expanded gdof optimality regime of treating interference as noise in the m times 2 x channel treating interference as noise tin as the most appropriate approach in dealing with interference and the conditions on its optimality has attracted the interest of researchers recently however our knowledge on necessary and sufficient conditions of tin is restricted to a few setups with limited number of users in this paper we study the optimality of tin in terms of the generalized degrees of freedom gdof for a fundamental network namely the m times 2 x channel to this end the achievable gdof of tin with power allocations at the transmitters is studied it turns out that the transmit power allocation maximizing the achievable gdof is given by on off signaling as long as the receivers use tin this leads to two variants of tin namely p2p tin and 2 ic tin while in the first variant the m times 2 x channel is reduced to a point to point p2p channel in the second variant the setup is reduced to a two user interference channel in which the receivers use tin the optimality of these two variants is studied separately to this end novel genie aided upper bounds on the capacity of the x channel are established the conditions on the optimality of p2p tin can be summarized as follows p2p tin is gdof optimal if there exists a dominant multiple access channel or a dominant broadcast channel embedded in the x channel furthermore the necessary and sufficient conditions on the gdof optimality of 2 ic tin are presented interestingly it turns out that operating the m times 2 x channel in the 2 ic tin mode might be still gdof optimal although the conditions given by geng et al are violated however 2 ic tin is sub optimal if there exists a single interferer which causes sufficiently strong interference at both receivers the comparison of the results with the state of the art shows that the gdof optimality of tin is expanded significantldy

on a semilinear elliptic neumann problem with asymmetric nonlinearities abstract we consider the neumann problem 1 1 below we extend therange of applicability of the sharp nonresonance condition derived in go om so as in particular allow asymmetric nonlinearities 1 introduction this paper is mainly concerned with the neumann problem i au g u h x inq 1 1 du du 0 on oil here a is the laplacian operator q is a bounded domain of rn n 1 with c1 1 boundary and unit exterior normal v g is a continuous function on r and h is taken in l f2 or in lp q in a previous work go om we showed that if g s 2g s 1 2 lim sup oo s s oo s or s oo then a necessary and sufficient condition for 1 1 to be solvable for any h l f2 is that the range of g be all of k here kx 0 k2 denote the distinct eigenvalues of a on q with neumann boundary condition andg s jo g t dt the surjectivity of g thus provides a nonresonance condi tion at the eigenvalue xx 0 we refer to go om for historical background

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

precise asymptotics in the self normalized law of the iterated logarithm abstract let x x 1 x 2 be i i d nondegenerate random variables with zero means s n j 1 n x j and v n 2 j 1 n x j 2 we investigate the precise asymptotics in the law of the iterated logarithm for self normalized sums s n v n also for the maximum of self normalized sums max 1 k n s k v n when x belongs to the domain of attraction of the normal law

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

nonresonance conditions on the potential for a semilinear dirichlet problem abstract problem u g u h x in a b with u 0 on a b is solved under new nonresonance conditions between the first eigenvalue and the first curve in the fucik spectrum of the associated linear problem

darling erdős theorem for self normalized sums let x x1 x2 be i i d nondegenerate random variables sn nj 1xj and v2n nj 1x2j we investigate the asymptotic vspace 1pt behavior in distribution of the maximum of self normalized sums max1 k nsk vk and the law of the iterated logarithm for self normalized sums sn vn when x belongs to the domain of attraction of the normal law in this context we establish a darling erd s type theorem as well as an erd s feller kolmogorov petrovski type test for self normalized sums

self normalized processes exponential inequalities moment bounds and iterated logarithm laws self normalized processes arise naturally in statistical applications being unit free they are not affected by scale changes moreover self normalization often eliminates or weakens moment assumptions in this paper we present several exponential and moment inequalities particularly those related to laws of the iterated logarithm for self normalized random variables including martingales tail probability bounds are also derived for random variables bt 0 and at let yt exp at 2bt2 2 we develop inequalities for the moments of at bt or supt 0at bt log logbt 1 2 and variants thereof when eyt 1 or when yt is a supermartingale for all belonging to some interval our results are valid for a wide class of random processes including continuous martingales with at mt and b t sqrt langle m rangle t and sums of conditionally symmetric variables di with at i 1tdi and b t sqrt sum i 1 t d i 2 a sharp maximal inequality for conditionally symmetric random variables and for continuous local martingales with values in rm m 1 is also established another development in this paper is a bounded law of the iterated logarithm for general adapted sequences that are centered at certain truncated conditional expectations and self normalized by the square root of the sum of squares the key ingredient in this development is a new exponential supermartingale involving i 1tdi and i 1tdi2 a compact law of the iterated logarithm for self normalized martingales is also derived in this connection

