scholarly journals Computational Information Geometry For Binary Classification of High-Dimensional Random Tensors

2018 ◽  
Author(s):  
Gia-Thuy Pham ◽  
Rémy Boyer ◽  
Frank Nielsen
Keyword(s):  
Upper Bound ◽  
Error Probability ◽  
Matrix Theory ◽  
Signal To Noise Ratio ◽  
Information Geometry ◽  
Difficult Problem ◽  
Signal To Noise ◽  
Error Exponent ◽  
Noise Ratio ◽  
Finite Constant

The performance in terms of minimal Bayes’ error probability for detection of ahigh-dimensional random tensor is a fundamental under-studied difficult problem. In this work, weconsider two Signal to Noise Ratio (SNR)-based detection problems of interest. Under the alternativehypothesis, i.e., for a non-zero SNR, the observed signals are either a noisy rank-R tensor admitting aQ-order Canonical Polyadic Decomposition (CPD) with large factors of size Nq R, i.e, for 1 q Q,where R, Nq ! ¥ with R1/q/Nq converge towards a finite constant or a noisy tensor admittingTucKer Decomposition (TKD) of multilinear (M1, . . . ,MQ)-rank with large factors of size Nq Mq,i.e, for 1 q Q, where Nq,Mq ! ¥ with Mq/Nq converge towards a finite constant. The detectionof the random entries (coefficients) of the core tensor in the CPD/TKD is hard to study since theexact derivation of the error probability is mathematically intractable. To circumvent this technicaldifficulty, the Chernoff Upper Bound (CUB) for larger SNR and the Fisher information at low SNRare derived and studied, based on information geometry theory. The tightest CUB is reached forthe value minimizing the error exponent, denoted by s?. In general, due to the asymmetry of thes-divergence, the Bhattacharyya Upper Bound (BUB) (that is, the Chernoff Information calculated ats? = 1/2) can not solve this problem effectively. As a consequence, we rely on a costly numericaloptimization strategy to find s?. However, thanks to powerful random matrix theory tools, a simpleanalytical expression of s? is provided with respect to the Signal to Noise Ratio (SNR) in the twoschemes considered. A main conclusion of this work is that the BUB is the tightest bound at lowSNRs. This property is, however, no longer true for higher SNRs.

scholarly journals A Fundamental Upper Bound for Signal to Noise Ratio of Quantum Detectors

2020 ◽  
Vol 89 (5) ◽  
pp. 054005
Author(s):  
Ryota Katsube ◽  
Masahiro Hotta ◽  
Koji Yamaguchi
Keyword(s):  
Upper Bound ◽  
Signal To Noise Ratio ◽  
Signal To Noise ◽  
Noise Ratio

scholarly journals Joint use of frequency-time division and antinoise coding in radio communication systems with FHSS

2021 ◽  
Vol 9 (4) ◽  
pp. 77-84
Author(s):  
A. A. Paramonov ◽  
Van Zung Hoang
Keyword(s):  
Data Transmission ◽  
Communication Systems ◽  
Error Probability ◽  
Noise Immunity ◽  
Signal To Noise Ratio ◽  
Frequency Division ◽  
Radio Communication ◽  
Signal To Noise ◽  
Noise Ratio ◽  
Time Division

In the context of continuous improvement of radio prospecting and active radio jamming technics along with introduction of automated active countermeasures systems (ACS), the frequency-hopping spread spectrum (FHSS) radio communication systems (RCS) are widely used in order to improve reliability and noise immunity of data transmission. The noise immunity of the RCS affected by unintentional or deliberate interference can be significantly perfected by the combined use of frequency-time division and antinoise coding. This paper explores the case when the interference created by an ACS system with a limited transmitter power covers a part of the RCS frequency range. The receiver gets input mix of the wanted signal, the receiver noise, and probably a deliberate interference also considered as a noise. The article analyzes the noise immunity of signals reception with FHSS in the low-speed radio systems with joint use of frequency-time division of information subsymbols and noise combating codes when the deliberate interference destructively impacts a part of the RCS working band. Dependence of the bit error probability on the signal-to-noise ratio is calculated for the joint use of frequency division of information subsymbols and noise combating codes. It is shown that due to effective use of the frequency-energy resource of a radio line, considering the use of correction codes, a quite high noise immunity of RCS under the influence of deliberate interference can be assured. The indicated dependences of the error probability on the signal-to-noise ratio confirm that the reliability of data transmission can be significantly increased by the proper combination of signal spectrum spreading, applying of correction codes, and frequency division of subsymbols followed by their weight processing.

scholarly journals Обнаружение хаотических радиоимпульсов с помощью ансамбля детекторов огибающих

2021 ◽  
Vol 47 (1) ◽  
pp. 27
Author(s):  
Ю.В. Андреев
Keyword(s):  
Analytical Solution ◽  
Error Probability ◽  
Signal To Noise Ratio ◽  
Radio Pulse ◽  
Detection Error ◽  
Signal To Noise ◽  
Pulse Detection ◽  
Noise Ratio

Detection of ultrawideband chaotic radio pulses with ensemble of noncoherent receivers based on envelope detectors is investigated. Analytical solution is derived for the detection error probability as a function of signal-to-noise ratio at the detector input. The sensitivity of the radio pulse detection (by signal-to-noise ratio) is shown to increase in proportion to the number of detectors.

scholarly journals Comparative analysis of noise immunity of reception of nonlinear complex discrete signals with standard signals AFM-16 BPSK

Radiotekhnika ◽  
2020 ◽  
pp. 133-140
Author(s):  
S.G. Rassomakhin ◽  
A.A. Zamula ◽  
I.D. Gorbenko ◽  
Ho Tri Luc
Keyword(s):  
Comparative Analysis ◽  
Error Probability ◽  
Noise Immunity ◽  
Signal To Noise Ratio ◽  
Statistical Simulation ◽  
Gaussian Channel ◽  
Signal To Noise ◽  
Discrete Signals ◽  
Noise Ratio ◽  
Correlation Properties

