on the capacity achieving distribution of the discrete time noncoherent and partially coherent awgn channels we investigate the communication limits over rapid phase varying channels and consider the capacity of a discrete time noncoherent additive white gaussian noise ncawgn channel under the average power constraint we obtain necessary and sufficient conditions for the capacity achieving input distribution and show that this distribution is discrete and possesses an infinite number of mass points using this characterization of the capacity achieving distribution we compute a tight lower bound on the capacity of the channel based on examining suboptimal input distributions in addition we provide some easily computable lower and upper bounds on the channel capacity finally we extend some of these results to the partially coherent channel where it is assumed that a phase locked loop pll is used to track the carrier phase at the receiver and that an ideal interleaver and de interleaver are employed rendering the tikhonov distributed residual phase errors statistically independent from one symbol interval to another

a compute and forward scheme for gaussian bi directional relaying with inter symbol interference we provide inner and outer bounds on the capacity region for the gaussian bi directional relaying over inter symbol interference channels the outer bound is obtained by the conventional cut set argument for the inner bound we propose a compute and forward coding scheme based on lattice partition chains and study its achievable rate the coding scheme is a time domain coding scheme which uses a novel precoding scheme at the transmitter in combination with lattice precoding and a minimum mean squared error receiver to recover linear combinations of lattice codewords the proposed compute and forward coding scheme substantially outperforms decode and forward schemes while it is well known that for the point to point communication case both independent coding along sub channels and time domain coding can approach the capacity limit as a byproduct of the proposed scheme we show that for the bi directional relay case independent coding along sub channels is not optimal in general and joint coding across sub channels can improve the capacity for some channel realizations

monodromy of a two degrees of freedom liouville integrable system with many focus focus singular points this letter deals with the global monodromy of singular lagrangian toral fibrations defined by two degrees of freedom liouville integrable systems with only focus focus singular points we show that any global monodromy matrix in sl 2 is realizable by such a system

a lower bound on the cutoff rate for gaussian channels with peak limited inputs a lower bound on the cutoff rate r sub o of a dispersive gaussian channel with peak rather than average power limited input is evaluated and compared to the lower bound on capacity under the same input constraints it is assumed that the input symbols are independent and uniformly distributed both bounds exhibit the same behavior as a function of an appropriately defined signal to noise ratio snr with a discrepancy of 1 68 db to the disadvantage of r sub o at high snrs the lower bound on r sub o is evaluated for peak and slope limited signals that model magnetic recording systems and is compared to the lower bound on capacity

fractional hamiltonian monodromy from a gauss manin monodromy fractional hamiltonian monodromy is a generalization of the notion of hamiltonian monodromy recently introduced by nekhoroshev sadovskii and zhilinskii c r acad sci paris ser 1 335 985 2002 nekhoroshev sadovskii and zhilinskii ann henri poincare 7 1099 2006 for energy momentum maps whose image has a particular type of nonisolated singularities in this paper we analyze the notion of fractional hamiltonian monodromy in terms of the gauss manin monodromy of a riemann surface constructed from the energy momentum map and associated with a loop in complex space which bypasses the line of singularities we also prove some propositions on fractional hamiltonian monodromy for 1 n and m n resonant systems

channel capacity under sub nyquist nonuniform sampling this paper investigates the effect of sub nyquist sampling upon the capacity of an analog channel the channel is assumed to be a linear time invariant gaussian channel where perfect channel knowledge is available at both the transmitter and the receiver we consider a general class of right invertible time preserving sampling methods which includes irregular nonuniform sampling and characterize in closed form the channel capacity achievable by this class of sampling methods under a sampling rate and power constraint our results indicate that the optimal sampling structures extract out the set of frequencies that exhibits the highest signal to noise ratio among all spectral sets of measure equal to the sampling rate this can be attained through filterbank sampling with uniform sampling grid employed at each branch with possibly different rates or through a single branch of modulation and filtering followed by uniform sampling these results reveal that for a large class of channels employing irregular nonuniform sampling sets while are typically complicated to realize in practice does not provide capacity gain over uniform sampling sets with appropriate preprocessing our findings demonstrate that aliasing or scrambling of spectral components does not provide capacity gain in this scenario which is in contrast to the benefits obtained from random mixing in spectrum blind compressive sampling schemes

on the finiteness of the capacity of continuous channels evaluating the channel capacity is one of many key problems in information theory in this work we derive rather mild sufficient conditions under which the capacity of continuous channels is finite and achievable these conditions are derived for generic memoryless and possibly nonlinear additive noise channels the results are based on a novel sufficient condition that guarantees the convergence of differential entropies under point wise convergence of probability density functions perhaps surprisingly the finiteness of channel capacity holds for the majority of setups including those where inputs and outputs have possibly infinite second moments

quantum monodromy and pattern formation hamiltonian monodromy is known to be the first obstruction to the existence of global action coordinates in integrable systems its manifestation in quantum systems can be seen as characteristic defects of the regular lattice formed by the joint eigenvalues of mutually commuting quantum operators the relation between topology of singular fibers of classical integrable fibrations and patterns formed by joint spectrum of corresponding quantum systems is discussed the notion of the sign of elementary monodromy defect is introduced on the basis of cut and glue construction of the lattice defects special attention is paid to non elementary defects which generically appear in phyllotaxis patterns and can be associated with plant morphology

