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

asymptotic a priori estimates for the error in the nonlinear filtering problem corresp the minimal mean square error for the scalar nonlinear filtering problem is considered asymptotic lower and upper bounds on the error are derived for the case where the intensity of the observation noise tends to zero

poisson co homology of polynomial poisson algebras in dimension four sklyanin s case abstract in this paper we compute the poisson co homology of a polynomial poisson structure given by two casimir polynomial functions which define a complete intersection with an isolated singularity

bounds on the information rate of intertransition time restricted binary signaling over an awgn channel upper and lower bounds on the capacity of a continuous time additive white gaussian noise awgn channel with bilevel spl plusmn spl radic p input signals subjected to a minimum inter transition time t sub min constraint are derived the channel model and input constraints reflect basic features of certain magnetic recording systems the upper bounds are based on duncan s relation between the average mutual information in an awgn regime and the mean square error mse of an optimal causal estimator evaluation or upper bounding the mse of suboptimal causal estimators yields the desired upper bounds the lower bound is found by invoking the extended mrs gerber s lemma and asymptotic properties of the entropy of max entropic bipolar d k codes asymptotic results indicate that at low snr pt sub min n sub 0 with n sub 0 designating the noise one sided power spectral density the capacity tends to p n sub 0 nats per second nats s i e it equals the capacity in the simplest average power limited case at high snr the capacity in the simplest average power limited case at high snr the capacity behaves asymptotically as t sub min sup 1 ln snr ln snr nats s demonstrating the degradation relatively to t sub avg sup 1 lnsnr which is the asymptotic known behavior of the capacity with a bilevel average intertransition time t sub avg restricted channel input additional lower bounds are obtained by considering specific signaling formats such as pulsewidth modulation the effect of mild channel filtering on the lower bounds on capacity is also addressed and novel techniques to lower bound the capacity in this case are introduced

information rates for magnetic recording channels with peak and slope limited magnetization a model for magnetic recording is proposed which uses two parameters to describe the limitations on the remanent magnetization in the medium the dimensionless peak value a sub m and the steepest slope b s sup 1 a low pass bandwidth restriction w s sup 1 due to read circuits is also included lower and upper bounds on the achievable transmission rates are derived in terms of the signal to noise ratio for the case of ideal low pass restriction with b

on the capacity penalty due to input bandwidth restrictions with an application to rate limited binary signaling it is well known that in cases of unlimited channel bandwidth and unconstrained signal spectrum a constant envelope constraint on the signal does not reduce the capacity of an additive gaussian channel as compared to its capacity with the optimum signals of similar average power for band limited channels of bandwidth b however the constant envelope constraints does reduce the capacity even if the signals themselves are allowed arbitrarily rapid alternations transitions here using a recently introduced technique it is shown that the capacity is further drastically reduced if in addition to the channel limitation the constant envelope signal is itself restricted to a small fractional out of band power epsilon ideal lowpass and bandpass channel filters are considered and upper bounds on the capacity are derived the out of band power restrictions can be met for example by restricting the average rate of transitions rho of the binary input signal it is shown that in this case epsilon

twisted poincare duality between poisson homology and poisson cohomology abstract a version of the twisted poincare duality is proved between the poisson homology and cohomology of a polynomial poisson algebra with values in an arbitrary poisson module the duality is achieved by twisting the poisson module structure in a canonical way which is constructed from the modular derivation in the case that the poisson structure is unimodular the twisted poincare duality reduces to the poincare duality in usual sense the main result generalizes the work of launois and richard 8 for the quadratic poisson structures and zhu 25 for the linear poisson structures

poisson spectra in polynomial algebras abstract a significant class of poisson brackets on the polynomial algebra c x 1 x n is studied and for this class of poisson brackets the poisson prime ideals poisson primitive ideals and symplectic cores are determined moreover it is established that these poisson algebras satisfy the poisson dixmier moeglin equivalence

