random coding error exponents for two dimensional flat fading channels with complete channel state information in this correspondence we consider the random coding error exponent for nondispersive two dimensional 2 d quadrature fading channels for which the channel state information csi is perfectly known at the receiver and the input to the transmitter is constrained in its average power also the effect of space diversity on improving the performance is demonstrated the results obtained in this correspondence shed light on the effect of fading on communications reliability as well as the amount of coding complexity required to achieve a certain decoding error rate a treatment for the random coding error exponent for time correlated flat fading channels with rayleigh fading and bessel function correlation the jake s model is also provided

motivic integral of k3 surfaces over a non archimedean field abstract we prove a formula expressing the motivic integral loeser and sebag 2003 34 of a k3 surface over c t with semi stable reduction in terms of the associated limit mixed hodge structure secondly for every smooth variety over a complete discrete valuation field we define an analogue of the monodromy pairing constructed by grothendieck in the case of abelian varieties and prove that our monodromy pairing is a birational invariant of the variety finally we propose a conjectural formula for the motivic integral of maximally degenerate k3 surfaces over an arbitrary complete discrete valuation field and prove this conjecture for kummer k3 surfaces

full diversity blind space time block codes in this paper the systematic design of a space time block code is considered for a wireless communication system with multiple transmitter receiver antennas and flat fading in which channel state information is completely unknown from the viewpoint of blind signal processing a necessary and sufficient condition is given for the unique identification of the multi input multi output flat fading channel and transmitted signal then some novel unique factorizations for a pair of coprime p ary and q ary phase shift keying psk constellations are established with this and currently available coherent space time block code designs a method is developed to systematically construct full diversity blind nonunitary space time block codes as well as unitary codes by just performing the qr decomposition of the nonunitary codes it is proved that under a noise free environment the code design proposed in this paper can guarantee that the transmitted signals and the channel coefficients are uniquely identified and that under a complex gaussian noise environment in which pth order and q th order statistics p and q are co prime of the received signals are available the channel coefficients can be still uniquely identified in addition a closed form solution to determine the channel coefficients is obtained

an analytical constant modulus algorithm iterative constant modulus algorithms such as godard 1980 and cma have been used to blindly separate a superposition of cochannel constant modulus cm signals impinging on an antenna array these algorithms have certain deficiencies in the context of convergence to local minima and the retrieval of all individual cm signals that are present in the channel we show that the underlying constant modulus factorization problem is in fact a generalized eigenvalue problem and may be solved via a simultaneous diagonalization of a set of matrices with this new analytical approach it is possible to detect the number of cm signals present in the channel and to retrieve all of them exactly rejecting other non cm signals only a modest amount of samples is required the algorithm is robust in the presence of noise and is tested on measured data collected from an experimental set up

closed form correlative coding cfc sub 2 blind identification of mimo channels isometry fitting to second order statistics we present a blind closed form consistent channel estimator for multiple input multiple output mimo systems that uses only second order statistics we spectrally modulate the output of each source by correlative coding it with a distinct filter the correlative filters are designed to meet the following desirable characteristics no additional power or bandwidth is required no synchronization between the sources is needed the original data rate is maintained we first prove an identifiability theorem under a simple spectral condition on the transmitted random processes the mimo channel is uniquely determined up to a phase offset per user from the second order statistics of the received data we then develop the closed form algorithm that attains this identifiability bound we show that minimum phase finite impulse response filters with arbitrary memory satisfy our sufficient spectral identifiability condition this results in a computationally attractive scheme for retrieving the data information sequences after the mimo channel has been identified we assess the performance of the proposed algorithms by computer simulations in particular the results show that our technique outperforms the previously introduced transmitter induced conjugate cyclostationarity approach when there are carrier frequency misadjustments

amplify and forward two way relay networks error exponents and resource allocation in a two way relay network two terminals exchange information over a shared wireless half duplex channel with the help of a relay due to its fundamental and practical importance there has been an increasing interest in this channel however there has been little work that characterizes the fundamental tradeoff between the communication reliability and transmission rate across all signal to noise ratios in this paper we consider amplify and forward af two way relaying due to its simplicity we first derive the random coding error exponent for the link in each direction from the exponent expression the capacity and cutoff rate for each link are also deduced we then put forth the notion of bottleneck error exponent which is the worst exponent decay between the two links to give us insight into the fundamental tradeoff between the rate pair and information exchange reliability in the two way relay network as applications of the error exponent analysis to design a reliable af two way relay network we present two optimization framework to maximize the bottleneck error exponent namely i the optimal rate allocation under a sum rate constraint and its closed form quasi optimal solution that requires only knowledge of the capacity and cutoff rate of each link and ii the optimal power allocation under a total power constraint and perfect global channel state information which is shown equivalently to a quasi convex optimization problem numerical results verify our analysis and the effectiveness of the optimal rate and power allocations in maximizing the bottleneck error exponent i e the network information exchange reliability