poisson mechanics for perturbed mic kepler problems at both positive and negative energies the mic kepler problem an extension of the kepler problem is known to admit the symmetry group su 2 su 2 or according to whether the energy is negative or positive in general each of the co adjoint orbits of a lie group carries the canonical symplectic form called the kks form and a hamiltonian dynamical system is defined on it if a suitable hamiltonian is given perturbed mic kepler problems can be treated in this setting if a perturbed hamiltonian in normal form is determined according to whether the energy is negative or positive since the co adjoint orbit in question can be viewed as a symplectic leaf of the associated lie algebra or according to whether the energy is negative or positive the perturbed mic kepler problems in normal form can be described in the poisson mechanics defined on respective symmetry lie algebras thus the equations of motion for perturbed systems can be described in the form of poisson brackets for both cases of and on an equal footing it will be shown further how two parameters assigning a co adjoint orbit of su 2 su 2 or are related to the parameters contained in the mic kepler problem the perturbation of the mic kepler problem to be treated in this article is rather restricted to that caused by the presence of weak constant electric and magnetic fields orthogonal to each other when regularized the perturbed hamiltonians at both positive and negative energies are put in the birkhoff gustavson normal form and thereby the flows generated by the perturbed hamiltonians are studied in poisson mechanics in terms of variables associated with constants of motion for the mic kepler problem

capacity of the discrete time gaussian channel with intersymbol interference the discrete time gaussian channel with intersymbol interference isi where the inputs are subject to a per symbol average energy constraint is considered the capacity of this channel is derived by means of a hypothetical channel model called the n circular gaussian channel ncgc whose capacity is readily derived using the theory of the discrete fourier transform the results obtained for the ncgc are used further to prove that in the limit of increasing block length n the capacity of the discrete time gaussian channel dtgc with isi using a per block average energy input constraint n block dtgc is indeed also the capacity when using the per symbol average energy constraint

classification of perturbations of the hydrogen atom by small static electric and magnetic fields we consider perturbations of the hydrogen atom by sufficiently small homogeneous static electric and magnetic fields of all possible mutual orientations normalizing with regard to the keplerian sy

quantum monodromy in the two centre problem using modern tools from the geometric theory of hamiltonian systems it is shown that electronic excitations in diatoms which can be modelled by the two centre problem exhibit a complicated case of classical and quantum monodromy this means that there is an obstruction to the existence of global quantum numbers in these classically integrable systems the symmetric case of h 2 and the asymmetric case of h he are explicitly worked out the asymmetric case has a non local singularity causing monodromy it coexists with a second singularity which is also present in the symmetric case an interpretation of monodromy is given in terms of the caustics of invariant tori

complete classification of qualitatively different perturbations of the hydrogen atom in weak near orthogonal electric and magnetic fields we consider perturbations of the hydrogen atom by sufficiently small homogeneous static electric and magnetic fields in near orthogonal configurations normalization of the keplerian symmetry reveals that in the parameter space such systems belong in a zone of systems close to the 1 1 resonance the latter corresponding to the exactly orthogonal configuration integrable approximations obtained from second normalization of systems in the 1 1 zone are classified into several different qualitative types many of which possess nontrivial monodromy we compute monodromy of the complete three dimensional energy momentum map compare the joint quantum spectrum to classical bifurcation diagrams and show the effect of second normalization to the joint spectrum

monodromy in the hydrogen atom in crossed fields abstract we show that the hydrogen atom in orthogonal electric and magnetic fields has a special property of certain integrable classical hamiltonian systems known as monodromy the strength of the fields is assumed to be small enough to validate the use of a truncated normal form h snf which is obtained from a two step normalization of the original system we consider the level sets of h snf on the second reduced phase space for an open set of field parameters we show that there is a special dynamically invariant set which is a doubly pinched 2 torus this implies that the integrable hamiltonian h snf has monodromy manifestation of monodromy in quantum mechanics is also discussed

non hamiltonian monodromy abstract it is well known that the energy momentum map of a two degree of freedom integrable hamiltonian system with a focus focus singularity has monodromy in this paper we generalize this result to systems which are not necessarily hamiltonian

capacity of the gaussian two hop full duplex relay channel with residual self interference in this paper we investigate the capacity of the gaussian two hop full duplex fd relay channel with residual self interference this channel is comprised of a source an fd relay and a destination where a direct source destination link does not exist and the fd relay is impaired by residual self interference we adopt the worst case linear self interference model with respect to the channel capacity and model the residual self interference as a gaussian random variable whose variance depends on the amplitude of the transmit symbol of the relay for this channel we derive the capacity and propose an explicit capacity achieving coding scheme thereby we show that the optimal input distribution at the source is gaussian and its variance depends on the amplitude of the transmit symbol of the relay on the other hand the optimal input distribution at the relay is discrete or gaussian where the latter case occurs only when the relay destination link is the bottleneck link the derived capacity converges to the capacity of the two hop ideal fd relay channel without self interference and to the capacity of the two hop half duplex hd relay channel in the limiting cases when the residual self interference is zero and infinite respectively our numerical results show that significant performance gains are achieved with the proposed capacity achieving coding scheme compared with the achievable rates of conventional hd relaying and or conventional fd relaying

