions in particular we find the smooth solitons whose characteristics are different from those of the camassa holm equation as well as the novel types of singular solitons a remarkable feature of the soliton solutions is that the underlying structure of the associated tau functions is the same as that of a model equation for shallow water waves introduced by ablowitz et al 1974 stud appl math 53 249 315 finally we demonstrate that the short wave limit of the soliton solutions recovers the soliton solutions of the short pulse equation which describes the propagation of ultra short optical pulses in nonlinear media

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

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

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

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

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

nonlinear differential difference equations as backlund transformations shows that the best known nonlinear differential difference equations associated with the discrete schrodinger spectral problem and also with the discrete zakharov shabat spectral problem can be interpreted as backlund transformations for some continuous nonlinear evolution equations

lax integrability and the peakon problem for the modified camassa holm equation peakons are special weak solutions of a class of nonlinear partial differential equations modelling non linear phenomena such as the breakdown of regularity and the onset of shocks we show that the natural concept of weak solutions in the case of the modified camassa holm equation studied in this paper is dictated by the distributional compatibility of its lax pair and as a result it differs from the one proposed and used in the literature based on the concept of weak solutions used for equations of the burgers type subsequently we give a complete construction of peakon solutions satisfying the modified camassa holm equation in the sense of distributions our approach is based on solving certain inverse boundary value problem the solution of which hinges on a combination of classical techniques of analysis involving stieltjes continued fractions and multi point pade approximations we propose sufficient conditions needed to ensure the global existence of peakon solutions and analyze the large time asymptotic behaviour whose special features include a formation of pairs of peakons that share asymptotic speeds as well as toda like sorting property

direct recovery of wave penetrable scatterers in a stratified ocean waveguide abstract we shall derive a direct sampling method for the recovery of wave penetrable inhomogeneous scatterers in a three dimensional stratified ocean waveguide the proposed method is simple straightforward and computationally efficient since no matrix inversions optimizations or solutions of ill posed linear systems are involved moreover it is highly tolerant to noise and is applicable with a few scattered fields corresponding to only two or four incidences in addition a priori knowledge of either the number of disconnected components or the physical features of the unknown obstacles is not required by the direct sampling method a mathematical derivation is provided for its validation and several extensive numerical experiments are shown to evaluate the effectiveness and feasibility of the newly proposed method

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

grassmannian beamforming for multiple input multiple output wireless systems transmit beamforming and receive combining are simple methods for exploiting the significant diversity that is available in multiple input multiple output mimo wireless systems unfortunately optimal performance requires either complete channel knowledge or knowledge of the optimal beamforming vector both are hard to realize in this article a quantized maximum signal to noise ratio snr beamforming technique is proposed where the receiver only sends the label of the best beamforming vector in a predetermined codebook to the transmitter by using the distribution of the optimal beamforming vector in independent and identically distributed rayleigh fading matrix channels the codebook design problem is solved and related to the problem of grassmannian line packing the proposed design criterion is flexible enough to allow for side constraints on the codebook vectors bounds on the codebook size are derived to guarantee full diversity order results on the density of grassmannian line packings are derived and used to develop bounds on the codebook size given a capacity or snr loss monte carlo simulations are presented that compare the probability of error for different quantization strategies

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

the modified camassa holm equation backlund transformation and nonlinear superposition formula this paper is concerned with the modified camassa holm equation and its backlund transformation with the aid of reciprocal transformation and the associated modified camassa holm equation a backlund transformation which involves both dependent and independent variables is constructed for the modified camassa holm equation the related nonlinear superposition formula is worked out and applications of both backlund transformation and nonlinear superposition formula are considered

symplectic structures their backlund transformations and hereditary symmetries abstract it is shown that compatible symplectic structures lead in a natural way to hereditary symmetries we recall that a hereditary symmetry is an operator valued function which immediately yields a hierarchy of evolution equations each having infinitely many commuting symmetries all generated by this hereditary symmetry furthermore this hereditary symmetry usually describes completely the soliton structure and the conservation laws of these equations this result then provide us with a method for constructing hereditary symmetries and hence exactly solvable evolution equations in addition we show how symplectic structures transform under backlund transformations this leads to a method for generating a whole class of symplectic structures from a given one several examples and applications are given illustrating the above results also the connection of our results with those of gelfand and dikii and of magri is briefly pointed out

a riemann hilbert approach to the modified camassa holm equation with nonzero boundary conditions this paper aims at developing the riemann hilbert problem approach to the modified camassa holm mch equation in the case when the solution is assumed to approach a non zero constant at both infinities of the space variable in this case the spectral problem for the associated lax pair equation has a continuous spectrum which allows formulating the inverse spectral problem as a riemann hilbert factorization problem with jump conditions across the real axis we obtain a representation for the solution of the cauchy problem for the mch equation and also a description of certain soliton type solutions both regular and non regular

wave breaking and peakons for a modified camassa holm equation in this paper we investigate the formation of singularities and the existence of peaked traveling wave solutions for a modified camassa holm equation with cubic nonlinearity the equation is known to be integrable and is shown to admit a single peaked soliton and multi peakon solutions of a different character than those of the camassa holm equation singularities of the solutions can occur only in the form of wave breaking and a new wave breaking mechanism for solutions with certain initial profiles is described in detail