a coordinate system for gaussian networks this paper investigates network information theory problems where the external noise is gaussian distributed in particular the gaussian broadcast channel with coherent fading and the gaussian interference channel are considered it is shown that in these problems non gaussian code ensembles can achieve higher rates than the gaussian ones it is also shown that the strong shamai laroia conjecture on the gaussian isi channel does not hold in order to analyze non gaussian code ensembles over gaussian networks a geometrical tool using the hermite polynomials is proposed this tool provides a coordinate system to analyze a class of non gaussian input distributions that are invariant over gaussian networks

the law of the iterated logarithm for the rescaled rs statistics without the second moment abstract in the paper we show a law of the iterated logarithm for rescaled r s statistics without second moment

on the capacity of the gaussian channel with a finite number of input levels an analytic confirmation of an observation made by g ungerboeck 1965 that approximately optimal performance on a gaussian channel with capacity c can be obtained with about 2 sup c 1 levels is given in particular the results imply that by using about 2 sup c 1 levels a rate of nearly c 1 bit can be achieved and that by using 2 sup c 1 levels a rate of about c 0 4 bits can be achieved

an exponential nonuniform berry esseen bound for self normalized sums in this paper we shall derive exponential nonuniformberry esseen bounds in the central limit theorem for self normalized sums we show that the size of the error can be reduced considerably by replacing the usual standardization by self normalization in particular we establish the exponential bounds for the probability of the self normalized sums under the condition that the third moment is finite whereas an exponential moment assumption is required for the standardized sums applications to t statistics and the probabilities of moderate deviations of self normalized sums are also discussed

nonresonance conditions on the potential for a semilinear elliptic problem abstract we prove the solvability of the dirichlet problem formula for every given h under the following set of assumptions formula and formula and formula here m and m 1 denote two consecutive higher eigenvalues of on h 1 0 and g is the potential of g similar results are also obtained in the case where the nonlinearity interacts with the first eigenvalue 1

interference as noise friend or foe this paper shows that for the two user gaussian interference channel g ic treating interference as noise without time sharing tinnots achieves the closure of the capacity region to within either a constant gap or to within a gap of the order o log ln min mathsf s mathsf i gamma up to a set of lebesgue measure gamma in 0 1 where mathsf s is the largest signal to noise ratio on the direct links and mathsf i is the largest interference to noise ratio on the cross links as a consequence tinnots is optimal from a generalized degrees of freedom gdof perspective for all channel gains except for a subset of zero measure tinnots with gaussian inputs is known to be optimal within 1 2 bit for a subset of the weak interference regime rather surprisingly this paper shows that tinnots is gdof optimal in all parameter regimes even in the strong and very strong interference regimes where joint decoding of gaussian inputs is optimal for approximate optimality of tinnots in all parameter regimes it is critical to use non gaussian inputs this paper thus proposes to use mixed inputs as channel inputs for the g ic where a mixed input is the sum of a discrete and a gaussian random variable interestingly with reference to the han kobayashi achievable scheme the discrete part of a mixed input is shown to effectively behave as a common message in the sense that although treated as noise its effect on the achievable rate region is as if it were jointly decoded together with the desired messages at a non intended receiver the practical implication is that a discrete interfering input is a friend while an gaussian interfering input is in general a foe this paper also discusses other practical implications of the proposed tinnots scheme with mixed inputs since tinnots requires neither explicit joint decoding nor time sharing the results of this paper are applicable to a variety of oblivious or asynchronous channels such as the block asynchronous g ic which is not an information stable channel and the g ic with partial codebook knowledge at one or more receivers

