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

gaussian interference channel capacity to within one bit the capacity of the two user gaussian interference channel has been open for 30 years the understanding on this problem has been limited the best known achievable region is due to han and kobayashi but its characterization is very complicated it is also not known how tight the existing outer bounds are in this work we show that the existing outer bounds can in fact be arbitrarily loose in some parameter ranges and by deriving new outer bounds we show that a very simple and explicit han kobayashi type scheme can achieve to within a single bit per second per hertz bit s hz of the capacity for all values of the channel parameters we also show that the scheme is asymptotically optimal at certain high signal to noise ratio snr regimes using our results we provide a natural generalization of the point to point classical notion of degrees of freedom to interference limited scenarios

kernel estimates for nonautonomous kolmogorov equations abstract using time dependent lyapunov functions we prove pointwise upper bounds for the heat kernels of some nonautonomous kolmogorov operators with possibly unbounded drift and diffusion coefficients

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

real algebraic numbers and polynomial systems of small degree based on precomputed sturm habicht sequences discriminants and invariants we classify isolate with rational points and compare the real roots of polynomials of degree up to 4 in particular we express all isolating points as rational functions of the input polynomial coefficients although the roots are algebraic numbers and can be expressed by radicals such representation involves some roots of complex numbers this is inefficient and hard to handle in applications in geometric computing and quantifier elimination we also define rational isolating points between the roots of the quintic we combine these results with a simple version of rational univariate representation to isolate all common real roots of a bivariate system of rational polynomials of total degree 2 and to compute the multiplicity of these roots we present our software within library synaps and perform experiments and comparisons with several public domain implementations our package is 2 10 times faster than numerical methods and exact subdivision based methods including software with intrinsic filtering

a theorem of the dore venni type for noncommuting operators a theorem of the dore venni type for the sum of two closed linear operators is proved where the operators are noncommuting but instead satisfy a certain commutator condition this result is then applied to obtain optimal regularity results for parabolic evolution equations u t l t u t f t and evolutionary integral equations u t t 0 a t s l s u s ds g t which are nonautonomous the domains of the involved operators l t may depend on t but l t 1 is required to satisfy a certain smoothness property the results are then applied to parabolic partial differential and integro differential equations

the two user causal cognitive interference channel novel outer bounds and constant gap result for the symmetric gaussian noise channel in weak interference this paper studies the two user causal cognitive interference channel ccic where two transmitters aim to communicate independent messages to two different receivers via a common channel one source referred to as the cognitive is capable of overhearing the other source referred to as the primary through a noisy in band link and thus can assist in sending the primary s data the authors of this paper recently characterized to within a constant gap the capacity of the symmetric gaussian ccic in 1 the strong interference regime and 2 for a subset of the weak interference regime when the cooperation link is larger than a given threshold this paper characterizes to within a constant gap the capacity for the symmetric gaussian ccic in the regime that was still open to this end two novel outer bounds of the types 2 r mathsf p r mathsf c and r mathsf p 2 r mathsf c are derived for the class of injective semideterministic ccics where the noises at the different source destination pairs are independent these outer bounds as well as an achievable rate region based on gelfand pinsker binning superposition coding and simultaneous decoding at the receivers are then specialized to the gaussian noise case it is shown that the novel outer bounds are necessary to characterize the capacity within a constant gap when the cooperation link is weaker than the direct links that is in this regime unilateral cooperation leaves some system resources underutilized

new inner and outer bounds for the memoryless cognitive interference channel and some new capacity results the cognitive interference channel is a two user interference channel in which one transmitter is non causally provided with the message of the other transmitter this channel model has been extensively studied in the past years and capacity results have been proved for certain classes of channels this paper presents new inner and outer bounds for the capacity region of the cognitive interference channel as well as new capacity results previously proposed outer bounds are expressed in terms of auxiliary random variables for which no cardinality constraint of their alphabet is known consequently it is not possible to evaluate such outer bounds explicitly for a given channel the outer bound derived in this work is based on an idea originally devised by sato for channels without receiver cooperation and results in an outer bound that does not contain auxiliary random variables thus allowing it to be more easily evaluated the inner bound presented in this work which includes rate splitting superposition coding a broadcast channel like binning scheme and gel fand pinsker coding is the largest known to date and is explicitly shown to include all previously proposed achievable rate regions the novel inner and outer bounds are shown to coincide in certain cases in particular capacity is proved for a class of channels in the so called better cognitive decoding regime which includes the regimes in which capacity was known finally the capacity region of the semi deterministic cognitive interference channel in which the signal at the cognitive receiver is an arbitrary deterministic function of the channel inputs is established

