Finite Number Of Channels Research Articles

Analyzing and stabilizing multichannel ALOHA with the use of the preamble-based exploration phase

Introduction: Internet of Things devices are actively used within the framework of Massive Machine-Type Communication scenarios. The interaction of devices is carried out by random multiple-access algorithms with limited throughput. To improve throughput one can use orthogonal preambles in the ALOHA-type class of algorithms. Purpose: To analyze ALOHA-based algorithms using the exploration phase and to calculate the characteristics for the algorithm with and without losses with a finite number of channels. Results: We have described a system model that employs random access for data transmission over a common communication channel with the use of orthogonal preambles and exploration phase. We have obtained a formula for numerical calculation of the throughput of an algorithm channel with losses with an infinite number of preambles and a given finite number of channels. The calculation results for several values of the number of independent channels are presented. A modification of the algorithm using the exploration phase and repeated transmissions is proposed and described. The system in question can work without losses. For this system, we have given the analysis of the maximum input throughput up to which the system operates stably. Also, the average delay values for the algorithm that were obtained by simulation modeling are shown. By reducing the number of available preambles, the results obtained can be used as an upper bound on the system throughput. Practical relevance: The results obtained allow to assess the potential for improving the throughput of random multiple-access systems in 6G networks through the application of the exploration phase.

Tight bounds for private communication over bosonic Gaussian channels based on teleportation simulation with optimal finite resources

Upper bounds for private communication over quantum channels can be derived by adopting channel simulation, protocol stretching, and relative entropy of entanglement. All these ingredients have led to single-letter upper bounds to the secret key capacity which can be directly computed over suitable resource states. For bosonic Gaussian channels, the tightest upper bounds have been derived by employing teleportation simulation over asymptotic resource states, namely the asymptotic Choi matrices of these channels. In this work, we adopt a different approach. We show that teleporting over an analytical class of finite-energy resource states allows us to closely approximate the ultimate bounds for increasing energy, so as to provide increasingly tight upper bounds to the secret-key capacity of one-mode phase-insensitive Gaussian channels. We then show that an optimization over the same class of resource states can be used to bound the maximum secret key rates that are achievable in a finite number of channel uses.

Delay-Intolerant Covert Communications With Either Fixed or Random Transmit Power

In this paper, we study delay-intolerant covert communications in additive white Gaussian noise (AWGN) channels with a finite block length, i.e., a finite number of channel uses. Considering the maximum allowable number of channel uses to be N, it is not immediately clear whether the actual number of channel uses, denoted by n, should be as large as N or smaller for covert communications. This is because a smaller n reduces a warden's chance to detect the communications due to fewer observations, but also reduces the chance to transmit information. We show that n = N is indeed optimal to maximize the amount of information bits that can be transmitted, subject to any covert communication constraint in terms of the warden's detection error probability. To better make use of the warden's uncertainty due to the finite block length, we also propose to use uniformly distributed random transmit power to enhance covert communications. Our examination shows that the amount of information that can be covertly transmitted logarithmically increases with the number of random power levels, which indicates that most of the benefit of using random transmit power is achieved with just a few different power levels.

Finite-Length Linear Schemes for Joint Source-Channel Coding over Gaussian Broadcast Channels with Feedback

In this paper, we study linear encoding for a pair of correlated Gaussian sources transmitted over a two-user Gaussian broadcast channel in the presence of unit-delay noiseless feedback, abbreviated as the GBCF. Each pair of source samples is transmitted using a linear transmission scheme in a finite number of channel uses. We investigate three linear transmission schemes: A scheme based on the Ozarow–Leung (OL) code, a scheme based on the linear quadratic Gaussian (LQG) code of Ardestanizadeh et al., and a novel scheme derived in this paper using a dynamic programming (DP) approach. For the OL and LQG schemes we present lower and upper bounds on the minimal number of channel uses needed to achieve a target mean-square error (MSE) pair. For the LQG scheme in the symmetric setting, we identify the optimal scaling of the sources, which results in a significant improvement of its finite horizon performance, and, in addition, characterize the (exact) minimal number of channel uses required to achieve a target MSE. Finally, for the symmetric setting, we show that for any fixed and finite number of channel uses, the DP scheme achieves an MSE lower than the MSE achieved by either the LQG or the OL schemes.

