Relevant bibliographies by topics / Random noise theory

Academic literature on the topic 'Random noise theory'

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Published: 4 June 2021
Last updated: 27 July 2024

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Journal articles on the topic "Random noise theory"

1

Veraart, Jelle, Els Fieremans, and Dmitry S. Novikov. "Diffusion MRI noise mapping using random matrix theory." Magnetic Resonance in Medicine 76, no. 5 (November 24, 2015): 1582–93. http://dx.doi.org/10.1002/mrm.26059.

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Hida, Takeyuki, and Si Si. "Innovations for Random Fields." Infinite Dimensional Analysis, Quantum Probability and Related Topics 01, no. 04 (October 1998): 499–509. http://dx.doi.org/10.1142/s0219025798000272.

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There is a famous formula called Lévy's stochastic infinitesimal equation for a stochastic process X(t) expressed in the form [Formula: see text] We propose a generalization of this equation for a random field X(C) indexed by a contour C. Assume that the X(C) is homogeneous in a white noise x, say of degree n, we can then appeal to the classical theory of variational calculus and to the modern theory of white noise analysis in order to discuss the innovation for the X(C) and hence its probabilistic structure. Some of future directions are also mentioned.
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Hara, Hiroaki, Sang Don Choi, and Yeon Choon Chung. "A theory of noise based on generalized random walks." Physica A: Statistical Mechanics and its Applications 144, no. 2-3 (August 1987): 481–94. http://dx.doi.org/10.1016/0378-4371(87)90203-2.

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Thorarinsdottir, Thordis Linda. "BAYESIAN IMAGE RESTORATION, USING CONFIGURATIONS." Image Analysis & Stereology 25, no. 3 (May 3, 2011): 129. http://dx.doi.org/10.5566/ias.v25.p129-143.

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In this paper, we develop a Bayesian procedure for removing noise from images that can be viewed as noisy realisations of random sets in the plane. The procedure utilises recent advances in configuration theory for noise free random sets, where the probabilities of observing the different boundary configurations are expressed in terms of the mean normal measure of the random set. These probabilities are used as prior probabilities in a Bayesian image restoration approach. Estimation of the remaining parameters in the model is outlined for salt and pepper noise. The inference in the model is discussed in detail for 3 X 3 and 5 X 5 configurations and examples of the performance of the procedure are given.
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White, Benjamin S., Werner E. Kohler, and Leonard J. Srnka. "Random scattering in magnetotellurics." GEOPHYSICS 66, no. 1 (January 2001): 188–204. http://dx.doi.org/10.1190/1.1444894.

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Typical well logs show substantial variations of formation electrical resistivity over small spatial scales, down to the resolution of the logging tool. Using a plane stratified earth model, we examine the effects of this fine‐scale microstructure on scattering of the naturally occurring electromagnetic (EM) waves used in magnetotellurics. We show how 1-D magnetotelluric (MT) data may be viewed as arising statistically from a smoothed effective medium version of the resistivity‐depth profile. The difference between the data produced by the true medium and the effective medium is attributable to random scattering noise. This noise is fundamental to magnetotellurics and other diffusive‐wave EM exploration methods since it arises from the very small spatial scales that are usually ignored. The noise has unique statistical properties, which we characterize. We show that if scattering is the dominant noise source, a thin layer of increased resistivity at depth can be reliably detected only if the noise statistics are incorporated properly into the detection algorithm. This sets a new fundamental limit on the vertical detection capability of MT data. The theory agrees well with Monte Carlo simulations of MT responses from random resistivity microlayers.
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Miyoshi, Naoto. "A NOTE ON BOUNDS AND MONOTONICITY OF SPATIAL STATIONARY COX SHOT NOISES." Probability in the Engineering and Informational Sciences 18, no. 4 (October 2004): 561–71. http://dx.doi.org/10.1017/s026996480418409x.

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We consider shot-noise and max-shot-noise processes driven by spatial stationary Cox (doubly stochastic Poisson) processes. We derive their upper and lower bounds in terms of the increasing convex order, which is known as the order relation to compare the variability of random variables. Furthermore, under some regularity assumption of the random intensity fields of Cox processes, we show the monotonicity result which implies that more variable shot patterns lead to more variable shot noises. These are direct applications of the results obtained for so-called Ross-type conjectures in queuing theory.
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Duc, Luu Hoang. "Random attractors for dissipative systems with rough noises." Discrete & Continuous Dynamical Systems 42, no. 4 (2022): 1873. http://dx.doi.org/10.3934/dcds.2021176.