rotation forms and local hamiltonian monodromy the monodromy of torus bundles associated with completely integrable systems can be computed using geometric techniques constructing homology cycles or analytic arguments computing discontinuities of abelian integrals in this article we give a general approach to the computation of monodromy that resembles the analytical one reducing the problem to the computation of residues of polar 1 forms we apply our technique to three celebrated examples of systems with monodromy the champagne bottle the spherical pendulum the hydrogen atom and to the case of non degenerate focus focus singularities re obtaining the classical results an advantage of this approach is that the residue like formula can be shown to be local in a neighborhood of a singularity hence allowing the definition of monodromy also in the case of non compact fibers this idea has been introduced in the literature under the name of scattering monodromy we prove the coincidence of the two definitions with the monodromy of an appropr

normal forms for perturbed keplerian systems abstract perturbations of rotating and nonrotating keplerian systems with two and three degrees of freedom are considered the dominant unperturbed part of the hamilton function is the sum of the two body part and the coriolis term the flows associated to these two components are used to put the whole system into normal form by means of symplectic transformations three different situations are analysed i the two body effect dominates the coriolis part slow rotations ii the coriolis effect is stronger than the two body hamiltonian very fast rotations and iii the two effects are comparable moderate rotations after performing the transformations to normal form the system is reduced by one or two degrees of freedom we describe the reduced phase spaces by calculating the invariants of the symmetry groups associated to the different normal forms reduced systems the technique is applied to the reduction of a hamiltonian system modelling the trapping mechanisms for the electron of a strongly ionized hydrogen atom

proper complex random processes with applications to information theory the covariance of complex random variables and processes when defined consistently with the corresponding notion for real random variables is shown to be determined by the usual complex covariance together with a quantity called the pseudo covariance a characterization of uncorrelatedness and wide sense stationarity in terms of covariance and pseudo covariance is given complex random variables and processes with a vanishing pseudo covariance are called proper it is shown that properness is preserved under affine transformations and that the complex multivariate gaussian density assumes a natural form only for proper random variables the maximum entropy theorem is generalized to the complex multivariate case the differential entropy of a complex random vector with a fixed correlation matrix is shown to be maximum if and only if the random vector is proper gaussian and zero mean the notion of circular stationarity is introduced for the class of proper complex random processes a discrete fourier transform correspondence is derived relating circular stationarity in the time domain to uncorrelatedness in the frequency domain an application of the theory is presented

the problem of two fixed centers bifurcations actions monodromy abstract a comprehensive analysis of the euler jacobi problem of motion in the field of two fixed attracting centers is given first classically and then quantum mechanically in semiclassical approximation the system was originally studied in the context of celestial mechanics but starting with pauli s dissertation became a model for one electron molecules such as h 2 symmetric case of equal centers or hhe2 asymmetric case of different centers the present paper deals with arbitrary relative strength of the two centers and considers separately the planar and the three dimensional problems all versions represent non trivial examples of integrable dynamics and are studied here from the unifying point of view of the energy momentum mapping from phase space to the space of integration constants the interesting objects are the critical values of this mapping i e its bifurcation diagram and their pre images which organize the foliation of phase space into liouville arnold tori the classical analysis culminates in the explicit derivation of the action variable representation of iso energetic surfaces the attempt to identify a system of global actions smoothly dependent on the integration constants wherever these are non critical leads to the detection of monodromy of a special kind which is here described for the first time the classical monodromy has its counterpart in the quantum version of the two center problem where it prevents the assignments of unique quantum numbers even though the system is separable

a universal procedure for normalizing n degree of freedom polynomial hamiltonian systems we depart from an n degree of freedom hamiltonian formed by the sum of homogeneous polynomials in n coordinates and n momenta with arbitrary coefficients by extending formally an integral of the principal part of the system to the full hamiltonian and truncating higher order terms we obtain a simplified hamiltonian this normalization procedure can be used to extract qualitative features of the departure system in this paper we present the symbolic routines needed to achieve the normalization the power and generality of the algorithm are exhibited through two examples

optimal feedback communication via posterior matching in this paper we introduce a fundamental principle for optimal communication over general memoryless channels in the presence of noiseless feedback termed posterior matching using this principle we devise a simple sequential generic feedback transmission scheme suitable for a large class of memoryless channels and input distributions achieving any rate below the corresponding mutual information this provides a unified framework for optimal feedback communication in which the horstein scheme bsc and the schalkwijk kailath scheme awgn channel are special cases thus as a corollary we prove that the horstein scheme indeed attains the bsc capacity settling a longstanding conjecture we further provide closed form expressions for the error probability of the scheme over a range of rates and derive the achievable rates in a mismatch setting where the scheme is designed according to the wrong channel model several illustrative examples of the posterior matching scheme for specific channels are given and the corresponding error probability expressions are evaluated the proof techniques employed utilize novel relations between information rates and contraction properties of iterated function systems

on the discreteness of capacity achieving distributions we consider a scalar additive channel x spl rarr x n whose input is amplitude constrained by extending smith s 1969 argument we derive a sufficient condition on noise probability density functions pdf that guarantee finite support for the associated capacity achieving distribution s

rates of approximation of bounded variation functions by two generalized meyer konig and zeller type operators abstract in this paper the approximation behaviours of two generalized meyer konig and zeller type operators m n and m n are studied by means of the decomposition technique of functions of bounded variation and the method of bojanic 1 bojanic and vuilleumier 2 and cheng 3 together with some results from probability theory and the exact bound of meyer konig and zeller operators basis functions the rates of convergence of these two operators for functions of bounded variation are obtained

