the poisson multiple access channel the poisson multiple access channel mac models many to one optical communication through an optical fiber or in free space for this model we compute the capacity region for the two user case as a function of the allowed peak power focusing on the maximum throughput we generalize our results to the case where the users are subjected to an additional average power constraint and to the many users case we show that contrary to the gaussian mac in the poisson mac the maximum throughput is bounded in the number of users we quantify the loss that is incurred when time division multiple access tdma is employed and show that while in the two user case and in the absence of dark current the penalty is rather mild the penalty can be quite severe in the many users case in the presence of large dark current we introduce a generalized tdma technique that mitigates this loss to a large extent

on the laplace transform of the frechet distribution we calculate exactly the laplace transform of the frechet distribution in the form x 1 exp x 0 0 x for arbitrary rational values of the shape parameter i e for l k with l k 1 2 the method employs the inverse mellin transform the closed form expressions are obtained in terms of meijer g functions and their graphical illustrations are provided a rescaled frechet distribution serves as a kernel of frechet integral transform it turns out that the frechet transform of one sided levy law reproduces the frechet distribution

on the capacity of free space optical intensity channels upper and lower bounds are derived on the capacity of the free space optical intensity channel this channel has a nonnegative input representing the transmitted optical intensity which is corrupted by additive white gaussian noise to preserve the battery and for safety reasons the input is constrained in both its average and its peak power for a fixed ratio of the allowed average power to the allowed peak power the difference between the upper and the lower bound tends to zero as the average power tends to infinity and their ratio tends to one as the average power tends to zero when only an average power constraint is imposed on the input the difference between the bounds tends to zero as the allowed average power tends to infinity and their ratio tends to a constant as the allowed average power tends to zero

modulation and coding for throughput efficient optical systems optical direct detection systems are currently being considered for some high speed intersatellite links where data rates of a few hundred megabits per second are envisioned under power and pulsewidth constraints the authors investigate the capacity cutoff rate and error probability performance of uncoded and trellis coded systems for various modulation schemes and under throughput and power constraints modulation schemes considered are on off keying pulse position modulation ppm overlapping ppm and multipulse combinatorial ppm

new q deformed coherent states with an explicitly known resolution of unity we construct a new family of q deformed coherent states zq where 0 q 1 these states are normalizable on the whole complex plane and continuous in their label z they allow the resolution of unity in the form of an ordinary integral with a positive weight function obtained through the analytic solution of the associated stieltjes power moment problem and expressed in terms of one of the two jacksons s q exponentials they also permit exact evaluation of matrix elements of physically relevant operators we use this to show that the photon number statistics for the states is sub poissonian and that they exhibit quadrature squeezing as well as an enhanced signal to quantum noise ratio over the conventional coherent state value finally we establish that they are the eigenstates of some deformed boson annihilation operator and study some of their characteristics in deformed quantum optics

quantum algebraic structures compatible with the harmonic oscillator newton equation we study some of the algebraic structures that are compatible with the quantization of the harmonic oscillator through its newton equation examples of such structures are given they include undeformed and q deformed oscillators as well as the su 2 and the deformed suq 2 lie algebras which appear in a variety of physical models

difference ladder operators for a harmonic schrodinger oscillator using unitary linear lattices the formalism of raising and lowering operators is developed for the difference operator analogue of a quantum harmonic oscillator which acts on functions on a discrete support the grid under consideration is a mixed version of an equidistant lattice and a q linear grid several properties of the grid are described the grids under consideration are referred to by the name unitary linear lattices the ladder difference operators are derived and compared with the continuum situation the arising spectral problems for these operators are dealt by using the theory of bilateral jacobi operators in weighted l2 z spaces eventual applications to mathematical physics and numerical schrodinger theory are briefly discussed

practical codes for photon communication in a recent paper pierce studied the problems of communicating at optical frequencies using photon counting techniques and concluded that at low temperatures we encounter insuperable problems of encoding long before we approach channel capacity in this paper it is shown that even assuming a noiseless model for photon communication for which capacity measured in nats photon is infinite it is unlikely that a signaling efficiency of even 10 nats photon could be achieved practically on the positive side it is shown that pulse position modulation plus reed solomon coding yields practical results in the range of 2 to 3 nats photon

a bregman matrix and the gradient of mutual information for vector poisson and gaussian channels a generalization of bregman divergence is developed and utilized to unify vector poisson and gaussian channel models from the perspective of the gradient of mutual information the gradient is with respect to the measurement matrix in a compressive sensing setting and mutual information is considered for signal recovery and classification existing gradient of mutual information results for scalar poisson models are recovered as special cases as are known results for the vector gaussian model the bregman divergence generalization yields a bregman matrix and this matrix induces numerous matrix valued metrics the metrics associated with the bregman matrix are detailed as are its other properties the bregman matrix is also utilized to connect the relative entropy and mismatched minimum mean squared error two applications are considered 1 compressive sensing with a poisson measurement model and 2 compressive topic modeling for analysis of a document corpora word count data in both of these settings we use the developed theory to optimize the compressive measurement matrix for signal recovery and classification

capacity of the l p norm constrained poisson channel the capacity of the poisson channel is derived with a specified constraint imposed on the lp norm t p of the encoder intensity formulae are given for the capacity which establish previously known results for p 1 p 2 and p to be part of a system of capacity problems with common form and solution these formulae apply with or without causal feedback and whether or not the encoder intensity is ook on off keying constrained

an optimal basis of band limited functions for signal analysis and design this paper studies signal concentration in the time and frequency domains using the general constrained variational method of franks the minimum k th k 0 2 4 moment time duration measure for band limited signals is formulated a complete orthonormal set of band limited functions in l2 w w with the minimum fourth moment time duration measure is obtained numerical investigations of our optimal 4th moment functions show 1 less energy concentration in the main lobe than the prolate spheroidal wave functions pswf 2 higher energy concentration in the main lobe than gabor s function and 3 a larger main lobe than both pswf and gabor applications for our basis functions include 1 radar systems and high resolution communication systems and 2 representation and approximation to any band limited signal in a given time interval