The article shows that the solution to the problem of increasing the noise immunity (noise immunity and secrecy of functioning) of the ICS can be achieved using systems of nonlinear signals with improved ensemble, structural and correlation properties. Two classes of nonlinear complex discrete signals are considered: characteristic discrete signals (CDS) and cryptographic signals (CS). Methods for the synthesis of these signals are presented. The paper gives a statistical simulation model for studying the noise immunity of various classes of signals in the Gaussian channel. Using this model, estimates of the dependence of the error probability on the signal-to-noise ratio were obtained for various classes of signals, namely: CDS, KS and standard BPSK AFM-16 signals. It is shown that for the signal-to-noise ratio – 10 the error probability for the CDR is 4.6875e-06, for the CS is 3.515625e-06, and for the AFM-16 is 0.002025. Thus, the use of nonlinear complex discrete signals, in particular, CDS and KS, can significantly increase the noise immunity of signal reception in modern ICS. At the same time, taking into account the improved ensemble and structural properties of these nonlinear signals, it is possible to improve significantly the indicators of crypto- and imitation security of the systems functioning.

scholarly journals DIVERSITY SIGNAL PROCESSING OVER WEIBULL FADING CHANNELS

Doklady BGUIR ◽  
2019 ◽  
pp. 13-21
Author(s):  
V. P. Tuzlukov
Keyword(s):  
Output Signal ◽  
Error Probability ◽  
Signal To Noise Ratio ◽  
Moment Generating Function ◽  
Maximal Ratio Combining ◽  
Symbol Error Probability ◽  
Signal To Noise ◽  
Equal Gain Combining ◽  
Weibull Fading ◽  
Noise Ratio

We present a moments-based approach to the performance analysis of L-branch equal-gain combining and maximal-ratio combining receivers, operating in independent or correlated, not necessarily identically distributed, Weibull fading. For both equal-gain combining and maximal-ratio combining receivers the moments of the output signal-to-noise ratio are obtained in closed-form. An accurate approximate expression is derived for the moment-generating function of the output signal-to-noise ratio of the equal-gain combining receiver utilizing the Padé approximants theory, while a closed-form expression for the corresponding MGF of the maximal-ratio combining receiver, is obtained. Significant performance criteria, such as average output signal-to-noise ratio, amount of fading and spectral efficiency at the low power regime, are extracted in closed-forms, using the moments of the output signal-to-noise ratio for both independent and correlative fading. Moreover, using the well-known moment-generating function approach, the outage and the average symbol error probability for several coherent, non-coherent, binary, and multilevel modulation schemes, are studied. The average symbol error probability of dual-branch equal-gain combining and maximal-ratio combining receivers is also obtained when correlative fading is considered in the diversity input branches. The proposed mathematical analysis is illustrated by various numerical results and validated by computer simulations.

Determination of the Best Emulsion for the Microscopy of Crystals

1981 ◽  
Vol 39 ◽  
pp. 32-33
Author(s):  
David A. Grano ◽  
Kenneth H. Downing
Keyword(s):  
Spatial Frequency ◽  
Information Transfer ◽  
Signal To Noise Ratio ◽  
Experimental Situation ◽  
Photographic Emulsion ◽  
Modulation Transfer ◽  
Signal To Noise ◽  
Frequency Space ◽  
Noise Ratio

The retrieval of high-resolution information from images of biological crystals depends, in part, on the use of the correct photographic emulsion. We have been investigating the information transfer properties of twelve emulsions with a view toward 1) characterizing the emulsions by a few, measurable quantities, and 2) identifying the “best” emulsion of those we have studied for use in any given experimental situation. Because our interests lie in the examination of crystalline specimens, we've chosen to evaluate an emulsion's signal-to-noise ratio (SNR) as a function of spatial frequency and use this as our critereon for determining the best emulsion.The signal-to-noise ratio in frequency space depends on several factors. First, the signal depends on the speed of the emulsion and its modulation transfer function (MTF). By procedures outlined in, MTF's have been found for all the emulsions tested and can be fit by an analytic expression 1/(1+(S/S0)2). Figure 1 shows the experimental data and fitted curve for an emulsion with a better than average MTF. A single parameter, the spatial frequency at which the transfer falls to 50% (S0), characterizes this curve.

Experiments in Bright-Field Imaging with Hollow-Cone Illumination

1981 ◽  
Vol 39 ◽  
pp. 226-227
Author(s):  
W. Kunath ◽  
K. Weiss ◽  
E. Zeitler
Keyword(s):  
Signal To Noise Ratio ◽  
Carbon Support ◽  
Electronic System ◽  
Optic Axis ◽  
Hollow Cone ◽  
Signal To Noise ◽  
Bright Field ◽  
Noise Ratio ◽  
Single Field ◽  
Field Imaging

Bright-field images taken with axial illumination show spurious high contrast patterns which obscure details smaller than 15 ° Hollow-cone illumination (HCI), however, reduces this disturbing granulation by statistical superposition and thus improves the signal-to-noise ratio. In this presentation we report on experiments aimed at selecting the proper amount of tilt and defocus for improvement of the signal-to-noise ratio by means of direct observation of the electron images on a TV monitor.Hollow-cone illumination is implemented in our microscope (single field condenser objective, Cs = .5 mm) by an electronic system which rotates the tilted beam about the optic axis. At low rates of revolution (one turn per second or so) a circular motion of the usual granulation in the image of a carbon support film can be observed on the TV monitor. The size of the granular structures and the radius of their orbits depend on both the conical tilt and defocus.

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