the quantum mechanical spherical pendulum on decrit le comportement asymptotique du spectre du pendule quantique spherique quand la constante de planck tend vers zero

hamiltonian monodromy and morse theory we show that hamiltonian monodromy of an integrable two degrees of freedom system with a global circle action can be computed by applying morse theory to the hamiltonian of the system our proof is based on takens s index theorem which specifies how the energy h chern number changes when h passes a non degenerate critical value and a choice of admissible cycles in fomenko zieschang theory connections of our result to some of the existing approaches to monodromy are discussed

parallel transport along seifert manifolds and fractional monodromy the notion of fractional monodromy was introduced by nekhoroshev sadovskii and zhilinskii as a generalization of standard integer monodromy in the sense of duistermaat from torus bundles to singular torus fibrations in the present paper we prove a general result that allows one to compute fractional monodromy in various integrable hamiltonian systems in particular we show that the non triviality of fractional monodromy in 2 degrees of freedom systems with a hamiltonian circle action is related only to the fixed points of the circle action our approach is based on the study of a specific notion of parallel transport along seifert manifolds

degree of approximation to function of bounded variation by bezier variant of mkz operators abstract guo approx theory appl 4 1988 9 18 introduced the integral modification of meyer konig and zeller operators m n and studied the rate of convergence for functions of bounded variation in this paper we introduce the bezier variant of these integrated mkz operators and study the rate of convergence by means of the decomposition technique of functions of bounded variation together with some results of probability theory and the exact bound of mkz basis functions recently zeng j math anal appl 219 1998 364 376 claimed to improve the results of guo and gupta approx theory appl 11 1995 106 107 but there is a major mistake in the paper of zeng for special case our main theorem gives the correct estimate on the rate of convergence over the result of zeng

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

communication over individual channels a communication problem in considered where no mathematical model is specified for the channel the achievable rates are determined as a function of the channel input and output sequences known a posteriori without assuming any a priori relation between them for discrete channels the empirical mutual information between the input and output sequences is shown to be achievable while for continuous channels the achievable rate is based on the empirical correlation between the sequences a rate adaptive scheme employing feedback which achieves these rates asymptotically with a guaranteed reliability without prior knowledge of the channel behavior is presented

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

feedback rate capacity loss tradeoff for limited feedback mimo systems multiple input multiple output mimo communication systems can provide large capacity gains over traditional single input single output siso systems and are expected to be a core technology of next generation wireless systems often these capacity gains are achievable only with some form of adaptive transmission in this paper we study the capacity loss defined as the rate loss in bits s hz of the mimo wireless system when the covariance matrix of the transmitted signal vector is designed using a low rate feedback channel for the mimo channel we find a bound on the ergodic capacity loss when random codebooks generated from the uniform distribution on the complex unit sphere are used to convey the second order statistics of the transmitted signal from the receiver to the transmitter in this case we find a closed form expression for the ergodic capacity loss as a function of the number of bits fed back at each channel realization these results show that the capacity loss decreases at least as o 2 sup b 2mmt 2 where b is the number of feedback bits m sub t is the number of transmit antennas and m min m sub r m sub t where m sub r is the number of receive antennas in the high snr regime we present a new bound on the capacity loss that is tighter than the previously derived bound and show that the capacity loss decreases exponentially as a function of the number of feedback bits

bezout space time precoders and equalizers for mimo channels the transmitter receiver diversities in p input q output multiple input multiple output mimo channels will play a key role in future high rate wireless communication the major challenge in mimo signal recovery is the mitigation of the inevitable intersymbol interference isi and interchannel interference ici in multipath mimo channels the bezout system theory provides a simple solution for isi ici cancellation and thus can serve as a powerful mathematical foundation for mimo systems if p q and the mimo system h d is left coprime the system is perfectly recoverable via a bezout precoder assuming the channel information is available at the transmitter for a robust channel design a quantitative analysis of signal to noise ratio snr of the optimal bezout equalizer precoder can be derived from the bezout null space compared with the alamouti see ieee j select areas commun vol 16 p 1451 58 oct 1998 space time coding the bezout precoder is shown to be more appealing in slowly time varying channels where the feedback of the channel information induces minor overhead the bezout system can work well jointly with the space time block coding stbc the stbc can be adopted to artificially construct a larger q spl times p q p virtual transfer function without the channel information a necessary and sufficient condition is provided for perfect recoverability pr for the stbc induced virtual mimo systems based on the virtual transfer function both channel independent and channel dependent precoding strategies are feasible via a singular value decomposition svd analysis the bezout precoder can be shown to outperform the orthogonal frequency division multiplexing ofdm precoder in bit error rate ber transmission rate and receiver implementation the interplay of the two design parameters n and spl rho is analyzed to provide a simple guideline for an optimal configuration the combined stbc and bezout equalization techniques offer a broader spectrum of transceiver system configuration to achieve optimal design tradeoff among ber transmission rate and implementation complexity

fractional monodromy in systems with coupled angular momenta we present a one parameter family of systems with fractional monodromy which arises from a 1 2 diagonal action of a dynamical symmetry so 2 i n a regime of adiabatic separation of slow and fast motions we relate the presence of fractional monodromy to a redistribution of states both in the quantum and in the semi quantum spectra