capacity and reliability function for small peak signal constraints the capacity and the reliability function as the peak constraint tends to zero are considered for a discrete time memoryless channel with peak constrained inputs prelov and van der meulen 1993 showed that under mild conditions the ratio of the capacity to the squared peak constraint converges to one half the maximum eigenvalue of the fisher information matrix and if the fisher information matrix is nonzero the asymptotically optimal input distribution is symmetric antipodal signaling under similar conditions it is shown in the first part of the paper that the reliability function has the same asymptotic shape as the reliability function for the power constrained infinite bandwidth white gaussian noise channel the second part of the paper deals with rayleigh fading channels for such channels the fisher information matrix is zero indicating the difficulty of transmission over such channels with small peak constrained signals asymptotics for the rayleigh channel are derived and applied to obtain the asymptotics of the capacity of the marzetta and hochwald 1999 fading channel model for small peak constraints and to obtain a result of the type of medard and gallager for wide band fading channels

characterization on practical photon counting receiver in optical scattering communication we characterize the practical photon counting receiver in optical scattering communication with a finite sampling rate and electrical noise finite small pulse width incurs dead time effect that may lead to sub poisson distribution on the recorded pulses we analyze the first order and second order moments on the number of recorded pulses with a finite sampling rate at the receiver side under two cases where the sampling period is shorter than or equal to the pulse width as well as longer than the pulse width moreover we adopt the maximum likelihood ml detection in order to simplify the analysis we adopt binomial distribution approximation on the number of recorded pulses in each slot a tractable holding time and decision threshold selection rule is provided to maximize the minimal kullback leibler kl distance between the two distributions the performances of proposed sub poisson distribution and the binomial approximation are verified by the experimental results the equivalent photon arrival rate and pulse holding time predicted by the sub poisson model and the associated proposed binomial distribution are well validated by the simulation results where the finite sampling rate and electrical noise are considered the proposed holding time and decision threshold selection rule performs close to the optimal ml receiver

factorization little or great algorithm the progress of the factorization method since the 1935 work of dirac is briefly reviewed though linked with older mathematical theories the factorization seems an autonomous driving force offering substantial support to the present day darboux and backlund approaches

affine kac moody algebras and semi infinite flag manifolds we study representations of affine kac moody algebras from a geometric point of view it is shown that wakimoto modules introduced in 18 which are important in conformal field theory correspond to certain sheaves on a semi infinite flag manifold with support on its schhubert cells this manifold is equipped with a remarkable semi infinite structure which is discussed in particular the semi infinite homology of this manifold is computed the cousin grothendieck resolution of an invertible sheaf on a semi infinite flag manifold gives a two sided resolution of an irreducible representation of an affine algebras consisting of wakimoto modules this is just the brst complex as a byproduct we compute the homology of an algebra of currents on the real line with values in a nilpotent lie algebra

the t analogs of q characters at roots of unity for quantum affine algebras and beyond abstract the q characters were introduced by frenkel and reshetikhin the q characters of representations of quantum affine algebras and deformations of w algebras in recent developments in quantum affine algebras and related topics in contemp math vol 248 amer math soc providence ri 1999 pp 163 205 to study finite dimensional representations of the untwisted quantum affine algebra u q g for q generic the e characters at roots of unity were constructed by frenkel and mukhin the q characters at roots of unity adv math 171 1 2002 139 167 to study finite dimensional representations of various specializations of u q g at q s 1 in the finite simply laced case nakajima t analogue of the q characters of finite dimensional representations of quantum affine algebras in physics and combinatorics proc nagoya 2000 internat workshop world scientific singapore 2001 pp 181 212 quiver varieties and t analogs of q characters of quantum affine algebras ann of math in press preprint arxiv math qa 0105173 defined deformations of q characters called q t characters for q generic and also at roots of unity the definition is combinatorial but the proof of the existence uses the geometric theory of quiver varieties which holds only in the simply laced case in algebraic approach to q t characters adv math in press preprint arxiv math qa 0212257 we proposed an algebraic general non necessarily simply laced new approach to q t characters for q generic in this paper we propose two developments of this approach we treat the root of unity case and the case of a larger class of generalized cartan matrices including finite and affine cases except a 1 1 a 2 2 in particular we generalize the construction of analogs of kazhdan lusztig polynomials at roots of unity of h nakajima quiver varieties and t analogs of q characters of quantum affine algebras ann of math in press preprint arxiv math qa 0105173 to those cases we also study properties of various objects used in this article deformed screening operators at roots of unity t deformed polynomial algebras bicharacters arising from symmetrizable cartan matrices deformation of the frenkel mukhin s algorithm

information rates of photon limited overlapping pulse position modulation channels a direct detection photon limited optical communication channel that uses pulse position modulation ppm under a pulsewidth constraint is considered overlapping ppm oppm allows multiple positions per pulsewidth as well as fractional modulation indices number of pulsewidths per frame requiring more refined timing than that needed for conventional disjoint ppm djppm it is shown that even at moderate values of the expected photon count per pulse q such as needed for high data rates oppm outperforms on off keying ook in both capacity and cutoff rate even though ook is uniformly superior to djppm moreover efficient use of oppm is possible with equiprobable input symbols whereas ook requires inconvenient asymmetrical inputs to achieve capacity and high cutoff rate efficiencies nats photon at lower data rates where capacity efficiency is the prime criterion a significant advantage 20 percent over djppm can be achieved up to efficiencies of about 0 7 nats photon the m ary photon limited oppm channel can be viewed as an ambiguity and erasure channel in the sense that some channel outputs are ambiguous in only some input symbols and only if no photons are counted is there ambiguity in all input symbols for large m ambiguities cause bursts of erasures of data symbols massey s interlaced encoding as well as conventional encoding followed by interleaving are adaptable to this bursty channel and effect an increase in its cutoff rate comparable to the increase obtainable with djppm by the same techniques