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<p style='text-indent:20px;'>We provide an analytic approach to study the asymptotic dynamics of rough differential equations, with the driving noises of Hölder continuity. Such systems can be solved with Lyons' theory of rough paths, in particular the rough integrals are understood in the Gubinelli sense for controlled rough paths. Using the framework of random dynamical systems and random attractors, we prove the existence and upper semi-continuity of the global pullback attractor for dissipative systems perturbed by bounded noises. Moreover, if the unperturbed system is strictly dissipative then the random attractor is a singleton for sufficiently small noise intensity.</p>
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Kuang, Z. F., and I. Pázsit. "The generalized theory of neutron noise in a random medium." Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences 458, no. 2017 (January 8, 2002): 233–52. http://dx.doi.org/10.1098/rspa.2001.0856.

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Demers, Matthew, Herb Kunze, and Davide La Torre. "ON RANDOM ITERATED FUNCTION SYSTEMS WITH GREYSCALE MAPS." Image Analysis & Stereology 31, no. 2 (May 17, 2012): 109. http://dx.doi.org/10.5566/ias.v31.p109-120.

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In the theory of Iterated Function Systems (IFSs) it is known that one can find an IFS with greyscale maps (IFSM) to approximate any target signal or image with arbitrary precision, and a systematic approach for doing so was described. In this paper, we extend these ideas to the framework of random IFSM operators. We consider the situation where one has many noisy observations of a particular target signal and show that the greyscale map parameters for each individual observation inherit the noise distribution of the observation. We provide illustrative examples.
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Liu, Xin, and Yanjiao Li. "Dynamics of Non-Autonomous Stochastic Semi-Linear Degenerate Parabolic Equations with Nonlinear Noise." Mathematics 11, no. 14 (July 18, 2023): 3158. http://dx.doi.org/10.3390/math11143158.

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In the present paper, we aim to study the long-time behavior of a stochastic semi-linear degenerate parabolic equation on a bounded or unbounded domain and driven by a nonlinear noise. Since the theory of pathwise random dynamical systems cannot be applied directly to the equation with nonlinear noise, we first establish the existence of weak pullback mean random attractors for the equation by applying the theory of mean-square random dynamical systems; then, we prove the existence of (pathwise) pullback random attractors for the Wong–Zakai approximate system of the equation. In addition, we establish the upper semicontinuity of pullback random attractors for the Wong–Zakai approximate system of the equation under consideration driven by a linear multiplicative noise.
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Dissertations / Theses on the topic "Random noise theory"

1

Arrowood, Jon A. "Using observation uncertainty for robust speech recognition." Diss., Available online, Georgia Institute of Technology, 2004:, 2003. http://etd.gatech.edu/theses/available/etd-04082004-180005/unrestricted/arrowood%5Fjon%5Fa%5F200312%5Fphd.pdf.

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Breen, Barbara J. "Computational nonlinear dynamics monostable stochastic resonance and a bursting neuron model /." Diss., Available online, Georgia Institute of Technology, 2004:, 2003. http://etd.gatech.edu/theses/available/etd-04082004-180036/unrestricted/breen%5Fbarbara%5Fj%5F200312%5Fphd.pdf.

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Furbeck, David S. "Fast determination of bit error rates on impulsive noise channels." Diss., Georgia Institute of Technology, 1995. http://hdl.handle.net/1853/15656.

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Kowalske, Kyle. "Performance of coherent and noncoherent RAKE receivers with convolutional coding ricean fading and pulse-noise interference /." Monterey, Calif. : Springfield, Va. : Naval Postgraduate School ; Available from National Technical Information Service, 2004. http://library.nps.navy.mil/uhtbin/hyperion/04Jun%5FKowalske.pdf.

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Thesis (Doctor of Philosophy in Electrical Engineering)--Naval Postgraduate School, June 2004.
Thesis advisor(s): Clark Robertson. Includes bibliographical references (p. 85-87). Also available online.
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Kwan, Jonathan Carleton University Dissertation Engineering Electrical. "Noise analysis and simulation of switched-capacitor circuits using a continuous time circuit simulator." Ottawa, 1988.