using hermite bases in studying capacity achieving distributions over awgn channels this paper studies classes of generic deterministic discrete time memoryless and nonlinear additive white gaussian noise awgn channels subject to multiple types of constraints such as the even moment and compact support constraints or a mixture the optimal input is proved to be discrete with finite number of mass points in the vast majority of the cases only under the even moment constraint and for special cases that emulate the average power constrained linear channel capacity is found to be achieved by an absolutely continuous input the results are extended to channels where the distortion is generally piecewise nonlinear where the discrete nature of the optimal input is conserved these results are reached through the development of methodology and tools that are based on standard decompositions in a hilbert space with the hermite polynomials as a basis and it is showcased how these bases are natural candidates for general information theoretic studies of the capacity of channels affected by awgn intermediately novel results regarding the output rate of decay of gaussian channels are derived namely the output probability distribution of any channel subjected to additive gaussian noise decays necessarily slower than the gaussian itself finally numerical computations are provided for some sample cases optimal inputs are determined and capacity curves are drawn these results put into question the accuracy of adopting the widely used expression 1 1 snr for computing capacities of gaussian deterministic channels

bounds on the symmetric binary cutoff rate for dispersive gaussian channels bounds on the symmetric binary cutoff rate for a pulse amplitude modulated pam signaling over dispersive gaussian channels are evaluated and discussed these easily calculable bounds can be used to estimate the reliable rate of information transmission and the error exponent behavior for binary two level pam schemes operating through a prefiltered additive white gaussian channel the memory of which is long enough to make the exact evaluation of the cutoff rate formidable the core of the bounding technique relies on a probabilistic interpretation of a fundamental theorem in matrix theory regarding the logarithm of the largest eigenvalue of a nonnegative primitive matrix commonly applied in large deviation problems these bounds are calculated for some examples and their respective tightness is considered further potential applications of the proposed bounding technique are pointed out

uncovering fractional monodromy the uncovering of the role of monodromy in integrable hamiltonian fibrations has been one of the major advances in the study of integrable hamiltonian systems in the past few decades on one hand monodromy turned out to be the most fundamental obstruction to the existence of global action angle coordinates while on the other hand it provided the correct classical analogue for the interpretation of the structure of quantum joint spectra fractional monodromy is a generalization of the concept of monodromy instead of restricting our attention to the toric part of the fibration we extend our scope to also consider singular fibres in this paper we analyze fractional monodromy for n1 n2 resonant hamiltonian systems with n1 n2 coprime natural numbers we consider in particular systems that for n1 n2 1 contain one parameter families of singular fibres which are curled tori we simplify the geometry of the fibration by passing to an appropriate branched covering in the branched covering the curled tori and their neighborhood become untwisted thus simplifying the geometry of the fibration we essentially obtain the same type of generalized monodromy independently of n1 n2 fractional monodromy is then recovered by pushing the results obtained in the branched covering back to the original system

trellis coding for partial response channels we consider trellis coding techniques for improving the reliability of digital transmission over noisy partial response channels such channels are commonly encountered in digital communication systems and also play a role in devices for data recording concentrating on the channels with characteristics 1 mp d we study methods to obtain codes which increase free euclidean distance between permitted sequences of channel outputs and avoid the occurrence of unlimited runs of identical outputs at the expense of some loss in data rate one technique employs the concept of set partitioning the other is based on using convolutional codes designed for maximum free hamming distance in conjunction with a precoder both methods lead to essentially equivalent codes

optimization of signal sets for partial response channels ii asymptotic coding gain for pt i see ibid vol 37 no 5 p 1327 141 1991 for a linear time invariant discrete time channel with a given transfer function h f and information rate r bits t where t is the symbol interval an optimal signal set of length k is defined to be a set of 2 sup rk inputs of length k that maximizes the minimum l sub 2 distance between pairs of outputs the author studies the minimum distance between outputs or equivalently the coding gain of optimal signal sets as k to infinity he shows how to estimate the coding gain relative to single step detection of an optimal signal set length k when k is large

hamiltonian hopf bifurcation of the hydrogen atom in crossed fields we consider the hydrogen atom in crossed electric and magnetic fields we prove that near the stark and zeeman limits the system goes through two qualitatively different hamiltonian hopf bifurcations we explain in detail the geometry of the bifurcations

the degrees of freedom of isotropic mimo interference channels without state information at the transmitters this paper fully determines the degree of freedom dof region of two user interference channels with arbitrary number of transmit and receive antennas in the case of isotropic and independent or block wise independent fading where the channel state information is available to the receivers but not to the transmitters thus the dof gap between previous upper and lower bounds due to the authors vaze and varanasi and huang jafar shamai and vishwanath is closed the dof result characterizes the capacity region to the first order of the logarithm of the signal to noise ratio snr in the high snr regime the dof region is achievable by using random gaussian codebooks independent of the channel states which implies that it is impossible to increase the dof using beamforming and interference alignment in the absence of channel state information at the transmitters