central extensions of current groups in two dimensions the paper is devoted to generalization of the theory of loop groups to the two dimensional case to every complex riemann surface we assign a central extension of the group of smooth maps from this surface to a simple complex lie group g by the jacobian of this surface this extension is topologically nontrivial as in the loop group case orbits of coadjoint representation of this extension correspond to equivalence classes of holomorphic principalg bundles over the surface when the surface is the torus elliptic curve classification of coadjoint orbits is related to linear difference equations in one variable and to classification of conjugacy classes in the loop group we study integral orbits for which the kirillov kostant form is a curvature form for some principal torus bundle the number of such orbits for a given level is finite as in the loop group case conjecturedly they correspond to analogues of integrable modules occurring in conformal field theory

on the capacity of the discrete time poisson channel the large inputs asymptotic capacity of a peak power and average power limited discrete time poisson channel is derived using a new firm nonasymptotic lower bound and an asymptotic upper bound the upper bound is based on the dual expression for channel capacity and the notion of capacity achieving input distributions that escape to infinity the lower bound is based on a lower bound on the entropy of a conditionally poisson random variable in terms of the differential entropy of its conditional mean

coding for dpsk noisy phase channels low to moderate complexity coding schemes are suggested and examined for binary dpsk modulation the model of the communication channel consists of both a brownian motion phase noise and an additive white gaussian noise decoding utilizes a mismatched soft decision metric which comprises the prefiltering of the phase noise impaired signals followed by differential demodulation the resulting equivalent binary input output symmetric discrete time coding channel is stationary and memoryless it accounts as well for an underlying time diversity thus providing an effective simple means of boosting the capabilities of less powerful codes to cope with the existing phase noise levels an analytical upper bound on the coded error probability is derived which strictly addresses the brownian motion phase model it features a convenient decoupling of the code structure from the coding channel the latter is completely specified via a single scalar generic parameter which relies on the univariate moments admitted by certain exponential functionals of the brownian motion sample path the exact statistics of which is intractable the theory is illustrated while studying the performance of low constraint length rate 1 n binary convolutional codes which are optimally combined with time diversity the advantages obtained by less trivial forms of code concatenation are examined the approach treated is to use a two level concatenation scheme for which the binary inner code dimension matches the alphabet size of an outer non binary code

optimum waveform signal sets with amplitude and energy constraints it is desirable to choose the waveforms making up a signaling alphabet so that they are maximally separated one from another this problem is considered in the space of square integrable functions for signals which have finite duration and are constrained in the ranges of their values as well as in energy corresponding to each of the following cases we establish sharp bounds for the minimum distance and for the average distance between elements of a fixed size signal set and construct sets of signals that attain both bounds simultaneously begin list item em case a energy constraint only the average energy of the waveforms in the signal set is at most sigma where 0 leq sigma item em case b energy and peak amplitude constraints the average energy of the waveforms in the signal set is leq sigma 0 leq sigma and the absolute value of each waveform is at most 1 item em case c energy and value constraints the average energy of the waveforms in the signal set is at most b 2 sigma a 2 1 sigma and each waveform takes values in the set a b where 0 leq a and 0 leq sigma leq 1 end list cases a and b are applicable to signal design for communication in channels with additive noise say gaussian and case c is applicable to signal design for optical channels where the signal represents the intensity of a photon stream the general character of the results is that the minimum distance behaves like gamma sigma in cases a and b and like gamma sigma 1 sigma in case c with gamma a suitable constant

localization for quantum groups at a root of unity let c be the field of complex numbers and fix q g c let g be a semi simple lie algebra over c and let g be the corresponding simply connected algebraic group let uq be the quantized enveloping algebra of q let oq be the algebra of quantized functions on g let oq b be the quotient hopf algebra of oq corresponding to a borel subgroup b of g in the paper bk we defined categories of equivariant quantum o modules and pg modules on the quantum flag variety of g we proved that the beilinson bernstein localization theorem holds at a generic q namely the global section functor gives an equivalence between categories of modules and vq iaod es on the quantum flag variety thus one can translate questions about the represen tation theory of quantum groups to the study of the noncommutative geometry of the quantum flag variety in this paper we prove that a derived version of this theorem holds at the root of unity case using this equivalence we get that one can understand the representation theory of quantum groups at roots of unity through the now commutative geometry of the springer fibers we now recall the main results in bk the constructions given there are crucial for the present paper and a fairly detailed survey of the material there is given in the next section we defined an equivariant sheaf of quasi coherent modules over the quantum flag variety to be a left oq mod e equipped with a right q b comod ile structure satisfying certain compatibility conditions such objects form a category denoted ai q gq it contains certain line bundles oq for in the weight lattice we proved that oq x is ample for 0 holds for every q this implies that the category m bq gq is a proj category in the sense of serre

coherent states and hermite polynomials on quaternionic hilbert spaces coherent states similar to the canonical coherent states of the harmonic oscillator labeled by quaternions are established on the right and left quaternionic hilbert spaces on the left quaternionic hilbert space reproducing kernels are established as was claimed by adler and millard j math phys 1997 38 2117 26 it is proved that these coherent states cannot be realized as a group action on a quaternionic hilbert space as an extension of the complex hermite polynomials quaternionic hermite polynomials are defined and these polynomials are associated with an operator as eigenfunctions

the quantum group suq 2 and a q analogue of the boson operators a new realisation of the quantum group suq 2 is constructed by means of a q analogue to the jordan schwinger mapping determining thereby both the complete representation structure and q analogues to the wigner and racah operators to achieve this realisation a new elementary object is defined a q analogue to the harmonic oscillator the uncertainty relation for position and momentum in a q harmonic oscillator is quite unusual