description of a class of superstring compactifications related to semi simple lie algebras a class of vacuum configurations in the superstring theory obtained by compactification of physical dimensions from ten to four is constructed the compactification scheme involves taking quotients of tori of semisimple lie algebras by finite symmetry group actions the complete list of such configurations arising from actions by a coxeter transformation is given some topological invariants having physical interpretations are calculated

blind separation of synchronous co channel digital signals using an antenna array ii performance analysis we have recently proposed a blind maximum likelihood approach for demodulating multiple co channel digital signals received synchronously at an antenna array this approach exploits the finite alphabet fa property of digital signals to simultaneously estimate the array response and symbol sequence for each signal we have presented two computationally efficient block algorithms for computing the array response and signal estimates iterative least squares with projection ilsp and iterative least squares with enumeration ilse in this paper we study the performance of these algorithms using both analysis and simulation we derive the probability of error in detecting the signals under the assumption that the array responses are known we use this probability to estimate the probability of error in the algorithms simulation results confirm that the detection error probability yields a good approximation to the performance of the blind algorithms

uncoded and coded performance of mfsk and dpsk in nakagami fading channels the author presents uncoded and coded performance results for noncoherent m ary frequency shift keying mfsk and differentially coherent binary phase shift keying dpsk in a slow nonselective nakagami m 1960 fading channel he gives simple expressions for the asymptotic slopes of probability of bit error for large signal to noise ratio and shows that the effective order of diversity compared to an uncoded rayleigh channel is the product of two parameters one for the channel and one for the code he also compares the uncoded nakagami m results to those of the rician channel in order to show performance differences between these two generalized fading channel models

statistical performance analysis of the algebraic constant modulus algorithm this paper presents a large sample analysis of the covariance of the beamformers computed by the analytical constant modulus algorithm acma method for blindly separating constant modulus sources this can be used to predict the signal to interference plus noise ratio sinr performance of these beamformers as well as their deviation from the nonblind wiener receivers to which they asymptotically converge the analysis is based on viewing acma as a subspace fitting optimization where the subspace is spanned by the eigenvectors of a fourth order covariance matrix the theoretical performance is illustrated by numerical simulations and shows a good match

achievable performance over the correlated rician channel the correlated rician channel is a useful model for a slowly fading channel in which the complex fading process is composed of two quadrature gaussian processes with a given autocorrelation function for slow fading the correlation between adjacent symbols is relatively high the authors investigate the achievable error probabilities over the channel employing coherent detection and ideal side information on the realization of the fading processes at the receiver an underlying decoding delay constraint which precludes the use of ideal interleaving is assumed coded bpsk performance is addressed both with and without the piecewise constant approximation according to which the fading value remains constant during the symbol duration for the latter case that is no piecewise constant approximation the analysis relies on the fredholm determinant associated with the fading process autocorrelation function the authors focus on the exponentially correlated channel the worst case pairs of codewords are identified the exponential behavior of the error probability with random coding and i i d gaussian inputs is analyzed and the behavior of the cut off rate and capacity is addressed the results enhance the insight to the effect of the basic parameters governing the performance and these are examined in view of previous works and compared to relevant performance results for the block fading channel model

the weil petersson geometry of the moduli space of su n 3 calabi yau manifolds i the weil petersson metric is defined on the moduli space of calabi yau manifolds the curvature of this weil petersson metrics is computed and its potential is explicitely defined it is proved that the moduli space of calabi yau manifolds is unobstructed see tian

an integral structure in quantum cohomology and mirror symmetry for toric orbifolds abstract we introduce an integral structure in orbifold quantum cohomology associated to the k group and the class in the case of compact toric orbifolds we show that this integral structure matches with the natural integral structure for the landau ginzburg model under mirror symmetry by assuming the existence of an integral structure we give a natural explanation for the specialization to a root of unity in y ruan s crepant resolution conjecture yongbin ruan the cohomology ring of crepant resolutions of orbifolds in contemp math vol 403 amer math soc providence ri 2006 pp 117 126