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Crnkovich, Joseph G. "Efficacy of various waveforms to support geolocation." Thesis, Monterey, Calif. : Naval Postgraduate School, 2009. http://handle.dtic.mil/100.2/ADA501141.

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Thesis (M.S. in Electrical Engineering)--Naval Postgraduate School, June 2009.
Thesis Advisor(s): Kragh, Frank ; Loomis, Herschel H. "June 2009." Description based on title screen as viewed on July 10, 2009. DTIC Identifiers: Theses, geolocation, cross ambiguity function, matched filter detection. Author(s) subject terms: Geolocation, Cross Ambiguity Function, CAF, Matched Filter Detection. Includes bibliographical references (p. 155-157). Also available in print.
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Zhu, Ying. "Signal detection on two-dimensional intersymbol interference channels correlated sources and reduced complexity algorithms /." [Pullman, Wash.] : Washington State University, 2008. http://www.dissertations.wsu.edu/Dissertations/Fall2008/y_zhu_081408.pdf.

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Thesis (Ph. D.)--Washington State University, December 2008.
Title from PDF title page (viewed on Sept. 23, 2008) "School of Electrical Engineering and Computer Science." Includes bibliographical references (p. 83-90).
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Ni, Li. "Non-equiprobable multi-level coding for the additive white Gaussian noise channel with Tikhonov phase error." Online access for everyone, 2005. http://www.dissertations.wsu.edu/Dissertations/Fall2005/l%5Fni%5F120905.pdf.

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Anilkumar, A. K. "Application Of Controlled Random Search Optimization Technique In MMLE With Process Noise." Thesis, Indian Institute of Science, 2000. https://etd.iisc.ac.in/handle/2005/232.

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Generally in most of the applications of estimation theory using the Method of Maximum Likelihood Estimation (MMLE) to dynamical systems one deals with a situation where only the measurement noise alone is present. However in many present day applications where modeling errors and random state noise input conditions occur it has become necessary for MMLE to handle measurement noise as well as process noise. The numerical algorithms accounting for both measurement and process noise require significantly an order of magnitude higher computer time and memory. Further more, implementation difficulties and convergence problems are often encountered. Here one has to estimate the quantities namely, the initial state error covariance matrix Po, measurement noise covariance matrix R, the process noise covariance matrix Q and the system parameter 0 and the present work deals with the above. Since the above problem is fairly involved we need to have a good reference solution. For this purpose we utilize the approach and results of Gemson who considered the above problem via the extended Kalman filter (EKF) route to compare the present results from the MMLE route. The EKF uses the unknown parameters as additional states unlike in MMLE which uses only the system states. Chapter 1 provides a brief historical perspective followed by parameter identification in the presence of process and measurement noises. The earlier formulations such as natural, innovation, combined, and adaptive approaches are discussed. Chapter 2 deals with the heuristic adaptive tuning of the Kalman filter parameters for the matrices Q and R by Myers and Tapley originally developed for state estimation problems involving satellite orbit estimation. It turns out that for parameter estimation problems apart from the above matrices even the choice of the initial covariance matrix Po is crucial for obtaining proper parameter estimates with a finite amount of data and for this purpose the inverse of the information matrix for Po is used. This is followed by a description of the original Controlled Random Search (CRS) of Price and its variant as implemented and used in the present work to estimate or tune Q, R, and 0 which is the aim of the present work. The above help the reader to appreciate the setting under which the present study has been carried out. Chapter 3 presents the results and the analysis of the estimation procedure adopted with respect to a specific case study of the lateral dynamics of an aircraft involving 15 unknown parameters. The reference results for the present work are the ones based on the approach of Gemson and Ananthasayanam (1998). The present work proceeds in two phases. In the first case (i) the EKF estimates for Po, Q, and R are used to obtain 0 and in the second case (ii) the estimate of Po and Q together with a reasonable choice of R are utilized to obtain 0 from the CRS algorithm. Thus one is able to assess the capability of the CRS to estimate only the unknown parameters. The next Chapter 4 presents the results of utilizing the CRS algorithm with R based on a reasonable choice and for Po from the inverse of the information matrix to estimate both Q and 0. This brings out the efficiency of MMLE with CRS algorithm in the estimation of unknown process noise characteristics and unknown parameters. Thus it demonstratesthofcdifficult Q can be estimated using CRS technique without the attendant difficulties of the earlier MMLE formulations in dealing with process noise. Chapter 5 discusses the - implementation of CRS to estimate the unknown measurement noise covariance matrix R together with the unknown 0 by utilizing the values of Po and Q obtained through EKF route. The effect of variation of R in the parameter estimation procedure is also highlighted in This Chapter. This Chapter explores the importance of Po in the estimation procedure. It establishes the importance of Po though most of the earlier works do not appear to have recognized such a feature. It turned out that the CRS algorithm does not converge when some arbitrary value of Po is chosen. It has to be necessarily obtained from a scouting pass of the EKF. Some sensitivity studies based on variations of Po shows its importance. Further studies shows the sequence of updates, the random nature of process and measurement noise effects, the deterministic nature of the parameter, play a critical role in the convergence of the algorithm. The last Chapter 6 presents the conclusions from the present work and suggestions for further work.
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Anilkumar, A. K. "Application Of Controlled Random Search Optimization Technique In MMLE With Process Noise." Thesis, Indian Institute of Science, 2000. http://hdl.handle.net/2005/232.