covering point patterns a source generates a point pattern consisting of a finite number of points in an interval based on a binary description of the point pattern a reconstructor must produce a covering set that is guaranteed to contain the pattern we study the optimal tradeoff as the length of the interval tends to infinity between the description length and the least average lebesgue measure of the covering set the tradeoff is established for point patterns that are generated by homogeneous and inhomogeneous poisson processes the homogeneous poisson process is shown to be the most difficult to describe among all point patterns we also study a wyner ziv version of this problem where some of the points in the pattern are revealed to the reconstructor but not to the encoder we show that this scenario is as good as when they are revealed to both encoder and reconstructor a connection between this problem and the queueing distortion is established via feedforward finally we establish the aforementioned tradeoff when the covering set is allowed to miss some of the points in the pattern at a certain cost

new generalized coherent states we construct a new family of boson coherent states using a specially designed function which is a solution of a functional equation de q x dx e q qx with 0 q 1 and e q 0 1 we use this function in place of the usual exponential to generate new coherent states q z from the vacuum which are normalized and continuous in their label z these states allow the resolution of unity and a corresponding weight function is furnished by the exact solution of the associated stieltjes moment problem they also permit exact evaluation of matrix elements of an arbitrary polynomial given as a normally ordered function of boson operators we exemplify this by showing that the photon number statistics for these states is sub poissonian for any q 1 the states q z are squeezed we obtain and discuss their signal to quantum noise ratio the function e q x allows a natural generation of multiboson coherent states of arbitrary multiplicity which is impossible for the usual coherent states for q 1 all the above resul

on the capacity of a direct detection photon channel with intertransition constrained binary input the classical directed detection photon channel is modeled by an output nu sub t observed signal describing the photon arrival poisson count process with intensity rate lambda sub t lambda sub 0 where lambda sub t photons s is the channel input information carrying intensity and lambda sub 0 photons s is the dark current intensity upper and lower bounds on the capacity of this channel are presented for two level binary inputs taking on the extreme value lambda sub t in 0 a where a denotes the peak power satisfying an average power constraint e lambda sub t

on identification capacity of infinite alphabets or continuous time channels two kinds of channels are considered 1 discrete time channel with additive noise and 2 poisson and white gaussian i e continuous time channels for the type 1 channel there are given some sufficient conditions when the shannon and identification capacities coincide it is shown that the identification capacity of poisson and gaussian channels without bandwidth constraint is infinite conversely for a white gaussian channel with bandwidth constraint the identification capacity coincides with the shannon capacity

finite dimensional representations of quantum affine algebras at roots of unity we describe explicitly the canonical map x spec ue b spec ze where u b is a quantum loop algebra at an odd root of unity e here ze is the center of ue g and spec r stands for the set of all finite dimensional irreducible representations of an algebra r we show that spec z is a poisson proalgebraic group which is essentially the group of points of g over the regular adeles concentrated at 0 and oo our main result is that the image under x of spec u b is the subgroup of principal adeles department of mathematics harvard university cambridge massachusetts 02138 e mail address beckfmath harvard edu department of mathematics massachusetts institute of technology cambridge massachusetts 02139 e mail address kacimath mit edu this content downloaded from 207 46 13 124 on wed 22 jun 2016 06 11 29 utc all use subject to http about jstor org terms

directed information causal estimation and communication in continuous time a notion of directed information between two continuous time processes is proposed a key component in the definition is taking an infimum over all possible partitions of the time interval which plays a role no less significant than the supremum over space partitions inherent in the definition of mutual information properties and operational interpretations in estimation and communication are then established for the proposed notion of directed information for the continuous time additive white gaussian noise channel it is shown that duncan s classical relationship between causal estimation error and mutual information continues to hold in the presence of feedback upon replacing mutual information by directed information a parallel result is established for the poisson channel the utility of this relationship is demonstrated in computing the directed information rate between the input and output processes of a continuous time poisson channel with feedback where the channel input process is constrained to be constant between events at the channel output finally the capacity of a wide class of continuous time channels with feedback is established via directed information characterizing the fundamental limit on reliable communication

nonlinear semi coherent states their nonclassical features and phase properties semi coherent states semi css were previously introduced and their nonclassical properties studied in this paper we first propose a general formalism for the construction of nonlinear semi css as an extension of semi css and then their explicit form in the number state basis is generally deduced next as some physical appearances of the formalism after choosing two well known nonlinearity functions nonclassical features and quantum statistical properties of the associated states are studied by evaluating quadrature squeezing higher order squeezing and the mandel parameter as well as their phase properties and number and phase squeezing of the introduced states finally the results are compared with the properties of semi css

on the completeness of photon added coherent states we demonstrate explicitly the completeness of photon added coherent states pacss introduced by agarwal and tara agarwal g s and tara k 1991 phys rev a 43 492 and defined up to normalization by m z m 0 1 2 where is the boson creation operator and z are conventional glauber klauder coherent states we find the analytical form of the positive weight function in their resolution of unity by solving the associated stieltjes power moment problem we furnish an example of generation of another set of pacss which are complete

capacity results of an optical intensity channel with input dependent gaussian noise this paper investigates a channel model describing optical communication based on intensity modulation it is assumed that the main distortion is caused by additive gaussian noise however with a noise variance depending on the current signal strength both the high power and low power asymptotic capacities under simultaneously both a peak power and an average power constraint are derived the high power results are based on a new firm nonasymptotic lower bound and a new asymptotic upper bound the upper bound relies on a dual expression for channel capacity and the notion of capacity achieving input distributions that escape to infinity the lower bound is based on a new lower bound on the differential entropy of the channel output in terms of the differential entropy of the channel input the low power results make use of a theorem by prelov and van der meulen

temporally stable coherent states for infinite well and poschl teller potentials this article is a direct illustration of a construction of coherent states which has been recently proposed by two of us jpg and jk we have chosen the example of a particle trapped in an infinite square well and also in poschl teller potentials of the trigonometric type in the construction of the corresponding coherent states we take advantage of the simplicity of the solutions which ultimately stems from the fact they share a common su 1 1 symmetry a la barut girardello many properties of these states are then studied both from mathematical and from physical points of view