symplectic coordinates on s2 s2 for perturbed keplerian problems application to the dynamics of a generalised stormer problem abstract in order to analyse the dynamics of a given hamiltonian system in the space defined as the cartesian product of two spheres we propose to combine delaunay coordinates with poincare like coordinates the coordinates are of local character and have to be selected accordingly with the type of motions one has to take into consideration so we distinguish the following types i rectilinear motions ii circular and equatorial motions iii circular non equatorial motions iv non circular equatorial motions and v non circular and non equatorial motions we apply the theory to study the dynamics of the reduced flow of a generalised stormer problem that is modelled as a perturbation of the kepler problem after using averaging and reduction theories the corresponding flow is analysed on the manifold s 2 s 2 calculating the occurring equilibria and their stability finally the flow of the original problem is reconstructed concluding the existence of some families of periodic solutions and kam tori

capacity and rate regions of a class of broadcast interference channels in this paper a class of broadcast interference channels bic is investigated where one of the two broadcast receivers is subject to interference coming from a point to point transmission for a general discrete memoryless broadcast interference channel dm bic an achievable scheme based on message splitting superposition and binning is proposed and a concise representation of the corresponding achievable rate region mathcal r is obtained two partial order broadcast conditions interference oblivious less noisy and interference cognizant less noisy are defined thereby extending the usual less noisy condition for a regular broadcast channel by taking interference into account under these conditions a reduced form of mathcal r is shown to be equivalent to a rate region based on a simpler scheme where the broadcast transmitter uses only superposition furthermore if interference is strong for the interference oblivious less noisy dm bic the capacity region is given by the aforementioned two equivalent rate regions for the interference cognizant less noisy dm bic it is argued that the strong but not very strong interference condition does not exist and in this case the capacity region for the very strong interference is obtained for a gaussian broadcast interference channel channel parameters are categorized into three regimes for the first two regimes which are closely related to the two partial order broadcast conditions achievable rate regions are derived by specializing the corresponding achievable schemes of dm bics with gaussian input distributions the entropy power inequality based outer bounds are obtained by combining bounding techniques for a gaussian broadcast channel and a gaussian interference channel these inner and outer bounds lead to either exact or approximate characterizations of capacity regions and sum capacity under various conditions for the remaining complementing regime inner and outer bounds are also provided

capacity of gaussian channels with duty cycle and power constraints in many wireless communication systems radios are subject to a duty cycle constraint that is a radio can only actively transmit signals over a fraction of the time for example it is desirable to have a small duty cycle in some low power systems a half duplex radio cannot keep transmitting if it wishes to receive useful signals and a cognitive radio needs to listen and detect primary users frequently this paper studies the capacity of point to point scalar discrete time gaussian channels subject to a duty cycle constraint as well as an average transmit power constraint an idealized duty cycle constraint is first studied which can be regarded as a requirement on the minimum fraction of nontransmissions or zero symbols in each codeword independent input with a unique discrete distribution is shown to achieve the channel capacity in many situations numerically optimized on off signaling can achieve much higher rate than gaussian signaling over a deterministic transmission schedule this is in part because the positions of nontransmissions in a codeword can convey information a more realistic duty cycle constraint is also studied where the extra cost of transitions between transmissions and nontransmissions due to pulse shaping is accounted for the capacity achieving input is correlated over time and is hard to compute a lower bound of the achievable rate as a function of the input distribution is shown to be maximized by a first order markov input process whose stationary distribution is also discrete and can be computed efficiently the results in this paper suggest that under various duty cycle constraints departing from the usual paradigm of intermittent packet transmissions may yield substantial gain

optimal linear precoding strategies for wideband noncooperative systems based on game theory part i nash equilibria in this two part paper we propose a decentralized strategy based on a game theoretic formulation to find out the optimal precoding multiplexing matrices for a multipoint to multipoint communication system composed of a set of wideband links sharing the same physical resources i e time and bandwidth we assume as optimality criterion the achievement of a nash equilibrium and consider two alternative optimization problems 1 the competitive maximization of mutual information on each link given constraints on the transmit power and on the spectral mask imposed by the radio spectrum regulatory bodies and 2 the competitive maximization of the transmission rate using finite order constellations under the same constraints as above plus a constraint on the average error probability in this first part of the paper we start by showing that the solution set of both noncooperative games is always nonempty and contains only pure strategies then we prove that the optimal precoding multiplexing scheme for both games leads to a channel diagonalizing structure so that both matrix valued problems can be recast in a simpler unified vector power control game with no performance penalty thus we study this simpler game and derive sufficient conditions ensuring the uniqueness of the nash equilibrium interestingly although derived under stronger constraints incorporating for example spectral mask constraints our uniqueness conditions have broader validity than previously known conditions finally we assess the goodness of the proposed decentralized strategy by comparing its performance with the performance of a pareto optimal centralized scheme to reach the nash equilibria of the game in part ii we propose alternative distributed algorithms along with their convergence conditions

pointwise approximation by bezier variant of integrated mkz operators abstract in this paper the pointwise approximation of bezier variant of integrated mkz operators for general bounded functions is studied two estimate formulas of this type approximation are obtained the approximation of functions of bounded variation becomes a special case of the main result of this paper in the case of functions of bounded variation theorem b of the paper corrects the mistake of theorem 1 of the article v gupta degree of approximation to functions of bounded variation by bezier variant of mkz operators j math anal appl 289 2004 292 300