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Generally in most of the applications of estimation theory using the Method of Maximum Likelihood Estimation (MMLE) to dynamical systems one deals with a situation where only the measurement noise alone is present. However in many present day applications where modeling errors and random state noise input conditions occur it has become necessary for MMLE to handle measurement noise as well as process noise. The numerical algorithms accounting for both measurement and process noise require significantly an order of magnitude higher computer time and memory. Further more, implementation difficulties and convergence problems are often encountered. Here one has to estimate the quantities namely, the initial state error covariance matrix Po, measurement noise covariance matrix R, the process noise covariance matrix Q and the system parameter 0 and the present work deals with the above. Since the above problem is fairly involved we need to have a good reference solution. For this purpose we utilize the approach and results of Gemson who considered the above problem via the extended Kalman filter (EKF) route to compare the present results from the MMLE route. The EKF uses the unknown parameters as additional states unlike in MMLE which uses only the system states. Chapter 1 provides a brief historical perspective followed by parameter identification in the presence of process and measurement noises. The earlier formulations such as natural, innovation, combined, and adaptive approaches are discussed. Chapter 2 deals with the heuristic adaptive tuning of the Kalman filter parameters for the matrices Q and R by Myers and Tapley originally developed for state estimation problems involving satellite orbit estimation. It turns out that for parameter estimation problems apart from the above matrices even the choice of the initial covariance matrix Po is crucial for obtaining proper parameter estimates with a finite amount of data and for this purpose the inverse of the information matrix for Po is used. This is followed by a description of the original Controlled Random Search (CRS) of Price and its variant as implemented and used in the present work to estimate or tune Q, R, and 0 which is the aim of the present work. The above help the reader to appreciate the setting under which the present study has been carried out. Chapter 3 presents the results and the analysis of the estimation procedure adopted with respect to a specific case study of the lateral dynamics of an aircraft involving 15 unknown parameters. The reference results for the present work are the ones based on the approach of Gemson and Ananthasayanam (1998). The present work proceeds in two phases. In the first case (i) the EKF estimates for Po, Q, and R are used to obtain 0 and in the second case (ii) the estimate of Po and Q together with a reasonable choice of R are utilized to obtain 0 from the CRS algorithm. Thus one is able to assess the capability of the CRS to estimate only the unknown parameters. The next Chapter 4 presents the results of utilizing the CRS algorithm with R based on a reasonable choice and for Po from the inverse of the information matrix to estimate both Q and 0. This brings out the efficiency of MMLE with CRS algorithm in the estimation of unknown process noise characteristics and unknown parameters. Thus it demonstratesthofcdifficult Q can be estimated using CRS technique without the attendant difficulties of the earlier MMLE formulations in dealing with process noise. Chapter 5 discusses the - implementation of CRS to estimate the unknown measurement noise covariance matrix R together with the unknown 0 by utilizing the values of Po and Q obtained through EKF route. The effect of variation of R in the parameter estimation procedure is also highlighted in This Chapter. This Chapter explores the importance of Po in the estimation procedure. It establishes the importance of Po though most of the earlier works do not appear to have recognized such a feature. It turned out that the CRS algorithm does not converge when some arbitrary value of Po is chosen. It has to be necessarily obtained from a scouting pass of the EKF. Some sensitivity studies based on variations of Po shows its importance. Further studies shows the sequence of updates, the random nature of process and measurement noise effects, the deterministic nature of the parameter, play a critical role in the convergence of the algorithm. The last Chapter 6 presents the conclusions from the present work and suggestions for further work.
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Books on the topic "Random noise theory"

1

White noise distribution theory. Boca Raton: CRC Press, 1996.

