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 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

invariants on projective space this article is concerned with the construction of invariant nonlinear differential operators for projective space pn p r n 1 there is no loss in working at first on the projective n sphere sn that is the space of rays in rn l the consequences for pn will be explained at the end of the article working on sn avoids notational difficulties arising from the nonorientablity of pn when n is even we shall use the general notion of a homogeneous bundle as in 2 suppose e and f are homogeneous vector bundles on x a homogeneous space for some lie group g the polynomials of degree at most d on a vector space v themselves form a vector space namely ehdo 0h v where o is the symmetric tensor product therefore the g invariant differential operators e f of order k and which are polynomial in the jets of e are precisely the g invariant homomorphisms d c h jk e f

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

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

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

non systematic complex number rs coded ofdm by unique word prefix in this paper we expand our recently introduced concept of unique word orthogonal frequency division multiplexing uw ofdm in uw ofdm the cyclic prefixes cps are replaced by deterministic sequences the so called unique words uws the uws are generated by appropriately loading a set of redundant subcarriers by that a systematic complex number reed solomon rs code construction is introduced in a quite natural way because an rs code may be defined as the set of vectors for which a block of successive zeros occurs in the other domain w r t a discrete fourier transform for a fixed block different to zero i e a uw a coset code of an rs code is generated a remaining problem in the original systematic coded uw ofdm concept is the fact that the redundant subcarrier symbols disproportionately contribute to the mean ofdm symbol energy in this paper we introduce the concept of non systematic coded uw ofdm where the redundancy is no longer allocated to dedicated subcarriers but distributed over all subcarriers we derive optimum complex valued code generator matrices matched to the best linear unbiased estimator blue and to the linear minimum mean square error lmmse data estimator respectively with the help of simulations we highlight the advantageous spectral properties and the superior bit error ratio ber performance of non systematic coded uw ofdm compared to systematic coded uw ofdm and to cp ofdm in additive white gaussian noise awgn as well as in frequency selective environments

an averaging principle for filtering a jump process with point process observations a proof of the following result is given le x sub t and y sub t be two jump processes which modulate the intensity of a multivariate point process n sub t and suppose that the process x sub t is a fast markov chain with a unique invariant probability distribution then the filtering equations for y sub t can be obtained by considering instead of the original problem the averaged problem where the intensity is replaced by the averaged intensity

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

near optimal iterative channel estimation for ksp ofdm in this correspondence we propose an iterative turbo channel estimation algorithm for known symbol padding ksp orthogonal frequency division multiplexing ofdm where the guard interval is filled with pilot symbols additional pilot symbols are transmitted on some of the ofdm carriers the channel estimation algorithm is based on the expectation maximization em algorithm in the initialization phase of this iterative algorithm the received time domain samples are first converted to the frequency domain and the initial channel estimate is based on the observation of the pilot carriers only then the em algorithm switches back to the time domain and updates the channel estimates until convergence is reached the proposed estimator performs very good the mean square error mse performance of the proposed estimator is close to the cramer rao lower bound crb corresponding to the all pilots case for the snr region of practical interest and the resulting bit error rate essentially coincides with the case of the perfectly known channel

classical and bayesian linear data estimators for unique word ofdm unique word orthogonal frequency division multiplexing uw ofdm is a novel ofdm signaling concept where the guard interval is built of a deterministic sequence the so called unique word instead of the conventional random cyclic prefix in contrast to previous attempts with deterministic sequences in the guard interval the addressed uw ofdm signaling approach introduces correlations between the subcarrier symbols which can be exploited by the receiver in order to improve the bit error ratio performance in this paper we develop several linear data estimators specifically designed for uw ofdm some based on classical and some based on bayesian estimation theory furthermore we derive complexity optimized versions of these estimators and we study their individual complex multiplication count in detail finally we evaluate the estimators performance for the additive white gaussian noise channel as well as for selected indoor multipath channel scenarios

theoretical performance evaluation and optimization of uw ofdm unique word uw ofdm is a new ofdm variant that offers several advantages over cyclic prefix ofdm such as better bit error rate ber performance in frequency selective channels and much lower out of band radiation however all results with respect to the ber performance are based on monte carlo simulations only and offer little insight in the behaviour of the system performance as function of its parameters in this paper we theoretically analyse the performance of the uw ofdm system for both a deterministic channel and a fading channel and offer a systematic way to generate the uw ofdm signal to optimize the performance of the system when the fading channel is known at the transmitter we show that we can obtain a diversity order that is of the same order of magnitude as the theoretically maximum diversity order but when the channel is not known at the transmitter it will be very hard to achieve maximum diversity order although the obtained diversity order is larger than one

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

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

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

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

fundamentals of statistical signal processing estimation theory minimum variance unbiased estimation cramer rao lower bound linear models general minimum variance unbiased estimation best linear unbiased estimators maximum likelihood estimation least squares method of moments the bayesian philosophy general bayesian estimators linear bayesian estimators kalman filters summary of estimators extension for complex data and parameters

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

sharp bounds on the entropy of the poisson law and related quantities one of the difficulties in calculating the capacity of certain poisson channels is that h the entropy of the poisson distribution with mean is not available in a simple form in this paper we derive upper and lower bounds for h that are asymptotically tight and easy to compute the derivation of such bounds involves only simple probabilistic and analytic tools this complements the asymptotic expansions of knessl 1998 jacquet and szpankowski 1999 and flajolet 1999 the same method yields tight bounds on the relative entropy d n p between a binomial and a poisson thus refining the work of harremoe s and ruzankin 2004 bounds on the entropy of the binomial also follow easily

on conformally invariant differential operators in odd dimensions this is a brief announcement in which we identify all the conformally invariant differential operators acting on densities other than n 2 k and other than l where k is a positive integer and l is a nonnegative integer

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