dual capacity upper bounds for binary input single tap isi channels the capacity of noisy channels with memory and finite input has been difficult to characterize explicitly in many cases in this paper we consider single tap binary input gaussian channels with inter symbol interference isi the dual capacity method is used to obtain upper bounds using markov test distributions the bound expressed as a single letter optimization problem is solved numerically for higher memory the notion of cycle basis is used to provide an exponential reduction in the computational complexity of the optimization problem bounds were obtained for the important case of the dicode channel and these are better than the previously known upper bounds and are close to achievable rates over a wide range of snrs

the rate loss in the wyner ziv problem the rate distortion function for source coding with side information at the decoder the wyner ziv problem is given in terms of an auxiliary random variable which forms a markov chain with the source and the side information this markov chain structure typical to the solution of multiterminal source coding problems corresponds to a loss in coding rate with respect to the conditional rate distortion function i e to the case where the encoder is fully informed we show that for difference or balanced distortion measures this loss is bounded by a universal constant which is the minimax capacity of a suitable additive noise channel furthermore in the worst case this loss is equal to the maximin redundancy over the rate distortion function of the additive noise test channel for example the loss in the wyner ziv problem is less than 0 5 bit sample in the squared error distortion case and it is less than 0 22 bit for a binary source with hamming distance these results have implications also in universal quantization with side information and in more general multiterminal source coding problems

optimal linear precoding strategies for wideband non cooperative systems based on game theory part ii algorithms in this two part paper we address the problem of finding the optimal precoding multiplexing scheme for a set of noncooperative links sharing the same physical resources e g time and bandwidth we consider two alternative optimization problems p l the maximization of mutual information on each link given constraints on the transmit power and spectral mask and p 2 the maximization of the transmission rate on each link using finite order constellations under the same constraints as in p l plus a constraint on the maximum average error probability on each link aiming at finding decentralized strategies we adopted as optimality criterion the achievement of a nash equilibrium and thus we formulated both problems p l and p 2 as strategic noncooperative matrix valued games in part i of this two part paper after deriving the optimal structure of the linear transceivers for both games we provided a unified set of sufficient conditions that guarantee the uniqueness of the nash equilibrium in this part ii of the paper we focus on the achievement of the equilibrium and propose alternative distributed iterative algorithms that solve both games specifically the new proposed algorithms are the following 1 the sequential and simultaneous iterative waterfilling based algorithms incorporating spectral mask constraints and 2 the sequential and simultaneous gradient projection based algorithms establishing an interesting link with variational inequality problems our main contribution is to provide sufficient conditions for the global convergence of all the proposed algorithms which although derived under stronger constraints incorporating for example spectral mask constraints have a broader validity than the convergence conditions known in the current literature for the sequential iterative waterfilling algorithm

the capacity of discrete time memoryless rayleigh fading channels we consider transmission over a discrete time rayleigh fading channel in which successive symbols face independent fading and where neither the transmitter nor the receiver has channel state information subject to an average power constraint we study the capacity achieving distribution of this channel and prove it to be discrete with a finite number of mass points one of them located at the origin we numerically compute the capacity and the corresponding optimal distribution as a function of the signal to noise ratio snr the behavior of the channel at low snr is studied and finally a comparison is drawn with the ideal additive white gaussian noise channel

on properties of the support of capacity achieving distributions for additive noise channel models with input cost constraints we study the classical problem of characterizing the channel capacity and its achieving distribution in a generic fashion we derive a simple relation between three parameters the input output function the input cost function and the noise probability density function one which dictates the type of the optimal input in layman terms we prove that the support of the optimal input is bounded whenever the cost grows faster than a cutoff growth rate equal to the logarithm of the inverse of the noise probability density function evaluated at the input output function furthermore we prove a converse statement that says whenever the cost grows slower than the cutoff rate the optimal input has necessarily an unbounded support in addition we show how the discreteness of the optimal input is guaranteed whenever the triplet satisfy some analyticity properties we argue that a suitable cost function to be imposed on the channel input is one that grows similarly to the cutoff rate our results are valid for any cost function that is super logarithmic they summarize a large number of previous channel capacity results and give new ones for a wide range of communication channel models such as gaussian mixtures generalized gaussians and heavy tailed noise models that we state along with numerical computations

quantum monodromy in integrable systems let p1 h pn h be a set of commuting self adjoint h pseudo differential operators on an n dimensional manifold if the joint principal symbol p is proper it is known from the work of colin de verdiere 6 and charbonnel 3 that in a neighbourhood of any regular value of p the joint spectrum locally has the structure of an affine integral lattice this leads to the construction of a natural invariant of the spectrum called the quantum monodromy we present this construction here and show that this invariant is given by the classical monodromy of the underlying liouville integrable system as introduced by duistermaat 9 the most striking application of this result is that all two degree of freedom quantum integrable systems with a focus focus singularity have the same non trivial quantum monodromy for instance this proves a conjecture of cushman and duistermaat 7 concerning the quantum spherical pendulum

the uniform distribution as a universal prior in this correspondence we discuss the properties of the uniform prior as a universal prior i e a prior that induces a mutual information that is simultaneously close to the capacity for all channels we determine bounds on the amount of the mutual information loss in using the uniform prior instead of the capacity achieving prior specifically for the class of binary input channels with any output alphabet we show that the z channel has the minimal mutual information with uniform prior out of all channels with a given capacity from this we conclude that the degradation of the mutual information with respect to the capacity is at most 0 011 bit and as was shown previously at most 6 a related result is that the capacity achieving prior for any channel is not far from uniform some of these results are extended to channels with nonbinary input