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Middleton, D. First-order non-gaussian class C interference models and their associated threshold detection algorithms. [Boulder, CO: U.S. Dept. of Commerce, National Telecommunications and Information Administration, 1987.

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Middleton, D. First-order non-gaussian class C interference models and their associated threshold detection algorithms. [Boulder, CO: U.S. Dept. of Commerce, National Telecommunications and Information Administration, 1987.

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Middleton, D. First-order non-gaussian class C interference models and their associated threshold detection algorithms. [Boulder, CO: U.S. Dept. of Commerce, National Telecommunications and Information Administration, 1987.

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Middleton, D. First-order non-gaussian class C interference models and their associated threshold detection algorithms. [Boulder, CO: U.S. Dept. of Commerce, National Telecommunications and Information Administration, 1987.

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Hans-Jürgen, Zepernick, ed. Pseudo random signal processing: Theory and application. Hoboken, NJ: Wiley, 2005.

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Etten, Wim C. Van. Introduction to Random Signals and Noise. New York: John Wiley & Sons, Ltd., 2006.

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Kotelʹnikov, V. A. Teorii͡a︡ potent͡s︡ialʹnoĭ pomekhoustoĭchivosti. Moskva: "Radio i svi͡a︡zʹ", 1998.

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Loecher, Markus. Noise sustained patterns: Fluctuations and nonlinearities. Singapore: World Scientific, 2004.

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Jacobsen, Gunnar. Noise in digital optical transmission systems. Boston: Artech House, 1994.

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Book chapters on the topic "Random noise theory"

1

Alencar, Marcelo Sampaio de. "Random Signals and Noise." In Modulation Theory, 39–98. New York: River Publishers, 2022. http://dx.doi.org/10.1201/9781003338864-2.

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Réfrégier, Philippe. "Random Variables." In Noise Theory and Application to Physics, 5–24. New York, NY: Springer New York, 2004. http://dx.doi.org/10.1007/978-0-387-22526-5_2.

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Moschytz, George S. "Random Signals and Noise." In Analog Circuit Theory and Filter Design in the Digital World, 335–56. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-00096-7_12.

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Veshkurtsev, Yury. "NOISE IMMUNITY OF THE MODEM IN THE CHANNEL WITH "WHITE" NOISE." In THE FOUNDATIONS OF THE THEORY OF CONSTRUCTION OF NEW-GENERATION MODEMS, 48–98. au: AUS PUBLISHERS, 2022. http://dx.doi.org/10.26526/chapter_628a89252a3fa2.30236651.

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The monography presents the fundamentals of the theory of construction new-generation modems. Modems are built on the principles of statistical communication theory, based on the use of a random signal (chaos) as a carrier of information. In such a signal, a characteristic function is modulated, which is a fundamental characteristic of a random process. The signal modulation and demodulation method is patented and allows you to create modems with efficiency and noise immunity indicators several orders of magnitude higher than those of the known devices of the same name. New-generation modems immediately improve the technical characteristics of digital IT equipment by several orders of magnitude, since they work without errors in wired and radio channels when receiving one hundred duodecillion of binary symbols. The book is recommended for scientists and specialists in the field of digital communication systems, statistical radio engineering and instrumentation, and may be useful for graduate students, masters and students of relevant specialties.
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Veshkurtsev, Yury. "NOISE IMMUNITY OF THE MODEM IN THE CHANNEL WITH "NON- WHITE" NOISE." In THE FOUNDATIONS OF THE THEORY OF CONSTRUCTION OF NEW-GENERATION MODEMS, 99–141. au: AUS PUBLISHERS, 2022. http://dx.doi.org/10.26526/chapter_628a89252b5337.85338589.