quasitriangularity of quantum groups at roots of 1 an important property of a hopf algebra is its quasitriangularity and it is useful for various applications this property is investigated for quantum groupssl2 at roots of 1 it is shown that different forms of the quantum groupsl2 at roots of 1 are either quasitriangular or have similar structure which will be called braiding in the most interesting cases this property means that braiding automorphism is a combination of some poisson transformation and an adjoint transformation with a certain element of the tensor square of the algebra

q graded heisenberg algebras and deformed supersymmetries the notion of q grading on the enveloping algebra generated by products of q deformed heisenberg algebras is introduced for q complex number in the unit disk within this formulation we consider the extension of the notion of supersymmetry in the enveloping algebra we recover the ordinary z2 grading or grassmann parity for associative superalgebra and a modified version of the usual supersymmetry as a specific problem we focus on the interesting limit q 1 for which the arik and coon deformation j math phys 17 524 1976 of the heisenberg algebra allows one to map fermionic modes to bosonic ones in a modified sense different algebraic consequences are discussed

on the capacity bounds for poisson interference channels the poisson interference channel which models optical communication systems with multiple transceivers in the short noise limited regime is investigated conditions for the strong interference regime are characterized and the corresponding capacity region is derived which is the same as that of the compound poisson multiple access channel with each receiver decoding both messages for the cases when the strong interference conditions are not satisfied inner and outer bounds on the capacity region are derived the inner bound is derived via approximating the poisson interference channel by a binary interference channel and then evaluating the corresponding han kobayashi region the outer bounds are obtained via various techniques including noise reduction genie aided scheme and channel transformation the poisson z interference channel is then studied the sum rate capacity is obtained when the cross link coefficient is either sufficiently small or sufficiently large

synchronizable codes for the optical oppm channel random overlapping pulse position modulation oppm sequences result in an unrecoverable error floor on both the probability of erroneous synchronization and the probability of symbol error when only chip synchronization is present it is known however that for a given sequence length m a subset of the set of all possible sequences is synchronizable in the sense that in the absence of noise the receiver can correctly symbol synchronize by observing m or more symbol intervals the authors design finite state machines and codes over a j ary alphabet which produce sequences with the property that every subsequence of length l is synchronizable some of the codes in addition to being synchronizable produce a coding gain for an optical poisson channel the authors introduce joint synchronization and detection algorithms that utilize the memory in the encoded sequences to produce joint estimates of timing and sequences their performance is analyzed through simulations and analytical results

on the completeness of coherent states generated by binomial distribution we demonstrate the completeness of boson and spin coherent states generated by binomial distribution by furnishing the exact analytical form of their respective positive weight functions in resolution of unity these weight functions are solutions of the associated truncated stieltjes power moment problem we elaborate on the non unique character of these solutions

moduli spaces of curves and representation theory we establish a canonical isomorphism between the second cohomology of the lie algebra of regular differential operators on x of degree 1 and the second singular cohomology of the moduli space hat f g 1 of quintuples c p z l wherec is a smooth genusg riemann surface p a point onc z a local parameter atp l a degreeg 1 line bundle onc and a class of local trivializations ofl atp which differ by a non zero factor the construction uses an interplay between various infinite dimensional manifolds based on the topological spaceh of germs of holomorphic functions in a neighborhood of 0 in x and related topological spaces the basic tool is a canonical map from hat f g 1 to the infinite dimensional grassmannian of subspaces ofh which is the orbit of the subspaceh of holomorphic functions on x vanishing at under the group auth as an application we give a lie algebraic proof of the mumford formula n 6n2 6n 1 1 where n is the determinant line bundle of the vector bundle on the moduli space of curves of genusg whose fiber overc is the space of differentials of degreen onc

capacity and error exponent for the direct detection photon channel ii for pt i see ibid vol 34 no 6 p 1449 61 1980 the discussion of the capacity and error exponent of the direct detection optical channel is continued the channel input in a t second interval is a waveform satisfying certain peak and average power constraints for the optical signals the channel output is a poisson process with an intensity parameter that accounts for the dark current component an upper bound is obtained on the error exponent which coincides with the lower bound thus this channel is one for which the error exponent can be known exactly

the degraded poisson wiretap channel optical and near optical band communication systems are known to be intrinsically more secure than comparable rf channels due to their narrow beamwidths and in some cases their high atmospheric absorption the use of coding against wiretapping for such channels is investigated for the degraded poisson wiretap channel model the secrecy capacity is determined exactly moreover a complete characterization of the rate equivocation region is presented for achievability an optimal code is constructed explicitly by using a code designed by wyner for the poisson channel the converse is proved in two ways the first method leverages the low snr nature of the channel and relies only on simple properties of conditional expectation and classical information inequalities the second method uses a link recently established between minimum mean square error estimation and mutual information over poisson channels

bounds on the capacity of a spectrally constrained poisson channel an upper bound is derived on the capacity of a poisson channel that has a stationary input process of a given spectrum and is subjected to peak and average power constraints the bound is shown to be asymptotically tight with the relaxation of the spectral constraints its maximization over a given set of admissible spectra is closely related to an analogous problem in the awgn regime the results are used for bounding the capacity of a poisson channel under a second moment bandwidth constraint as well as the capacity under a strict bandwidth constraint asymptotically tight lower bounds on the channel capacity for the above two cases are also presented the approach for lower bounding the capacity for the latter case yields as a by product improved bounds on the bit error probability in uncoded amplitude shift keying and on off modulation as a special case operating over a poisson channel impaired by intersymbol interference

the discrete time poisson channel at low input powers the asymptotic capacity at low input powers of an average power limited or an average and peak power limited discrete time poisson channel is considered for a poisson channel whose dark current is zero or decays to zero linearly with its average input power e capacity scales like e log 1 e for small e for a poisson channel whose dark current is a nonzero constant capacity scales to within a constant like e log log 1 e for small e