On the Ozarow-Leung Scheme for the Gaussian Broadcast Channel with Feedback

In this work, we consider linear-feedback schemes for the two-user Gaussian broadcast channel with noiseless feedback. We extend the transmission scheme of [Ozarow and Leung, 1984] by applying estimators with memory instead of the memoryless estimators used by Ozarow and Leung (OL) in their original work. A recursive formulation of the mean square errors achieved by the proposed estimators is provided, along with a proof for the existence of a fixed point. This enables characterizing the achievable rates of the extended scheme. Finally, via numerical simulations it is shown that the extended scheme can improve upon the original OL scheme in terms of achievable rates, as well as achieve a low probability of error after a finite number of channel uses.

Classical capacity of Gaussian communication under a single noisy channel

A long-standing problem on the classical capacity of bosonic Gaussian channels has recently been resolved by proving the minimum output entropy conjecture. It is also known that the ultimate capacity quantified by the Holevo bound can be achieved asymptotically by using an infinite number of channels. However, it is less understood to what extent the communication capacity can be reached if one uses a finite number of channels, which is a topic of practical importance. In this paper, we study the capacity of Gaussian communication, i.e., employing Gaussian states and Gaussian measurements to encode and decode information under a single-channel use. We prove that the optimal capacity of single-channel Gaussian communication is achieved by one of two well-known protocols, i.e., coherent-state communication or squeezed-state communication, depending on the energy (number of photons) as well as the characteristics of the channel. Our result suggests that the coherent-state scheme known to achieve the ultimate information-theoretic capacity is not a practically optimal scheme for the case of using a finite number of channels. We find that overall the squeezed-state communication is optimal in a small-photon-number regime whereas the coherent-state communication performs better in a large-photon-number regime.

Second-order coding rates for pure-loss bosonic channels

A pure-loss bosonic channel is a simple model for communication over free-space or fiber-optic links. More generally, phase-insensitive bosonic channels model other kinds of noise, such as thermalizing or amplifying processes. Recent work has established the classical capacity of all of these channels, and furthermore, it is now known that a strong converse theorem holds for the classical capacity of these channels under a particular photon number constraint. The goal of the present paper is to initiate the study of second-order coding rates for these channels, by beginning with the simplest one, the pure-loss bosonic channel. In a second-order analysis of communication, one fixes the tolerable error probability and seeks to understand the back-off from capacity for a sufficiently large yet finite number of channel uses. We find a lower bound on the maximum achievable code size for the pure-loss bosonic channel, in terms of the known expression for its capacity and a quantity called channel dispersion. We accomplish this by proving a general "one-shot" coding theorem for channels with classical inputs and pure-state quantum outputs which reside in a separable Hilbert space. The theorem leads to an optimal second-order characterization when the channel output is finite-dimensional, and it remains an open question to determine whether the characterization is optimal for the pure-loss bosonic channel.

Multichannel scattering amplitudes of microparticles in a quantum well with two-dimensional δ-potential

The quasi-one-dimensional scattering of a quantum particle on the two-dimensional δ-potential is considered. Analytical expressions for multi-channel transmission tn and reflection rn amplitudes are given. The problem is solved for the case of finite number of channels that is equal to N when the particle is incident on the potential while moving in l channel. The case of three-channel scattering was examined in details. As was shown within the frameworks of this problem, the “overpopulation” of particles in the second and third channels occurs when k2 → 0 and k3 → 0. The location points of δ-potential that provide the complete “overpopulation” of channels were also obtained.

Unbounded number of channel uses may be required to detect quantum capacity.

Transmitting data reliably over noisy communication channels is one of the most important applications of information theory, and is well understood for channels modelled by classical physics. However, when quantum effects are involved, we do not know how to compute channel capacities. This is because the formula for the quantum capacity involves maximizing the coherent information over an unbounded number of channel uses. In fact, entanglement across channel uses can even increase the coherent information from zero to non-zero. Here we study the number of channel uses necessary to detect positive coherent information. In all previous known examples, two channel uses already sufficed. It might be that only a finite number of channel uses is always sufficient. We show that this is not the case: for any number of uses, there are channels for which the coherent information is zero, but which nonetheless have capacity.