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The monography presents the fundamentals of the theory of construction new-generation modems. Modems are built on the principles of statistical communication theory, based on the use of a random signal (chaos) as a carrier of information. In such a signal, a characteristic function is modulated, which is a fundamental characteristic of a random process. The signal modulation and demodulation method is patented and allows you to create modems with efficiency and noise immunity indicators several orders of magnitude higher than those of the known devices of the same name. New-generation modems immediately improve the technical characteristics of digital IT equipment by several orders of magnitude, since they work without errors in wired and radio channels when receiving one hundred duodecillion of binary symbols. The book is recommended for scientists and specialists in the field of digital communication systems, statistical radio engineering and instrumentation, and may be useful for graduate students, masters and students of relevant specialties.
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Dai, Qionghai, and Yue Gao. "Hypergraph Structure Evolution." In Artificial Intelligence: Foundations, Theory, and Algorithms, 101–20. Singapore: Springer Nature Singapore, 2023. http://dx.doi.org/10.1007/978-981-99-0185-2_6.

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AbstractIn practice, noise exists in the process of data collection and hypergraph construction. Therefore, missing, abundant, and noisy connections may be introduced into the generated hypergraph structure, which may lead to inaccurate inference on hypergraph. Another issue comes from the increasing data stream, which is also very common in many applications. It is important to consider the structure evolution methods on the hypergraph, which optimize the hypergraph structure accordingly. Early hypergraph computation methods mainly rely on static hypergraph structure, which may suffer from the limitation of the static mechanism when confronting random and increasing data scenarios. In this chapter, we introduce dynamic hypergraph structure evolution methods, including both hypergraph component optimization and hypergraph structure optimization. Finally, we briefly introduce the incremental learning method on growing data.
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Jiang, Hongliang, Chaobo Lu, Chunfa Xiong, and Mengkun Ran. "Seismic Data Denoising Analysis Based on Monte Carlo Block Theory." In Lecture Notes in Civil Engineering, 339–49. Singapore: Springer Nature Singapore, 2023. http://dx.doi.org/10.1007/978-981-99-2532-2_28.

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AbstractDenoising of seismic data has always been an important focus in the field of seismic exploration, which is very important for the processing and interpretation of seismic data. With the increasing complexity of seismic exploration environment and target, seismic data containing strong noise and weak amplitude seismic in-phase axis often contain many weak feature signals. However, weak amplitude phase axis characteristics are highly susceptible to noise and useful signal often submerged by background noise, seriously affected the precision of seismic data interpretation, dictionary based on the theory of the monte carlo study seismic data denoising method, selecting expect more blocks of data, for more accurate MOD dictionary, to gain a higher quality of denoising of seismic data. Monte carlo block theory in this paper, the dictionary learning dictionary, rules, block theory and random block theory is example analysis test, the dictionary learning algorithm based on the results of three methods to deal with, and the numerical results show that the monte carlo theory has better denoising ability, the denoising results have higher SNR, and effectively keep the weak signal characteristics of the data; In terms of computational efficiency, the proposed method requires less time and has higher computational efficiency, thus verifying the feasibility and effectiveness of the proposed method.
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Fujii, Tomohiro, and Masao Hirokawa. "A Data Concealing Technique with Random Noise Disturbance and a Restoring Technique for the Concealed Data by Stochastic Process Estimation." In International Symposium on Mathematics, Quantum Theory, and Cryptography, 103–24. Singapore: Springer Singapore, 2020. http://dx.doi.org/10.1007/978-981-15-5191-8_11.

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Abstract We propose a technique to conceal data on a physical layer by disturbing them with some random noises, and moreover, a technique to restore the concealed data to the original ones by using the stochastic process estimation. Our concealing-restoring system manages the data on the physical layer from the data link layer. In addition to these proposals, we show the simulation result and some applications of our concealing-restoring technique.
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Walrand, Jean. "Digital Link—B." In Probability in Electrical Engineering and Computer Science, 143–62. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-49995-2_8.

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AbstractChapter 7 explained the detection and hypothesis testing problems, Huffman codes and the situation where errors are independent and Gaussian. In this chapter, we prove the optimality of the Huffman code in Sect. 8.1 and the Neyman–Pearson Theorem in Sect. 8.2. Section 8.3 discusses the theory of jointly Gaussian random variables that is used to analyze the modulation schemes of Sect. 7.5 . Section 8.4 uses the results on jointly Gaussian random variables to explain hypothesis tests that arise when analyzing data. That section discusses the chi-squared test and the F-test. Section 8.5 is devoted to the LDPC codes that are widely used in high-speed communication links. These codes augment a group of bits to be transmitted over a noisy channel with additional bits computed from those in the group. When it receives the bits, when the augmented bits are not consistent, the receiver attempts to determine the bits that are most likely to have been corrupted by noise.
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Veshkurtsev, Yury. "CHARACTERISTIC FUNCTION." In THE FOUNDATIONS OF THE THEORY OF CONSTRUCTION OF NEW-GENERATION MODEMS, 10–25. au: AUS PUBLISHERS, 2022. http://dx.doi.org/10.26526/chapter_628a8925276245.43662054.