optical intensity modulated direct detection channels signal space and lattice codes traditional approaches to constructing constellations for electrical channels cannot be applied directly to the optical intensity channel this work presents a structured signal space model for optical intensity channels where the nonnegativity and average amplitude constraints are represented geometrically lattice codes satisfying channel constraints are defined and coding and shaping gain relative to a baseline are computed an effective signal space dimension is defined to represent the precise impact of coding and shaping on bandwidth average optical power minimizing shaping regions are derived in some special cases example lattice codes are constructed and their performance on an idealized point to point wireless optical link is computed bandwidth efficient schemes are shown to have promise for high data rate applications but require greater average optical power

geometry of the analytic loop group abstract we introduce and study a notion of analytic loop group with a riemann hilbert factorization relevant for the representation theory of quantum affine algebras at roots of unity u g with non trivial central charge we introduce a poisson structure and study properties of its poisson dual group we prove that the hopf poisson structure is isomorphic to the semi classical limit of the center of u g it is a geometric realization of the center then the symplectic leaves and corresponding equivalence classes of central characters of u g are parameterized by certain g bundles on an elliptic curve

non binary ldpc code design for the poisson ppm channel this paper investigates the design of non binary protograph low density parity check codes for the poisson channel with m ary pulse position modulation the field order over which the code is constructed is matched to the pulse position modulation order yielding a coded modulation scheme the optimization of the low density parity check code structure is performed via protograph density evolution on a surrogate m ary erasure channel the surrogate design is illustrated to be not only accurate but also robust for a range of practical values of channel background noise and various modulation orders as a result the proposed codes show excellent performance over the poisson channel with pulse position modulation outperforming competing schemes as a side product of this paper finite length benchmarks on the block error probability are provided together with a union bound to characterize the code performance in the error floor region

zero rate reliability of the exponential server timing channel we determine the reliability function of the exponential server timing channel estc in the limit as the data rate approaches zero the limit shows that at low rates the estc is strictly more reliable than the poisson channel without dark current answering a question arikan posed in these transactions the proof employs a distance metric over inputs to timing channels that parallels euclidean and hamming distance for conventional channels a consequence of the proof is that bounded distance decoding with distance measured according to this metric is exponentially optimum for the estc in the low rate regime we also prove the straight line bound for the channel and a bound on the reliability of timing channels with general service distributions in the limit as the data rate approaches zero

an improved achievable region for the discrete memoryless two user multiple access channel with noiseless feedback an achievable region for the two user discrete memoryless multiple access channel dmmac with noiseless feedback is proposed the proposed region includes the cover leung region with the inclusion being for some channels strict this inner bound is demonstrated for the ideal two user poisson multiple access channel with noiseless feedback in which case it is shown to improve on the cover leung rate sum

new p q μ ν f deformed states we construct a new family of deformed states these states are normalizable on the whole complex plane and continuous in their label z under fixed values of parameters they allow the resolution of unity in the form of an ordinary integral with a positive weight function obtained through the analytic solution of the associated stieltjes power moment problem in addition to the mathematical characteristics the quantum statistical properties of these states are analytically and numerically discussed in detail in the context of conventional as well as deformed quantum optics we find that for non deformed photons the states exhibit quadrature squeezing and their photon number statistics is sub poissonian on the other hand for deformed photons the states are super poissonian and no quadrature squeezing occurs

coherent states for isospectral oscillator hamiltonians coherent states for a family of isospectral oscillator hamiltonians are derived from a suitable choice of annihilation and creation operators the fock bargmann representation is also considered

mittag leffler coherent states we create a family of boson coherent states using the functions of mittag leffler ml e z 0 and their generalizations e z 0 instead of exponentials these states are shown to satisfy the usual requirements of normalizability continuity in the label and the resolution of unity with a positive weight function this last quantity is found for arbitrary 0 as a solution of an associated stieltjes moment problem in addition for m 1 2 3 and 1 corresponding to em z we propose and analyse special q deformations 0 q1 of the functions em z which serve as a tool to define q deformed coherent states of ml type we provide the expressions for expectation values of physical quantities for all the above states we discuss physical properties of these states noting that they are squeezed the ml coherent states are sub poissonian in nature whereas the q deformed ml states can be sub and super poissonian depending on q all these states are shown to be eigenstates of deformed boson operators whose commutation relations are given

outage capacity of mimo poisson fading channels the information outage probability of a shot noise limited direct detection multiple input multiple output mimo optical channel subject to block fading is considered information is transmitted over this channel by modulating the intensity of a number of optical signals one corresponding to each transmit aperture and individual photon arrivals are observed at multiple receive photodetector apertures the transmitted signals undergo multiplicative fading the fading occurs in coherence intervals of fixed duration in each of which the channel fade matrix remains constant and changes across successive such intervals in an independent and identically distributed fashion the transmitter and the receiver are assumed to be provided with perfect channel state information csi an optimization formulation for the outage probability problem is outlined and an exact characterization of the optimal average conditional duty cycles is provided

information capacity of the poisson channel the information capacity of the poisson channel with random or time varying noise intensity is obtained for time varying peak and average constraints on the encoder intensity the channel model is specified and some definitions from information theory are given causal feedback is shown not to increase the channel capacity for the case of nonrandom noise intensity for random noise intensity use of causal feedback does increase capacity the extent of that increase is quantified jamming is considered and the optimal jamming signal is given poisson channels with thinning are introduced

counting sequences a gray sequence is a counter sequence where the hamming distance between successive states is one a construction for any fixed odd distance between successive states is given based on error correcting codes such sequences could be used in testing and fault diagnosis when sequencing through all possible input combinations sequences with the maximum possible difference between successive states alternately n and n 1 are given a characterization of such maximal change sequences is given the most nearly uniform even difference sequences are described the distribution of bit changes or transition counts for individual variables for a counting sequence is considered