Positivity, discontinuity, finite resources, and nonzero error for arbitrarily varying quantum channels

This work is motivated by a quite general question: Under which circumstances are the capacities of information transmission systems continuous? The research is explicitly carried out on finite arbitrarily varying quantum channels (AVQCs). We give an explicit example that answers the recent question whether the transmission of messages over AVQCs can benefit from assistance by distribution of randomness between the legitimate sender and receiver in the affirmative. The specific class of channels introduced in that example is then extended to show that the unassisted capacity does have discontinuity points, while it is known that the randomness-assisted capacity is always continuous in the channel. We characterize the discontinuity points and prove that the unassisted capacity is always continuous around its positivity points. After having established shared randomness as an important resource, we quantify the interplay between the distribution of finite amounts of randomness between the legitimate sender and receiver, the (nonzero) probability of a decoding error with respect to the average error criterion and the number of messages that can be sent over a finite number of channel uses. We relate our results to the entanglement transmission capacities of finite AVQCs, where the role of shared randomness is not yet well understood, and give a new sufficient criterion for the entanglement transmission capacity with randomness assistance to vanish.

Parameter estimation in hyperbolic multichannel models

A multichannel model is considered, with each channel represented by a linear second-order stochastic equation with two unknown coefficients. The channels are interpreted as the Fourier coefficients of the solution of a stochastic hyperbolic equation with possibly unbounded damping. The maximum likelihood estimator of the coefficients is constructed using the information from a finite number of channels. Necessary and sufficient conditions are determined for the consistency of the estimator as the number of channels increases, while the observation time and noise intensity remain fixed.

Design and analysis of a TDMA call assignment scheme for cellular networks

In this paper, we introduce a TDMA channel assignment scheme suitable for personal communication services (PCS) networks. This scheme, called Handoff TDMA (H-TDMA), assumes three type of traffic: new voice calls, handoff voice calls and data packets, all competing for a finite number of channels. In the present scheme, priority is given to handoff voice calls over data calls, while a number of channels is exclusively dedicated to data calls. The performance of the scheme is analyzed using a Markov chain model. We evaluate major performance metrics such as forced termination probability, blocking probability, and data packets loss probability. The analytical results obtained are validated by simulation and good agreement is obtained.

Modeling bufferless packet-switching networks with packet dependencies

In this paper we present a stochastic network model for packet-switching networks with no buffering capabilities at the nodes. This model can be directly used in the study of all-optical packet-switching (OPS) and optical burst switching (OBS) networks without fiber delay lines (FDLs). Our model provides for the first time a complete description of the dependencies arising among packets from different sources in the network. Such dependencies originate when packets from different sources share a finite number of channels for their transmission through a network link. We relate our model to well-known loss network models for circuit-switching networks and derive expressions for the packet loss probability. We briefly show how our work can be extended to model parallel hybrid optical networks, and propose some promising future lines of work. Our numerical results suggest that the well-known Erlang fixed-point approximation (EFPA) overestimates the blocking probability when compared to our model predictions. They also show that our model is scalable up to network scenarios with at least 30 links with 160 wavelength channels per link. This makes the proposed model an interesting tool for studying the dependencies arising among packets in a realistically-sized OPS/OBS network without FDLs.

Markovian receiver collision analysis of high-speed multi-channel networks

Two synchronous transmission multi-channel multi-access protocols for high-speed network architecture are studied in this paper. Analytic discrete time Markovian models are developed for finite number of stations and finite number of channels for the symmetric and asymmetric access rights proposed protocols. The effect of receiver collision phenomenon is examined and analysed on the performance measures evaluation and estimated by the probability of packet rejection at destination. Also, numerical results are presented for comparison for various numbers of data channels and stations. Copyright © 2005 John Wiley & Sons, Ltd.