upper and lower bounds to estimate the random coding exponent for a peak power limited channel in this paper we consider the estimation of gallager s 1968 random coding exponent rce for a peak power constraint at the transmitter for the two dimensional fading channel with additive white gaussian noise awgn and with perfect channel estimation at the receiver despite the fact that many wireless channels are peak power limited the rce for such channels has not been considered previously in the literature such a problem has only been partially solved for the awgn case due to the difficulty in finding an input signal distribution that yields the rce in this paper we adopt a different approach in which we develop upper and lower bounds to the rce with the hope of trapping it in a narrow region our quest is successful as we can estimate the rce to an error of only 0 72 bit per modulation symbol furthermore we find that the rce for the peak power limited channel does not represent a severe degradation relative to that attained for the average power limited channel thus good modulation and coding schemes at reasonable complexity should exist for a peak power constrained fading channel

mirror symmetry and rational curves on quintic threefolds a guide for mathematicians we give a mathematical account of a recent string theory calcula tion which predicts the number of rational curves on the generic quintic three fold our account involves the interpretation of yukawa couplings in terms of variations of hodge structure a new q expansion principle for functions on the moduli space of calabi yau manifolds and the mirror symmetry phe nomenon recently observed by string theorists department of mathematics duke university durham north carolina 27706 e mail address drm math duke edu this content downloaded from 157 55 39 224 on wed 14 dec 2016 04 59 36 utc all use subject to http about jstor org terms

h transforms for wireless communication the h transforms are integral transforms that involve fox s h functions as kernels a large variety of integral transforms can be put into particular forms of the h transform since h functions subsume most of the known special functions including meijer s g functions in this paper we embody the h transform theory into a unifying framework for modeling and analysis in wireless communication first we systematize the use of elementary identities and properties of the h transform by introducing operations on parameter sequences of h functions we then put forth h fading and degree 2 irregular h fading to model radio propagation under composite specular and or inhomogeneous conditions the h fading describes composite effects of multipath fading and shadowing as a single h variate including most of typical models such as rayleigh nakagami m weibull alpha mu n ast nakagami m generalized k fading and weibull gamma fading as its special cases as a new class of h variates called the degree zeta irregular h variate the degree 2 irregular h fading characterizes specular and or inhomogeneous radio propagation in which the multipath component consists of a strong specularly reflected or line of sight los wave as well as unequal power or correlated in phase and quadrature scattered waves this fading includes a variety of typical models such as rician nakagami q kappa mu eta mu rician los gamma and kappa mu los gamma fading as its special cases finally we develop a unifying h transform analysis for the amount of fading error probability channel capacity and error exponent in wireless communication using the new systematic language of transcendental h functions by virtue of two essential operations called mellin and convolution operations involved in the mellin transform and mellin convolution of two h functions the h transforms for these performance measures culminate in h functions using the algebraic asymptotic expansions of the h transform we further analyze the error probability and capacity at high and low signal to noise ratios in a unified fashion

n 2 supergravity type iib superstrings and algebraic geometry the geometry ofn 2 supergravity is related to the variations of hodge structure for formal calabi yau spaces all known results in this branch of algebraic geometry are easily recovered from supersymmetry arguments this identification has a physical meaning for a type iib superstring compactified on a calabi yau 3 fold we give exact non perturbative results for the string effective lagrangian our geometrical framework suggests a re formulation of the gepner conjecture about 2 2 superconformal theories as the solution to theschottky problem for algebraic complex manifolds having trivial canonical bundle

ising n fold integrals as diagonals of rational functions and integrality of series expansions we show that the n fold integrals n of the magnetic susceptibility of the ising model as well as various other n fold integrals of the ising class or n fold integrals from enumerative combinatorics like lattice green functions correspond to a distinguished class of functions generalizing algebraic functions they are actually diagonals of rational functions as a consequence the power series expansions of the analytic at x 0 solutions of these linear differential equations derived from geometry are globally bounded which means that after just one rescaling of the expansion variable they can be cast into series expansions with integer coefficients we also give several results showing that the unique analytical solution of calabi yau odes and more generally picard fuchs linear odes with solutions of maximal weights are always diagonals of rational functions besides in a more enumerative combinatorics context generating functions whose coefficients are expressed in terms of nested sums of products of binomial terms can also be shown to be diagonals of rational functions we finally address the question of the relations between the notion of integrality series with integer coefficients or more generally globally bounded series and the modularity of odes