the construction of some important classes of generalized coherent states the nonlinear coherent states method considering some important classes of generalized coherent states known in the literature we demonstrated that all of them can be created via conventional methods i e the lowering operator eigenstate and the displacement operator techniques using the nonlinear coherent states approach as a result we obtained a unified method to construct a large class of coherent states which have already been introduced by different prescriptions

q ν deformation of generalized basic hypergeometric states we provide with a q deformation of the generalized hypergeometric coherent states defined such that the normalization function is given by generalized basic hypergeometric functions these states are eigenstates of suitably defined deformed lowering operators we study the domain of convergence of the corresponding normalization function on the basis of these states we investigate generalized basic hypergeometric husimi distributions and corresponding phase distributions as well as new analytic basis representations of arbitrary quantum states in bargmann and hardy spaces the quantum statistical properties of the states such as photon counting statistics and quadrature squeezing are analytically and numerically discussed in the framework of conventional quantum optics

the truncated stieltjes moment problem solved by using kernel density functions in this work the problem of the approximate numerical determination of a semi infinite supported continuous probability density function pdf from a finite number of its moments is addressed the target space is carefully defined and an approximation theorem is proved establishing that the set of all convex superpositions of appropriate kernel density functions kdfs is dense in this space a solution algorithm is provided based on the established approximate representation of the target pdf and the exploitation of some theoretical results concerning moment sequence asymptotics the solution algorithm also permits us to recover the tail behavior of the target pdf and incorporate this information in our solution a parsimonious formulation of the proposed solution procedure based on a novel sequentially adaptive scheme is developed enabling a very efficient moment data inversion the whole methodology is fully illustrated by numerical examples

localization of modules for a semisimple lie algebra in prime characteristic with an appendix by r bezrukavnikov and s riche computation for sl 3 we show that on the level of derived categories representations of the lie algebra of a semisimple algebraic group over a field of finite characteristic with a given generalized regular central character are the same as coherent sheaves on the formal neighborhood of the corresponding generalized springer fiber the first step is to observe that the derived functor of global sections provides an equivalence between the derived category of d modules with no divided powers on the flag variety and the appropriate derived category of modules over the corresponding lie algebra thus the derived version of the beilinson bernstein localization theorem holds in sufficiently large positive characteristic next one finds that for any smooth variety this algebra of differential operators is an azumaya algebra on the cotangent bundle in the case of the flag variety it splits on springer fibers and this allows us to pass from d modules to coherent sheaves the argument also generalizes to twisted d modules as an application we prove lusztig s conjecture on the number of irreducible modules with a fixed central character we also give a formula for behavior of dimension of a module under translation functors and reprove the kac weisfeiler conjecture the sequel to this paper bmr2 treats singular infinitesimal characters

asymptotic error probability of binary hypothesis testing for poisson point process observations corresp it is shown that the asymptotic probability of error of a binary equiprobable hypothesis test for observed poisson point processes with rates lambda i t b i t rho i t z 2 i 0 1 z rightarrow infty is equal to the error probability of optimum deterministic signal detection in additive white gaussian noise when the signals coincide with the square roots of the point process rates the implication of this result in the error rate analysis of optical digital communication systems is discussed

second and third order asymptotics of the continuous time poisson channel the paper derives the optimal second order coding rate for the continuous time poisson channel we also obtain bounds on the third order coding rate this is the first instance of a second order result for a continuous time channel the converse proof hinges on a novel construction of an output distribution induced by wyner s discretized channel and the construction of an appropriate epsilon net of the input probability simplex while the achievability proof follows the general program to prove the third order term for non singular discrete memoryless channels put forth by polyanskiy several non standard techniques such as new definitions and bounds on the probabilities of typical sets using logarithmic sobolev inequalities are employed to handle the continuous nature of the channel

on the reliability function of the ideal poisson channel with noiseless feedback a coding scheme for the channel under peak power and average power constraints on the input is presented and its asymptotic error exponent is shown to coincide at all rates below capacity with the sphere packing error exponent which for the case at hand is known to be unachievable without feedback for rates below the critical rate an upper bound on the error exponent achievable with feedback is also derived and shown under a capacity reducing average power constraint to coincide with the error exponent achieved by the proposed coding scheme in such a case the coding scheme is asymptotically optimal thus the ideal poisson channel limited by a capacity reducing average power constraint provides a nontrivial example of a channel for which the reliability function is known exactly both with and without feedback it is shown that a slight modification of the coding scheme to one of random transmission time can achieve zero error probability for any rate lower than the ordinary average error channel capacity

on channel capacity per unit cost memoryless communication channels with arbitrary alphabets where each input symbol is assigned a cost are considered the maximum number of bits that can be transmitted reliably through the channel per unit cost is studied it is shown that if the input alphabet contains a zero cost symbol then the capacity per unit cost admits a simple expression as the maximum normalized divergence between two conditional output distributions the direct part of this coding theorem admits a constructive proof via stein s lemma on the asymptotic error probability of binary hypothesis tests single user multiple access and interference channels are studied

rate distortion theory of finite point processes we study the compression of data in the case where the useful information is contained in a set rather than a vector i e the ordering of the data points is irrelevant and the number of data points is unknown our analysis is based on rate distortion theory and the theory of finite point processes we introduce fundamental information theoretic concepts and quantities for point processes and present general lower and upper bounds on the rate distortion function to enable a comparison with the vector setting we concretize our bounds for point processes of fixed cardinality in particular we analyze a fixed number of unordered gaussian data points and show that we can significantly reduce the required rates compared to the best possible compression strategy for gaussian vectors as an example of point processes with variable cardinality we study the best possible compression of poisson point processes for the specific case of a poisson point process with uniform intensity on the unit square our lower and upper bounds are separated by only a small gap and thus provide a good characterization of the rate distortion function