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

long term memory in stock market prices a test for long term memory that is robust to short range dependence is developed it is a modification of the r s statistic and the relevant asymptotic sampling theory is derived via functional central limit theory contrary to previous findings when applied to daily and monthly stock returns indexes over several time periods this test yields no evidence of long range dependence once short range dependence is accounted for monte carlo experiments show that the modified r s test has power against at least two specific models of long term memory suggesting that models with short range dependence may adequately capture the behavior of historical stock returns copyright 1991 by the econometric society

gaussian mixture noise channels with minimum and peak amplitude constraints motivated by the idea of transmitting energy and information simultaneously we investigate in this paper the impact of constraints on the amount of energy that individual symbols carry i e minimum amplitude constraints we consider a gaussian mixture noise channel with both minimum and peak amplitude constraints first we prove that the capacity achieving input has a discrete distribution with a finite number of probability mass points then we further investigate the number and positions of the probability mass points for the capacity achieving input specifically when the interference is constant and known at both the transmitter and the receiver it can be totally eliminated so that the channel operates like an awgn channel in this case we give a theorem to determine whether the optimal input is binary for more general cases such as non binary inputs and non constant interference we investigate optimal inputs and capacities via numerical computations

on the optimality of treating interference as noise it is shown that in the k user interference channel if for each user the desired signal strength is no less than the sum of the strengths of the strongest interference from this user and the strongest interference to this user all values in decibel scale then the simple scheme of using point to point gaussian codebooks with appropriate power levels at each transmitter and treating interference as noise tin at every receiver in short tin scheme achieves all points in the capacity region to within a constant gap the generalized degrees of freedom gdof region under this condition is a polyhedron which is shown to be fully achieved by the same scheme without the need for time sharing the results are proved by first deriving a polyhedral relaxation of the gdof region achieved by tin and then providing a dual characterization of this polyhedral region via the use of potential functions and finally proving the optimality of this region in the desired regime

large deviations and law of the iterated logarithm for partial sums normalized by the largest absolute observation let x n 1 leq n infty be a sequence of independent identically distributed random variables in the domain of attraction of a stable law with index 0 alpha 2 the limit of x n 1 log p s n max x i geq x n is found when x n to infty and x n n to 0 the large deviation result is used to prove the law of the iterated logarithm for the self normalized partial sums

donsker s theorem for self normalized partial sums processes let x x1 x2 be a sequence of nondegenerate i i d random variables with zero means in this paper we show that a self normalized version of donsker s theorem holds only under the assumption that x belongs to the domain of attraction of the normal law a thus resulting extension of the arc sine law is also discussed we also establish that a weak invariance principle holds true for self normalized self randomized partial sums processes of independent random variables that are assumed to be symmetric around mean zero if and only if max1 j n xj vn p0 as n where v2n nj 1x2j

the degrees of freedom of the k user gaussian interference channel is discontinuous at rational channel coefficients the degrees of freedom of a k user gaussian interference channel gic has been defined to be the multiple of 1 2 log 2 p at which the maximum sum of achievable rates grows with increasing power p in this paper we establish that the degrees of freedom of three or more user real scalar gics viewed as a function of the channel coefficients is discontinuous at points where all of the coefficients are nonzero rational numbers more specifically for all k 2 we find a class of k user gics that is dense in the gic parameter space for which k 2 degrees of freedom are exactly achievable and we show that the degrees of freedom for any gic with nonzero rational coefficients is strictly smaller than k 2 these results are proved using new connections with number theory and additive combinatorics

the capacity of the gaussian interference channel under strong interference corresp the capacity region of a gaussian interference channel with two separate messages is obtained for the case of moderately strong interference it is shown that the region coincides with the one where both messages are required in both receiving terminals

self normalized laws of the iterated logarithm on demontre une loi du logarithme itere qui generalise la version classique pour toutes les distributions dans la classe de feller pour cette demonstration l auteur utilise une auto normalisation convenable pour les sommes partielles de variables aleatoires independantes et identiquement distribuees un cas particulier de ces resultats s applique a toute distribution dans le domaine de l attraction d une certaine loi stable

self normalized cramer type large deviations for independent random variables let x 1 x 2 be independent random variables with zero means and finite variances it is well known that a finite exponential moment assumption is necessary for a cramer type large deviation result for the standardized partial sums in this paper we show that a cramer type large deviation theorem holds for self normalized sums only under a finite 2 th moment 0 1 in particular we show p s n v n x 1 x 1 o 1 1 x 2 d 2 n for 0 x d n where d n n i 1 ex 2 i 1 2 n i 1 e x i 2 1 2 and v n n i 1 x 2 i 1 2 applications to the studentized bootstrap and to the self normalized law of the iterated logarithm are discussed