the two dimensional direct and inverse scattering problems with generalized oblique derivative boundary condition consider the two dimensional exterior problem for the helmholtz equation with a generalized oblique derivative boundary condition which arises in some new scattering problems such as the scattering of tidal waves by islands under suitable assumptions different from the well studied scattering problems with dirichlet neumann and impedance boundary conditions the boundary condition in our new model involves a linear combination of the normal and tangential derivatives of the wave field with complex coefficient compared with the classical scattering models the tangential derivative on the obstacle boundary leads to some essential differences such as the symmetric property of the green function and the reciprocity principle of the scattering data both the direct and inverse scattering problems are studied in this paper first based on the lax phillips method we show the unique solvability of the direct scattering problem and the analyticity of the solution on the wave number second we investigate

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

new integrable hierarchy its parametric solutions cuspons one peak solitons and m w shape peak solitons in this paper we propose a new completely integrable hierarchy particularly in the hierarchy we draw two new soliton equations 1 mt 12 1 m2 xxx 12 1 m2 x 2 mt mx u2 ux2 2m2ux 0 m u uxx the first one is the second positive member in the hierarchy while the second one is the second negative member in the hierarchy both equations can be derived from the two dimensional euler equation by using the approximation procedure all equations in the hierarchy are proven to have bi hamiltonian operators and lax pairs through solving a crucial matrix equation moreover we develop parametric solutions of the entire hierarchy through constructing two kinds of constraints one is for all negative members of the hierarchy on a symplectic submanifold and the other is for all positive members in the standard symplectic space the most interesting things are both equations possess new type of peaked solitons continuous and piecewise smooth w m shape peak soliton solutions in addition we find new cusp solit

some tricks from the symmetry toolbox for nonlinear equations generalizations of the camassa holm equation abstract the main subject of the paper is to give a survey and to present new methods on how integrability results i e results for symmetry groups inverse scattering formulations action angle transformations and the like can be transferred from one equation to others in case the equations are not related by backlund transformations as a main example the so called camassa holm equation is chosen for which the relevant results are obtained by having a look on the korteweg de vries kdv equation the camassa holm equation turns out to be a different factorization equation of the kdv it describes shallow water waves and reconciles the properties which were known for different orders of shallow water wave approximations we follow here an old method already marginally mentioned in fuchssteiner and fokas 1981 and fuchssteiner 1983 and recently applied by others olver and rosenau 1995 the method allows an immediate recovery of the recursion operator for the camassa holm equation from the invariance structure of the kdv although both equations are not related by backlund transformations however in addition and different from other approaches from there by use of the squared eigenfunction relation for the kdv equation the lax pair formulation for the different factorization equation is derived for the example under consideration it is of course the one obtained in camassa and holm 1993 since the methods proposed here can be transferred to any compatible factorization of recursion operators its application even in the special case which was chosen for illustration leads to a large class of integrable equations among which the camassa holm equation can be found as well as a three parameter family of generalizations of the equation the advantage of the general approach to the lax pair presentation is that direct transformations between action and angle variables are obtained so using this lax pair formulation as a novel result a direct transformation between action and angle variables for the camassa holm equation is derived further novel results in the paper are a hodograph link back from a backlund transformation of the camassa holm equation to a particular member of the kdv hierarchy additional symmetries and the construction of the conformal algebra for the hierarchy of the camassa holm equation the methods involved include hereditary operators bi hamiltonian formulations nilpotent flows and scaling symmetries

on beamforming with finite rate feedback in multiple antenna systems we study a multiple antenna system where the transmitter is equipped with quantized information about instantaneous channel realizations assuming that the transmitter uses the quantized information for beamforming we derive a universal lower bound on the outage probability for any finite set of beamformers the universal lower bound provides a concise characterization of the gain with each additional bit of feedback information regarding the channel using the bound it is shown that finite information systems approach the perfect information case as t 1 2 sup b t 1 where b is the number of feedback bits and t is the number of transmit antennas the geometrical bounding technique used in the proof of the lower bound also leads to a design criterion for good beamformers whose outage performance approaches the lower bound the design criterion minimizes the maximum inner product between any two beamforming vectors in the beamformer codebook and is equivalent to the problem of designing unitary space time codes under certain conditions finally we show that good beamformers are good packings of two dimensional subspaces in a 2t dimensional real grassmannian manifold with chordal distance as the metric

the dual modified korteweg de vries fokas qiao equation geometry and local analysis we study a bi hamiltonian equation with cubic nonlinearity shown to appear in the theory of water waves by fokas derived by qiao using the two dimensional euler equation and also known to arise as the dual of the modified korteweg de vries equation thanks to work by fokas fuchssteiner olver and rosenau we present a quadratic pseudo potential we compute infinite sequences of local and nonlocal conservation laws and we construct an infinite dimensional lie algebra of symmetries which contains a semi direct sum of the sl 2 r loop algebra and the centerless virasoro algebra as an application we prove a theorem on the existence of smooth solutions and we construct some explicit examples moreover we consider the cauchy problem and we prove existence and uniqueness of weak solutions in the sobolev space hq 2 r q 1 2

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