on quasi isomorphic dgbv algebras one of the methods to obtain frobenius manifold structures is via differential gerstenhaber batalin vilkovisky dgbv algebra construction an important problem as motivated from mirror symmetry is how to identify frobenius manifold structures constructed from two different dgbv algebras for dgbv algebras with suitable conditions we show the functorial property of a construction of deformations of the multiplicative structures of their cohomology in particular we show that quasi isomorphic dgbv algebras yield equivalent formal frobenius manifold structures

information theoretic considerations for coded modulation over fading channels we compute the random coding error exponent for coded modulation transmitted over a flat memoryless rayleigh fading channel in addition estimates of code lengths required to achieve a certain error probability are determined and compared to those required for the additive white gaussian noise channel finally the effect of receiver antenna diversity is also considered as a method to compensate for fading and is shown to have a significant positive impact on the error exponent the results we obtain represent an information theoretic view that complements the existing literature on the performance of coded modulation over fading channels with receiver diversity

mirror symmetry mirror map and applications to calabi yau hypersurfaces mirror symmetry picard fuchs equations and instanton corrected yukawa couplings are discussed within the framework of toric geometry it allows to establish mirror symmetry of calabi yau spaces for which the mirror manifold had been unavailable in previous constructions mirror maps and yukawa couplings are explicitly given for several examples with two and three moduli

the arithmetic mirror symmetry and calabi yau manifolds we extend our variant of mirror symmetry for k3 surfaces gn3 and clarify its relation with mirror symmetry for calabi yau manifolds we introduce two classes for the models a and b of calabi yau manifolds fibrated by k3 surfaces with some special picard lattices these two classes are related with automorphic forms on iv type domains which we studied in our papers gn1 gn6 conjecturally these automorphic forms take part in the quantum intersection pairing for model a yukawa coupling for model b and mirror symmetry between these two classes of calabi yau manifolds recently there were several papers by physicists where it was shown on some examples we propose a problem of classification of introduced calabi yau manifolds our papers gn1 gn6 and n3 n14 give hope that this is possible they describe possible picard or transcendental lattices of general k3 fibers of the calabi yau manifolds

coded diversity on block fading channels this paper considers coded diversity schemes over block fading rician channels using random coding techniques two random coding upper bounds on the error probability of block codes are derived a new bound and a simpler but looser bound assuming binary input distribution also a new lower bound for any block code is derived using the strong converse to channel coding theorem the lower bound shows that the new random coding upper bound is quite tight furthermore it is shown that the maximum achievable diversity order in a block fading channel with finite interleaving depends not only on the number of subchannels l but also on the code rate r and that the performance can only marginally be improved by increasing the block length of the code the random coding upper bound and the lower bound are shown to converge to the capacity outage for large channel block lengths n demonstrating that the capacity outage can be used for estimating the error probability of coded diversity schemes

blind separation of synchronous co channel digital signals using an antenna array i algorithms we propose a maximum likelihood ml approach for separating and estimating multiple synchronous digital signals arriving at an antenna array at a cell site the spatial response of the array is assumed to be known imprecisely or unknown we exploit the finite alphabet property of digital signals to simultaneously estimate the array response and the symbol sequence for each signal uniqueness of the estimates is established for bpsk signals we introduce a signal detection technique based on the finite alphabet property that is different from a standard linear combiner computationally efficient algorithms for both block and recursive estimation of the signals are presented this new approach is applicable to an unknown array geometry and propagation environment which is particularly useful in wireless communication systems simulation results demonstrate its promising performance

duality bounds on the cutoff rate with applications to ricean fading we propose a technique to derive upper bounds on gallager s cost constrained random coding exponent function applying this technique to the noncoherent peak power or average power limited discrete time memoryless ricean fading channel we obtain the high signal to noise ratio snr expansion of this channel s cutoff rate at high snr the gap between channel capacity and the cutoff rate approaches a finite limit this limit is approximately 0 26 nats per channel use for zero specular component rayleigh fading and approaches 0 39 nats per channel use for very large values of the specular component we also compute the asymptotic cutoff rate of a rayleigh fading channel when the receiver has access to some partial side information concerning the fading it is demonstrated that the cutoff rate does not utilize the side information as efficiently as capacity and that the high snr gap between the two increases to infinity as the imperfect side information becomes more and more precise