asymptotics for self normalized random products of sums of i i d random variables abstract let x x i i 1 be a sequence of independent and identically distributed positive random variables which is in the domain of attraction of the normal law and t n be a positive integer random variable denote s n i 1 n x i v n 2 i 1 n x i x 2 where x denotes the sample mean then we show that the self normalized random product of the partial sums k 1 t n s k k v t n is still asymptotically lognormal under a suitable condition about t n

information dimension and the degrees of freedom of the interference channel the degrees of freedom dofs of the k user gaussian interference channel determine the asymptotic growth of the maximal sum rate as a function of the signal to noise ratio subject to a very general sufficient condition on the cross channel gains we give a formula for the dofs of the scalar interference channel as a function of the deterministic channel matrix which involves maximization of a sum of information dimensions over k scalar input distributions known special cases are recovered and even generalized in certain cases with unified proofs

on limiting characterizations of memoryless multiuser capacity regions the restriction to gaussian inputs in the limiting expression for the capacity regions of memoryless gaussian interference and multiple access channels is shown to fall short of achieving capacity even if the inputs are allowed to be dependent and nonstationary in addition the equality between the limiting and the single letter characterizations of memoryless multiple access channel capacity is established directly without recourse to independent coding theorems

interference alignment from degrees of freedom to constant gap capacity approximations interference alignment is a key technique for communication scenarios with multiple interfering links in several such scenarios interference alignment was used to characterize the degrees of freedom of the channel however these degree of freedom capacity approximations are often too weak to make accurate predictions about the behavior of channel capacity at finite signal to noise ratios snrs the aim of this paper is to significantly strengthen these results by showing that interference alignment can be used to characterize capacity to within a constant gap we focus on real time invariant frequency flat x channels the only known solutions achieving the degrees of freedom of this channel are either based on real interference alignment or on layer selection schemes neither of these solutions seems sufficient for a constant gap capacity approximation in this paper we propose a new communication scheme and show that it achieves the capacity of the gaussian x channel to within a constant gap to aid in this process we develop a novel deterministic channel model this deterministic model depends on the 1 2 log snr most significant bits of the channel coefficients rather than only the single most significant bit used in conventional deterministic models the proposed deterministic model admits a wider range of achievable schemes that can be translated to the gaussian channel for this deterministic model we find an approximately optimal communication scheme we then translate this scheme for the deterministic channel to the original gaussian x channel and show that it achieves capacity to within a constant gap this is the first constant gap result for a general fully connected network requiring interference alignment

on the two user interference channel with lack of knowledge of the interference codebook at one receiver in multiuser information theory it is often assumed that every node in the network possesses all codebooks used in the network this assumption may be impractical in distributed ad hoc cognitive or heterogeneous networks this paper considers the two user interference channel with one oblivious receiver ic or i e one receiver lacks knowledge of the interfering cookbook whereas the other receiver knows both codebooks this paper asks whether and if so how much the channel capacity of the ic or is reduced compared with that of the classical ic where both receivers know all codebooks a novel outer bound is derived and shown to be achievable to within a gap for the class of injective semideterministic ic ors the gap is shown to be zero for injective fully deterministic ic ors an exact capacity result is shown for the general memoryless ic or when the nonoblivious receiver experiences very strong interference for the linear deterministic ic or that models the gaussian noise channel at high snr nonindependent identically distributed bernoulli 1 2 input bits are shown to achieve points not achievable by i i d bernoulli 1 2 input bits used in the same achievability scheme for the real valued gaussian ic or the gap is shown to be at most 1 2 bit per channel use even though the set of optimal input distributions for the derived outer bound could not be determined toward understanding the gaussian ic or an achievability strategy is evaluated in which the input alphabets at the nonoblivious transmitter are a mixture of discrete and gaussian random variables where the cardinality of the discrete part is appropriately chosen as a function of the channel parameters surprisingly as the oblivious receiver intuitively should not be able to jointly decode the intended and interfering messages whose codebook is unavailable it is shown that with this choice of input the capacity region of the symmetric gaussian ic or is to within 1 2 log 12 e 3 34 bits per channel use per user of an outer bound for the classical gaussian ic with full codebook knowledge at both receivers