Mobile Telecommunication Systems and Generalized Erlang Loss Formula

This paper studies a cellular system with mobile customers. The network system consists of cells, the tagged cell and the adjacent cells which surround the tagged one. Each cell has a finite number of channels that give calls to the mobile customers. The service (holding) time distribution of the calls is general. Customers in the adjacent cells inflow into the tagged cell according to a Poisson process. The sojourn time distribution of each customer in the tagged cell is general. Each customer without call in progress generates his call according to a Poisson process. It is proved that the steady state distribution in the tagged cell is the generalized Erlang loss formula which is the joint distribution of the number of customers with calls and the number of customers without calls. The distribution depends on the service time distribution and the sojourn time distribution only through their means.

Light traffic in a cellular system with mobile subscribers and its applications

This paper is concerned with a cellular system with mobile subscribers (customers). This system consists of a cell, called the tagged cell, and its adjacent cells. Each cell has some finite number of channels. The sojourn times of customers in the tagged cell have an exponential distribution. Customers in the adjacent cells move to the tagged cell according to a Poisson process whose rate depends on the number of customers in the tagged cell. Each customer without call in progress generates his call according to an exponential distribution and the channel holding times of calls at each cell have a common exponential distribution. We first show that under some restriction, the light traffic limit for the stationary state distribution in the tagged cell is given by a mixture of a Poisson and binominal distributions. Based on the limit, we develop formulae for evaluating the hand-off and blocking probabilities and the mean number of busy channels in the tagged cell. Several numerical examples are presented that demonstrate the practical usefulness of the formulae.

Adaptive Filtering for Flow-Cytometric Particles

Abstract This paper studies the effects of FIR filtering and introducesan adaptive FIR filtering technique designed specificallyto smooth one and two dimensional accumulated flow-cytometric particles through frequency histograms. Theadaptive smoothing technique illustrated here will beshown to be particularly useful in compensating the unevenhistogram accumulation effects which take place whendata is accumulated at the lower histogram channels versusthe higher histogram channels. Linear smoothing techni-ques will not compensate for this phenomenon which isinherent to all histograms of accumulated data. In this view,a thorough analysis is provided to deal with the dilemmasimposed by the uneven accumulation of data within thesehistograms. 1 Introduction When cytometric data from specific blood cell particles isaccumulated into a frequency histogram with a finitenumber of channels (or bins) the accumulation processinherently smoothes the histogram since an averaging effectis taking place. When the cytometric data is accumulated inthe higher channels of the frequency histogram, the dis-tribution appears more spread and noisier. This is due to thefact that more channels are available and the inherentaveraging effect is diminished as data is accumulated over alarger band of channels. Because of this, when data isaccumulated in a histogram with a discrete number ofchannels, it gives rise to an uneven resolution within thehistogram.The idea behind the adaptive smoothing is to take advan-tage of the fact that as the filter coefficients are varied overan appropriate range, less smoothing will take place. Thefilter coefficients can be made to vary proportionally withrespect to the histogram channel where smoothing is takingplace. Smoothing is usually required prior to the analysis offrequency histogrammed data to attenuate the effect ofnoise. Smoothing through FIR ‘‘Finite Impulse Response’’filtering is by far the preferred method since it will not shiftthe position of the data distributions. A perspective ondensity estimators from histograms to several univariate andmultivariate statistical data analyses can be found in studies[1–3]. Other studies using histograms bring to focus severalissues including the notions of stability in the appearance ofthe histogram [4], the interpolations that can be achieved inkernel density estimators [5], as well as the practical buttraditional aspect of enhancing images through an adaptivehistogram equalization method [6].In general, it is desirable to select a smoothing function thathas the following criteria to ensure that the resulting data isnot distorted:1–The area under the curve should be maintained2–The mean of the distribution should be unchanged3–The change in the standard deviation should be kept to aminimumThese criteria for smoothing are maintained by traditionalFIR filtering provided that boundary conditions are satis-fied. A modified filtering scheme is introduced in this studybased on these mechanisms to customize the traditionalFIR-type filtering schemes for discrete time signals toaccommodate for data accumulated into frequency histo-grams. This modified filtering scheme is viewed as anadaptive filtering scheme that linearizes and accommodatesfor uneven histogram accumulation effects.To illustrate this problem a random Gaussian distributionwas created using the Box-Muller Method. The samepseudo-random distribution is illustrated with three separategain settings (1, 5, 10) as shown in Figure 1. When this datais histogrammed, as shown in Figure 2, the uneven accu-mulation problem is encountered and analyzed. Forexperimental evaluation, similar histogram accumulationproblems are discussed and analyzed utilizing Phycoery-thrin (PE) bead particles containing a variety of beadpopulations at various amounts of fluorochromes.