quadratic variational framework for signal design on the 2 sphere this paper introduces a quadratic variational framework for solving a broad class of signal design problems on the 2 sphere the functional to be extremized combines energy concentration measures using a weighting function in the spatial domain multiplicative weights in the spectral domain and a total energy constraint this leads to two formulations of the signal design problem on the 2 sphere one a fredholm integral equation in the spatial domain and the other an infinite matrix equation in the spectral domain the framework is illustrated by deriving the key equations for the two classical spatio spectral concentration problems on the 2 sphere and for an isotropic filter design that maximizes the filtered energy in addition using the proposed framework we formulate a joint 3 d beamforming application which achieves optimal directivity and spatial resolution simultaneously

very noisy channels reliability functions and exponentially optimum codes a very noisy channel vnc is a discrete input memoryless channel whose capacity is close to zero very noisy channels are of interest since they serve as models for some important physical channels there are two distinct classes of vncs reiffen s class i reiffen 1963 and majani s class ii majani 1987 it is shown that the reliability function is known exactly for both classes of vncs by extending the results previously obtained only for class i it is then shown that an exponentially optimum code can be constructed for a channel if it can be modeled as repeated uses of a binary input class i vnc a binary input binary output class ii vnc or a class ii very noisy binary erasure channel the theory developed is illustrated by considering the direct detection optical channel used with polarization modulation the capacity reliability function and exponentially optimum code for this channel are derived

on optimum parameter modulation estimation from a large deviations perspective we consider the problem of jointly optimum modulation and estimation of a real valued random parameter conveyed over an additive white gaussian noise awgn channel where the performance metric is the large deviations behavior of the estimator namely the exponential decay rate as a function of the observation time of the probability that the estimation error would exceed a certain threshold our basic result is in providing an exact characterization of the fastest achievable exponential decay rate among all possible modulator estimator transmitter receiver pairs where the modulator is limited only in the signal power but not in bandwidth this exponential rate turns out to be given by the reliability function of the awgn channel we also discuss several ways to achieve this optimum performance and one of them is based on quantization of the parameter followed by optimum channel coding and modulation which gives rise to a separation based transmitter if one views this setting from the perspective of joint source channel coding this is in spite of the fact that in general when error exponents are considered the source channel separation theorem does not hold true we also discuss several observations modifications and extensions of this result in several directions including other channels and the case of multidimensional parameter vectors one of our findings concerning the latter is that there is an abrupt threshold effect in the dimensionality of the parameter vector below a certain critical dimension the probability of excess estimation error may still decay exponentially but beyond this value it must converge to unity

superposition coding is almost always optimal for the poisson broadcast channel this paper shows that the capacity region of the continuous time poisson broadcast channel is achieved via superposition coding for most channel parameter values interestingly the channel in some subset of these parameter values does not belong to any of the existing classes of broadcast channels for which superposition coding is optimal e g degraded less noisy and more capable in particular we introduce the notion of effectively less noisy broadcast channel and show that it implies less noisy but is not in general implied by more capable for the rest of the channel parameter values we show that there is a gap between marton s inner bound and the uv outer bound

performance of pll based optical oppm communication systems the power spectral density psd of a direct detected optical signal with overlapping pulse position modulation oppm scheme is derived it is demonstrated that this spectrum contains a strong periodic component at the signal symbol frequency thereby enabling a simple pll device to provide joint symbol and slot synchronization the variance of the timing error for a linearized pll synchronizer is shown to be mainly dominated by and is inversely proportional to the product of the pll closed loop bandwidth and symbol duration of the oppm signal the performance of a shot noise limited pll based optical oppm communication system is then assessed in terms of the overall system symbol error rate

orthogonal codes for robust low cost communication orthogonal coding schemes known to asymptotically achieve the capacity per unit cost cpuc for single user ergodic memoryless channels with a zero cost input symbol are investigated for single user compound memoryless channels which exhibit uncertainties in their input output statistical relationships a minimax formulation is adopted to attain robustness first a class of achievable rates per unit cost arpuc is derived and its utility is demonstrated through several representative case studies second when the uncertainty set of channel transition statistics satisfies a convexity property optimization is performed over the class of arpuc through utilizing results of minimax robustness the resulting cpuc lower bound indicates the ultimate performance of the orthogonal coding scheme and coincides with the cpuc under certain restrictive conditions finally still under the convexity property it is shown that the cpuc can generally be achieved through utilizing a so called mixed strategy in which an orthogonal code contains an appropriate composition of different nonzero cost input symbols

the quantum mechanical schrodinger picture of a q oscillator a q deformed version of standard quantum mechanics in the coordinate schrodinger picture is obtained by replacing the ordinary coordinate derivative by the so called q discrete derivative as the representative of the momentum operator the chosen q discrete derivative is symmetric with respect to the exchange of q and q 1 under the usually adopted assumptions a q deformed schrodinger equation is derived for a harmonic oscillator the complete set of eigenfunctions can be explicitly constructed as special q functions and the corresponding energy eigenvalues are identical to those obtained by biedenharn in his pioneering work 1989 this q deformed oscillator exhibits a rich novel structure including dynamical symmetry and in the limit q to 1 it reveals some hitherto unknown features of the harmonic oscillator eigenfunctions

the q characters at roots of unity abstract we consider various specializations of the untwisted quantum affine algebras at roots of unity we define and study the q characters of their finite dimensional representations

mutual information and conditional mean estimation in poisson channels following the discovery of a fundamental connection between information measures and estimation measures in gaussian channels this paper explores the counterpart of those results in poisson channels in the continuous time setting the received signal is a doubly stochastic poisson point process whose rate is equal to the input signal plus a dark current it is found that regardless of the statistics of the input the derivative of the input output mutual information with respect to the intensity of the additive dark current can be expressed as the expected difference between the logarithm of the input and the logarithm of its noncausal conditional mean estimate the same holds for the derivative with respect to input scaling but with the logarithmic function replaced by x log x similar relationships hold for discrete time versions of the channel where the outputs are poisson random variables conditioned on the input symbols

hopf algebras with trace and representations we study the restriction of representations of cayley hamilton algebras to subalgebras this theory is applied to determine tensor products and branching rules for representations of quantum groups at roots of 1