asymptotic analysis of the optimal filtering problem for two dimensional diffusions measured in a low noise channel we consider the problem of filtering one dimensional diffusions with nonlinear drift coefficients transmitted through a nonlinear fow noise channel we construct an asymptotic solution to zakai s equation for the unnormalized conditional probability density of the signal given the noisy measurements this expansion is used to find the asymptotic expansion of the minimum error variance filter and its mean square estimation error msee we construct approximate filters whose msee agrees with that of the optimal one to a given degree of accuracy the dimension of the approximate filter increases with the required degree of accuracy similarly we expand the maximum a posteriori probability estimator and the minimum energy estimator and compare their performance we also discuss some extended kalman filters and present some examples

channel coding with multilevel phase signals a coding technique is described which improves error performance of synchronous data links without sacrificing data rate or requiring more bandwidth this is achieved by channel coding with expanded sets of multilevel phase signals in a manner which increases free euclidean distance soft maximum likelihood ml decoding using the viterbi algorithm is assumed following a discussion of channel capacity simple hand designed trellis codes are presented for 8 phase shift keying psk and 16 quadrature amplitude shift keying qask modulation these simple codes achieve coding gains in the order of 3 4 db it is then shown that the codes can be interpreted as binary convolutional codes with a mapping of coded bits into channel signals which we call mapping by set partitioning based on a new distance measure between binary code sequences which efficiently lower bounds the euclidean distance between the corresponding channel signal sequences a search procedure for more powerful codes is developed codes with coding gains up to 6 db are obtained for a variety of multilevel phase modulation schemes simulation results are presented and an example of carrier phase tracking is discussed

on lower bounds for the nonlinear filtering problem corresp the system model dx t m x t dt sigma o dw t and the observation dy t h x t dt rho dv t are considered and a lower bound on the error for the least square estimate of a function of x t say z x t is derived this bound is then applied to derive a lower bound on the error in estimating x t in the case where the constant sigma o in the equation for the system dynamics is replaced by sigma x t

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

on zero rate error exponents of finite state channels with input dependent states we derive a single letter formula for the zero rate reliability error exponent of a finite state channel whose state variable depends deterministically and recursively on past channel inputs where the code complies with a given channel input constraint special attention is then devoted to the important special case of the gaussian channel with intersymbol interference where more explicit results are obtained

mutual information and minimum mean square error in gaussian channels this paper deals with arbitrarily distributed finite power input signals observed through an additive gaussian noise channel it shows a new formula that connects the input output mutual information and the minimum mean square error mmse achievable by optimal estimation of the input given the output that is the derivative of the mutual information nats with respect to the signal to noise ratio snr is equal to half the mmse regardless of the input statistics this relationship holds for both scalar and vector signals as well as for discrete time and continuous time noncausal mmse estimation this fundamental information theoretic result has an unexpected consequence in continuous time nonlinear estimation for any input signal with finite power the causal filtering mmse achieved at snr is equal to the average value of the noncausal smoothing mmse achieved with a channel whose snr is chosen uniformly distributed between 0 and snr

achievable rates for a constrained gaussian channel the authors obtained lower bounds to the capacity of the continuous time filtered additive gaussian noise channel with two valued inputs essentially the problem reduces to the continuous time peak limited case which remains an unsolved problem of primary importance in communication theory

on information transfer by envelope constrained signals over the awgn channel using t e duncan s theorem 1970 on the relation between mutual information and the mean square error of the optimum causal estimator of a random signal in additive white gaussian noise awgn the maximum achievable information transfer over the awgn channel is derived with the random telegraph wave input the information transfer is bounded and symptotically determined for the wiener phase modulated process input at large signal to noise ratio snr both results are compared to the information transfer for the capacity achieving gauss markov input process for both the wiener phase modulated and the gauss markov processes the information transfer increases asymptotically as the square root of snr but for the random telegraph wave it increases only as its logarithm

mmse dimension if n is standard gaussian the minimum mean square error mmse of estimating a random variable x based on snr x n vanishes at least as fast as 1 snr as snr we define the mmse dimension of x as the limit as snr of the product of snr and the mmse mmse dimension is also shown to be the asymptotic ratio of nonlinear mmse to linear mmse for discrete absolutely continuous or mixed distribution we show that mmse dimension equals renyi s information dimension however for a class of self similar singular x e g cantor dis tribution we show that the product of snr and mmse oscillates around information dimension periodically in snr db we also show that these results extend considerably beyond gaussian noise under various technical conditions