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

on a polynomial scalar perturbation of a schrodinger system in lp spaces abstract in the paper 10 the l p realization l p of the matrix schrodinger operator l u d i v q u v u was studied the generation of a semigroup in l p r d c m and characterization of the domain d l p has been established in this paper we perturb the operator l p by a scalar potential belonging to a class including all polynomials and show that still we have a strongly continuous semigroup on l p r d c m with domain embedded in w 2 p r d c m we also study the analyticity compactness positivity and ultracontractivity of the semigroup and prove gaussian kernel estimates further kernel estimates and asymptotic behaviour of eigenvalues of the matrix schrodinger operator are investigated

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

feedback capacity of the gaussian interference channel to within 2 bits we characterize the capacity region to within 2 bits s hz and the symmetric capacity to within 1 bit s hz for the two user gaussian interference channel ic with feedback we develop achievable schemes and derive a new outer bound to arrive at this conclusion one consequence of the result is that feedback provides multiplicative gain at high signal to noise ratio the gain becomes arbitrarily large for certain channel parameters this finding is in contrast to point to point and multiple access channels where feedback provides no gain and only bounded additive gain respectively the result makes use of a linear deterministic model to provide insights into the gaussian channel this deterministic model is a special case of the el gamal costa deterministic model and as a side generalization we establish the exact feedback capacity region of this general class of deterministic ics

kernel and eigenfunction estimates for some second order elliptic operators abstract for a potential v such that v x x with 2 we prove that the heat kernel k t x y associated to the uniformly elliptic operator a j k 1 n k a j k j v satisfies the estimate k t x y c e 0 t e c t b e 2 2 x 1 2 x 4 n 1 2 e 2 2 y 1 2 y 4 n 1 2 for large x y r n and all t 0 here 0 1 is an appropriate constant b 2 2 and 0 is the first eigenvalue of a we also obtain an estimate for large x of the eigenfunctions of a

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

outer bounds on the capacity of gaussian interference channels two outer bounds on the capacity region of the two user gaussian interference channel ifc are derived the idea of the first bound is to let a genie give each receiver just enough information to decode both messages this bound unifies and improves the best known outer bounds of sato and carleial furthermore the bound extends to discrete memoryless ifcs and is shown to be equivalent to another bound of carleial the second bound follows directly from existing results of costa and sato and possesses certain optimality properties for weak interference

dependence balance bounds for single output two way channels if in a transmission the inputs of a single output two way channel exhibit some interdependence this dependence must have been created during earlier transmissions the idea that no more dependence can be consumed than is produced is used to obtain new upper bounds to the capacity region of the discrete memoryless single output two way channel with these upper bounds it is shown that c e shannon 1961 inner bound region is the capacity region for channels in a certain class and the zhang berger schalkwijk upper bound 1986 for blackwell s multiplying channel is improved upon

inner and outer bounds for the gaussian cognitive interference channel and new capacity results the capacity of the gaussian cognitive interference channel a variation of the classical two user interference channel where one of the transmitters referred to as cognitive has knowledge of both messages is known in several parameter regimes but remains unknown in general this paper provides a comparative overview of this channel model as it proceeds through the following contributions first several outer bounds are presented a a new outer bound based on the idea of a broadcast channel with degraded message sets and b an outer bound obtained by transforming the channel into channels with known capacity next a compact fourier motzkin eliminated version of the largest known inner bound derived for the discrete memoryless cognitive interference channel is presented and specialized to the gaussian noise case where several simplified schemes with jointly gaussian input are evaluated in closed form and later used to prove a number of results these include a new set of capacity results for a the primary decodes cognitive regime a subset of the strong interference regime that is not included in the very strong interference regime for which capacity was known and b the s channel in strong interference in which the primary transmitter does not interfere with the cognitive receiver and the primary receiver experiences strong interference next for a general gaussian channel the capacity is determined to within one bit s hz and to within a factor two regardless of the channel parameters thus establishing rate performance guarantees at high and low snr respectively the paper concludes with numerical evaluations and comparisons of the various simplified achievable rate regions and outer bounds in parameter regimes where capacity is unknown leading to further insight on the capacity region

cylindrical algebraic decomposition i the basic algorithm given a set of r variate integral polynomials a cylindrical algebraic decomposition cad of euclidean r space e r partitions e r into connected subsets compatible with the zeros of the polynomials by compatible with the zeros of the polynomials we mean that on each subset of e r each of the polynomials either vanishes everywhere or nowhere for example consider the bivariate polynomial y 4 2 y 3 y 2 3 x 2 y 2 x 4

parallel computation of real solving bivariate polynomial systems by zero matching method we present a new algorithm for solving the real roots of a bivariate polynomial system s f x y g x y with a finite number of solutions by using a zero matching method the method is based on a lower bound for the bivariate polynomial system when the system is non zero moreover the multiplicities of the roots of s 0 can be obtained by the associated quotient ring technique and a given neighborhood from this approach the parallelization of the method arises naturally by using a multidimensional matching method this principle can be generalized to the multivariate equation systems