soft decoding based strategies for relay and interference channels analysis and achievable rates using ldpc codes we provide a rigorous mathematical analysis of two communication strategies soft decode and forward soft df for relay channels and soft partial interference cancelation soft ic for interference channels both strategies involve soft estimation which assists the decoding process we consider ldpc codes not because of their practical benefits but because of their analytic tractability which enables an asymptotic analysis similar to random coding methods of information theory unlike some works on the closely related demodulate and forward we assume non memoryless code structure aware estimation with soft df we develop simultaneous density evolution to bound the decoding error probability at the destination this result applies to erasure relay channels in one variant of soft df the relay applies wyner ziv coding to enhance its communication with the destination borrowing from compress and forward to analyze soft ic we adapt existing techniques for iterative multiuser detection and focus on binary input additive white gaussian noise interference channels we prove that optimal point to point codes are unsuitable for soft ic as well as for all strategies that apply partial decoding to improve upon single user detection and multiuser detection including han kobayashi

on the minimum mean p th error in gaussian noise channels and its applications the problem of estimating an arbitrary random vector from its observation corrupted by additive white gaussian noise where the cost function is taken to be the minimum mean p th error mmpe is considered the classical minimum mean square error mmse is a special case of the mmpe several bounds properties and applications of the mmpe are derived and discussed the optimal mmpe estimator is found for gaussian and binary input distributions properties of the mmpe as a function of the input distribution signal to noise ratio snr and order p are derived the single crossing point property scpp which provides an upper bound on the mmse and which together with the mutual information mmse relationship is a powerful tool in deriving converse proofs in multi user information theory is extended to the mmpe moreover a complementary bound to the scpp is derived as a first application of the mmpe a bound on the conditional differential entropy in terms of the mmpe is provided which then yields a generalization of the ozarow wyner lower bound on the mutual information achieved by a discrete input on a gaussian noise channel as a second application the mmpe is shown to improve on previous characterizations of the phase transition phenomenon that manifests in the limit as the length of the capacity achieving code goes to infinity as a discontinuity of the mmse as a function of snr as a final application the mmpe is used to show new bounds on the second derivative of mutual information or the first derivative of the mmse

a gaussian input is not too bad we consider the problem of choosing a robust input for communicating over an input constrained additive noise channel where the noise distribution is arbitrary we show that the mutual information rate achievable using a white gaussian input never incurs a loss of more than half a bit per sample with respect to the power constrained capacity for comparison for the family of colored gaussian noise channels a white gaussian input loses at most log e 2e spl ap 0 265 bit per sample with respect to the optimum water pouring solution for general input constraints we derive a formula for choosing the best input in the min max capacity loss bound sense the bound on the capacity loss is tight for pulse position modulation ppm in the presence of a bursty jammer

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

on communication through a gaussian channel with an mmse disturbance constraint this paper considers a gaussian channel with one transmitter and two receivers the goal is to maximize the communication rate at the intended primary receiver subject to a disturbance constraint at the unintended secondary receiver the disturbance is measured in terms of the minimum mean square error mmse of the interference that the transmission to the primary receiver inflicts on the secondary receiver this paper presents a new upper bound for the problem of maximizing the mutual information subject to an mmse constraint the new bound holds for vector inputs of any length and recovers a previously known limiting when the length of the vector input tends to infinity expression from the work of bustin et al the key technical novelty is a new upper bound on the mmse this bound allows one to bound the mmse for all signal to noise ratio snr values below a certain snr at which the mmse is known which corresponds to the disturbance constraint the bound also complements the single crossing point property of the mmse that upper bounds the mmse for all snr values above a certain value at which the mmse value is known the mmse upper bound provides a refined characterization of the phase transition phenomenon which manifests in the limit as the length of the vector input goes to infinity as a discontinuity of the mmse for the problem at hand for vector inputs of size n 1 a matching lower bound to within an additive gap of order o log log 1 sf mmse where sf mmse is the disturbance constraint is shown by means of the mixed inputs technique recently introduced by dytso et al