on universal quantization the quantization of n dimensional vectors in r n with an arbitrary probability measure under a mean square error constraint is discussed it is demonstrated that a uniform one dimensional quantizer followed by a noiseless digital variable rate encoder entropy encoding can yield a rate that is for any n no more than 0 754 bit per sample higher than the rate associated with the optimal n dimensionai quantizer regardless of the probabilistic characterization of the input n vector for the allowable mean square error

the algebraic quantisation of the birkhoff gustavson normal form the author develops an algebraic quantisation method for the birkhoff gustavson normal form for this purpose the weyl quantisation rule is used the method developed here for multidimensional systems allows one to calculate the energy levels and the transition probabilities the author gives a brief review of the normal form derives some of its general properties and finds a general analytic solution for the fourth degree normal form for hamiltonians of two degrees of freedom in particular this includes the henon heiles system the author compares the results of specific examples with other works the question of canonically invariant quantisation the relation to the quantum mechanical perturbation theory and the question of chaotic behaviour and quantum stochasticity are discussed the author shows that the operators corresponding to the formal integrals of the motion are also quantum mechanical integrals if the normal form accidentally terminates so that the classical system is integrable then this implies quantum integrability of the normal form hamiltonian

optimum power allocation for parallel gaussian channels with arbitrary input distributions the mutual information of independent parallel gaussian noise channels is maximized under an average power constraint by independent gaussian inputs whose power is allocated according to the waterfilling policy in practice discrete signaling constellations with limited peak to average ratios m psk m qam etc are used in lieu of the ideal gaussian signals this paper gives the power allocation policy that maximizes the mutual information over parallel channels with arbitrary input distributions such policy admits a graphical interpretation referred to as mercury waterfilling which generalizes the waterfilling solution and allows retaining some of its intuition the relationship between mutual information of gaussian channels and nonlinear minimum mean square error mmse proves key to solving the power allocation problem

capacity achieving input distributions of additive quadrature gaussian mixture noise channels this paper studies the characterization of the optimal input and the computation of the capacity of additive quadrature gaussian mixture gm noise channels under an average power constraint the considered model can be used to represent a wide variety of channels with impulsive interference such as the well known bernoulli gaussian and middleton class a impulsive noise channels as well as multiple access interference channels and cognitive radio channels under imperfect sensing at first we demonstrate that there exists a unique input distribution that achieves the channel capacity and the capacity achieving input distribution has a uniformly distributed phase by examining the kuhn tucker alignment conditions ktcs we further show that if the optimal input amplitude distribution contains an infinite number of mass points on a bounded interval the channel output must be gaussian distributed however by using bernstein s theorem to examine the completely monotonic condition it is shown that the assumption of a gaussian distributed output is not valid as a result there are always a finite number of mass points on any bounded interval in the optimal amplitude distribution in addition by applying a novel bounding technique on the ktc and using the envelop theorem we demonstrate that the optimal amplitude distribution cannot have an infinite number of mass points this gives us the unique solution of the optimal input having discrete amplitude with a finite number of mass points given this discrete nature of the optimal input we then develop a simple method to compute the discrete optimal input and the corresponding capacity our numerical examples show that in many cases the capacity achieving distribution consists of only one or two mass points

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

introduction to probability theory this chapter presents the probability theory in many examples of common experience there is a feeling of the chance or likelihood of a statement being either true or false the actual performance of experiments with articles such as coins cards and dice is of great help in understanding the ideas of probability and the relation between theory and practice the chapter presents a sample space for a real or imagined experiment as the set of symbols that indicate the total possible different outcomes of the experiment when each simple event in a sample space is equally likely and there are n simple events the fraction 1 n is assigned as the probability of each simple event the total probability of all the simple events is therefore 1 unity so that a probability of 1 is equivalent to a certainty that one or other of the constituent events will occur the probability of an event that is represented by the empty set is zero this is equivalent to saying that the event cannot occur within the given sample space

real discrete fourier transform the real discrete fourier transform rdft corresponds to the fourier series for sampled periodic signals with sampled periodic frequency responses just as discrete fourier transform dft corresponds to the complex fourier series for the same type of signals rdft has better performance than dft in data compression and filtering for all signals in the sense that pearl s measure for rdft is less than pearl s measure for dft by an amount w rdft also has better performance than dft in the computation of real convolution because of the reduced number of operations and the fact that forward and inverse transforms can be implemented with the same signal flowgraph thereby facilitating hardware and software design

comparison of the achievable rates in ofdm and single carrier modulation with i i d inputs we compare the maximum achievable rates in single carrier sc and orthogonal frequency division multiplexing ofdm modulation schemes under the practical assumptions of independent identically distributed finite alphabet inputs and linear intersymbol interference with additive gaussian noise we show that the shamai laroia approximation serves as a bridge between the two rates while it is well known that this approximation is often a lower bound on the sc achievable rate it is revealed to also essentially upper bound the ofdm achievable rate we apply information estimation relations in order to rigorously establish this result for both general input distributions and to sharpen it for commonly used pulse amplitude modulation pam and quadratic amplitude modulation constellations to this end novel bounds on minimum mean square error estimation of pam inputs to a scalar gaussian channel are derived which may be of general interest our results show that under reasonable assumptions optimal sc schemes may offer spectral efficiency significantly superior to that of ofdm motivating further research of such systems