nonlinear filtering of one dimensional diffusions in the case of a high signal to noise ratio in this paper we are concerned with the asymptotic nonlinear filtering of one dimensional diffusions as the observation noise tends to zero the intensity of the signal noise may be normal small or large we derive evaluations of the conditional moments and obtain one and two dimensional approximate filters we give upper bounds for the approximation errors and compare these filters with some classical suboptimal filters

on one class of exact poisson structures we discuss some properties of a natural class of poisson structures on euclidean spaces and abstract manifolds in particular it is proved that such structures are always exact and may be reconstructed from their casimir functions it is shown that in low dimensions they give the whole class of exact poisson structures the dimension of poisson homology of these structures is computed in terms of the milnor number of their casimir functions we also analyze some concrete examples of such structures in low dimensions and show that their centers are generated by casimir functions

jacobi structures in r3 the most general jacobi brackets in r3 are constructed after solving the equations imposed by the jacobi identity two classes of jacobi brackets were identified according to the rank of the jacobi structures the associated hamiltonian vector fields are also constructed

upper bounds on capacity for a constrained gaussian channel a low pass and a bandpass additive white gaussian noise channel with a peak power constraint imposed on otherwise arbitrary input signals are considered upper bounds on the capacity of such channels are derived they are strictly less than the capacity of the channel when the peak power constrain is removed and replaced by the average power constraint for which the gaussian inputs are optimum this provides the answer to an often posed question peak power limiting in the case of bandlimited channels does reduce capacity whereas in infinite bandwidth channels it does not as is well known for an ideal low pass filter of bandwidth b the upper bound is blog 0 934p n sub 0 b for p n sub 0 b 1 where p is the peak power of the input signal and n sub 0 2 is the double sided power spectral density of the additive white gaussian noise

the schouten nijenhuis bracket cohomology and generalized poisson structures newly introduced generalized poisson structures based on suitable skew symmetric contravariant tensors of even order are discussed in terms of the schouten nijenhuis bracket the associated jacobi identities are expressed as conditions on these tensors the cohomological contents of which is given in particular we determine the linear generalized poisson structures which can be constructed on the dual spaces of simple lie algebras

nambu jacobi and generalized jacobi manifolds the geometry of nambu jacobi and generalized jacobi manifolds is studied a large collection of examples is given the characteristic distribution generated by the hamiltonian vector fields on a nambu jacobi manifold is proved to be completely integrable and the induced geometrical structure of the leaves of the corresponding generalized foliation is ellucidated

the gauss map of a genus three theta divisor a smooth complex curve is determined by the gauss map of the theta divisor of the jacobian variety of the curve the gauss map is invariant with respect to the 1 map of the jacobian we show that for a generic genus three curve the gauss map is locally z 2 stable one method of proof is to analyze the first order z 2 deformations of the gauss map of a hyperelliptic theta divisor

efficiency of the extended kalman filter for nonlinear systems with small noise the problem of nonlinear filtering is studied asymptotically as the noise tends to zero detectability conditions ensuring that the filtering error tends to zero are derived and under these conditions it is proved that the extended kalman filter provides a good suboptimal filter the smoothing problem is also studied the proofs use some estimates for the linearization of stochastic systems some changes of probability and stochastic differentiation techniques

maximizing the output energy of a linear channel with a time and amplitude limited input the problem of maximizing the output energy of a linear time invariant channel given that the input signal is time and amplitude limited is considered it is shown that a necessary condition for an input mu to be optimal assuming a unity amplitude constraint is that it satisfy the fixed point equation sgn f mu where the functional f is the convolution of mu with the autocorrelation function of the channel impulse response it is also shown that all solutions to this equation for which mod mu mod 1 almost everywhere correspond to local maxima of the output energy iteratively recomputing mu from the fixed point equation leads to an algorithm for finding local optima numerical results are given for the cases where the transfer function is ideal low pass and has two poles these results support the conjecture that in the ideal low pass case the optimal input signal is a single square pulse a generalization of the preceding fixed point condition is also derived for the problem of maximally separating n outputs of a discrete time linear time invariant channel