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The monography presents the fundamentals of the theory of construction new-generation modems. Modems are built on the principles of statistical communication theory, based on the use of a random signal (chaos) as a carrier of information. In such a signal, a characteristic function is modulated, which is a fundamental characteristic of a random process. The signal modulation and demodulation method is patented and allows you to create modems with efficiency and noise immunity indicators several orders of magnitude higher than those of the known devices of the same name. New-generation modems immediately improve the technical characteristics of digital IT equipment by several orders of magnitude, since they work without errors in wired and radio channels when receiving one hundred duodecillion of binary symbols. The book is recommended for scientists and specialists in the field of digital communication systems, statistical radio engineering and instrumentation, and may be useful for graduate students, masters and students of relevant specialties.
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Conference papers on the topic "Random noise theory"

1

Duras, Maciej M. "Quantum fluctuations and random matrix theory." In SPIE's First International Symposium on Fluctuations and Noise, edited by Derek Abbott, Jeffrey H. Shapiro, and Yoshihisa Yamamoto. SPIE, 2003. http://dx.doi.org/10.1117/12.489003.

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Lu, X., S. Matsuda, T. Shimizu, and S. Nakamura. "Noise Reduction Based Random Matrix Theory." In 2008 6th International Symposium on Chinese Spoken Language Processing (ISCSLP). IEEE, 2008. http://dx.doi.org/10.1109/chinsl.2008.ecp.83.

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Lu, XU-Gang, S. Matsuda, T. Shimizu, and S. Nakamura. "Noise Reduction Based Random Matrix Theory." In Int. Symp. on Chinese Spoken Language Processing. ISCA: ISCA, 2008. http://dx.doi.org/10.21437/iscslp.2008-81.

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Aldroubi, Akram, Longxiu Huang, Ilya Krishtal, and Roy Lederman. "Dynamical sampling with random noise." In 2017 International Conference on Sampling Theory and Applications (SampTA). IEEE, 2017. http://dx.doi.org/10.1109/sampta.2017.8024372.

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Giles, Sammie. "Random-noise filter based on circular correlation." In 2009 41st Southeastern Symposium on System Theory (SSST). IEEE, 2009. http://dx.doi.org/10.1109/ssst.2009.4806850.

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HIDA, TAKEYUKI, and SI SI. "ELEMENTAL RANDOM VARIABLES IN WHITE NOISE THEORY: BEYOND REDUCTIONISM." In Proceedings of the Third International Conference. WORLD SCIENTIFIC, 2001. http://dx.doi.org/10.1142/9789812810267_0005.

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Weinberger, Nir, and Neri Merhav. "Codeword or noise? Exact random coding exponents for slotted asynchronism." In 2014 IEEE International Symposium on Information Theory (ISIT). IEEE, 2014. http://dx.doi.org/10.1109/isit.2014.6875286.

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Cohen, Asaf, Neri Merhav, and Tsachy Weissman. "Scanning, Filtering and Prediction for Random Fields Corrupted by Gaussian Noise." In 2007 IEEE International Symposium on Information Theory. IEEE, 2007. http://dx.doi.org/10.1109/isit.2007.4557305.

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Watanabe, S., R. Matsumoto, and R. Uyematsu. "Noise tolerance of the BB84 protocol with random privacy amplification." In Proceedings. International Symposium on Information Theory, 2005. ISIT 2005. IEEE, 2005. http://dx.doi.org/10.1109/isit.2005.1523492.

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Duffy, Ken R., and Muriel Medard. "Guessing random additive noise decoding with soft detection symbol reliability information - SGRAND." In 2019 IEEE International Symposium on Information Theory (ISIT). IEEE, 2019. http://dx.doi.org/10.1109/isit.2019.8849297.

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Reports on the topic "Random noise theory"

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Bucklew, James A., and Stamatis Cambanis. Estimating Random Integrals from Noisy Observations: Sampling Designs and Their Performance. Fort Belvoir, VA: Defense Technical Information Center, December 1985. http://dx.doi.org/10.21236/ada170330.

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