The Structure of the Doppler-difference Signal and the Analysis of its Autocorrelation Function

The Doppler-difference optical arrangement is nowadays the one most commonly used for fluid flow investigations with a laser anemometer. In this review, the essential characteristics of the Doppler-difference signal and of the associated autocorrelation function, obtained in general by integrating over many successive particle transits, are considered for both laminar and turbulent flows. Experimental conditions under which it is known that the autocorrelation function can be analysed to yield reliable estimates of mean velocity and turbulence intensity are specified; the stated restrictions are sufficient but may not all be necessary. In particular, it is shown that the effect on the autocorrelation function of the total velocity-component in the plane normal to the included bisector of the beam-axes is usually inseparable from the contribution due to the component u normal to the fringe system.The various data-reduction methods which have been proposed are classified and briefly reviewed. For laminar flows data-processing is relatively straightforward, but we are led to the conclusion that unknown flows having relatively high levels of turbulence (greater than about 15%) can only be treated successfully if there are very many fringes within a beam diameter, or if frequency-shifting techniques are used to achieve an equivalent effect. Under these circumstances, the relationship between the autocorrelation function and the distribution of the u-component of velocity reduces immediately to that of a simple Fourier cosine transform. When the measuring volume contains only a small number of fringes, certain approximations must always be made if interpretation of the data is to be possible in the general case, and it is shown that the Fourier transform relationship again arises in a natural way. However, the estimation of turbulence intensity in low-turbulence flows presents special difficulties, since truncation of the data at a finite number of channels causes broadening of the distribution in the transform plane. In these cases, it is often possible to assume that the velocity-distribution is approximately Gaussian in form, and curve-fitting methods can be used. An alternative procedure which uses information already available in the transform plane is described. Finally, the analysis of the autocorrelation function arising from a single transit in the presence of background radiation is briefly considered.

Curious random counting statistics: Theory, an actual flight experiment and possible applications for a suggested electrical circuit

A particular method of collecting and transmitting experimental data to Earth from a pair of balloon-borne cosmic ray electron detectors is shown to lead to a curious distribution in counting statistics which is not interpretable on the basis of a simple Poisson distribution. Dead-time corrections and a “house-keeping” mode, together with the fact that the instrumental scaler only has a finite number of channels, lead to a calculable distortion of the basic statistical distribution. When these effects are allowed for, remarkably good agreement is achieved between theoretical expectations and observations. The above results have led us to the design of a simple electrical circuit which incorporates the capability of (1) removing variable “seeing” conditions and (2) easily detecting periodic components in an event rate which has a high random component. These are features which are of great interest under particular experimental conditions.

Multi-step processes in high-energy elastic and inelastic nuclear scattering

Multi-step processes in elastic and inelastic nuclear scattering at intermediate and high energies are investigated using a formulation whereby a finite number of channels are explicitly treated while all the other channels are approximately accounted for through a “second-order potential matrix”. Within the framework of the eikonal approximation the problem reduces to a finite system of first-order coupled integro-differential equations with non-local potentials which depend on the two-body density matrix of the target nucleus. The relationship of the above formulation to the DWIA, the close-coupling method, and the Glauber multiple scattering model is examined. This approach is applied to the elastic and inelastic (2 +, 4.43 MeV) scattering of 1 GeV nucleons by 12C. The corrections to the DWIA are sizeable, and the inelastic scattering appears to be very sensitive to the multi-step contributions and the nuclear structure.