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

on the han kobayashi region for theinterference channel in this correspondence we derive a simplified description of the han kobayashi rate region for the general interference channel using this result we establish that the recently discovered chong motani garg rate region is a new representation of the han kobayashi region moreover a tighter bound for the cardinality of the time sharing auxiliary random variable emerges from our simplified description

a reliable algorithm for computing the topological degree of a mapping in r2 abstract in this paper we present a method to reliably compute the topological degree of a mapping in the plane over a simple closed polygon the method is based on henrici s argument principle and computes the degree using the winding number concept in range arithmetic the algorithm is then applied to the root computation of a univariate polynomial the proposed algorithms are demonstrated with examples

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

cylindrical algebraic decomposition ii an adjacency algorithm for the plane in part i of the present paper we defined cylindrical algebraic decompositions cad s and described an algorithm for cad construction in part ii we give an algorithm that provides information about the topological structure of a cad of the plane informally two disjoint cells in e r r 1 are adjacent if they touch each other formally they are adjacent if their union is connected in a picture of a cad eg fig 2 of part i it is obvious to the eye which pairs of cells are adjacent however the cad algorithm of part i does not actually produce this information nor did the original version of that algorithm in collins 1975

on diagonal estimates on schrodinger semigroup kernels and reduced heat kernels we prove various estimates for the kernels of semigroups generated by schrodinger operators with magnetic field and potential of polynomial growth we also investigate the reduced heat kernels

global properties of generalized ornstein uhlenbeck operators on lp rn rn with more than linearly growing coefficients we show that the realization ap of the elliptic operator au div q u f u vu in lp rn rn p 1 generates a strongly continuous semigroup and we determine its domain d ap u w2 p rn rn f u vu lp rn rn if 1 p the diffusion coefficients q qij are uniformly elliptic and bounded together with their first order derivatives the drift coefficients f can grow as x log x and v can grow logarithmically our approach relies on the monniaux pruss theorem on the sum of noncommuting operators we also prove lp lq estimates and under somewhat stronger assumptions we establish pointwise gradient estimates and smoothing of the semigroup in the spaces w p rn rn 0 1 where 1 p

approximate capacity region for the symmetric gaussian interference channel with noisy feedback recent results have shown that feedback can significantly increase the capacity of interference networks this paper considers the impact of noise on such gains due to feedback in particular this paper considers the two user linear deterministic interference channel with noisy feedback as a stepping stone to characterize the approximate capacity region for the two user gaussian interference channel with noisy feedback first the capacity region for the symmetric linear deterministic interference channel with noisy feedback is obtained it is shown that noisy feedback enlarges the capacity region if and only if the number of feedback bits l is greater than a certain threshold l it is found that excluding the regime 1 2 leq alpha leq 2 where alpha is the normalized interference level in which even full feedback does not increase symmetric capacity this threshold l is equal to the per user symmetric capacity without feedback one of the key ideas is a novel converse outer bounding technique for the weighted sum rates 2r 1 r 2 and r 1 2r 2 these results and the techniques developed for the linear deterministic model are then applied to characterize inner bounds and outer bounds for the symmetric gaussian interference channel with noisy feedback the outer bounds are shown to be at most 4 7 b s hz away from the achievable rate region as a corollary the generalized degrees of freedom region which approximates the capacity region of the symmetric gaussian interference channel at high snr is found

lp estimates for parabolic systems with unbounded coefficients coupled at zero and first order abstract we consider a class of nonautonomous parabolic first order coupled systems in the lebesgue space l p r d r m d m 1 with p 1 sufficient conditions for the associated evolution operator g t s in c b r d r m to extend to a strongly continuous operator in l p r d r m are given some l p l q estimates are also established together with l p gradient estimates

computing real roots of a polynomial in chebyshev series form through subdivision with linear testing and cubic solves abstract an arbitrary polynomial of degree n f n x can always be represented as a truncated chebyshev polynomial series chebyshev form this representation is much better conditioned than the usual power form of a polynomial we describe a new method for finding the real roots of f n x in chebyshev form the canonical interval x 1 1 is subdivided into n s subintervals each is tested for zeros using the error bound for linear interpolation on zero possible intervals f n is approximated by a cubic polynomial whose roots are then found by the usual sixteenth century formulas