Total Error Probability Research Articles

Theory of the performance of a DECT receiver in a multipath channel

The performance of a digital enhanced cordless telecommunications (DECT) receiver in a multipath channel is studied. The following issues were investigated: irreducible bit-error rate (BER) performance of the differentially coherent detector in Rayleigh and Rician channels; BER performance in the presence of both the noise in the receiver and a multipath interference. The theoretical estimates of the irreducible error rate developed in the paper showed reasonable agreement with the data obtained from computer-based simulation of the DECT link through a Rayleigh multipath channel. The combined effect from receiver noise and multipath interference has been studied, and asymptotic formulas for the total error probability have been developed. The results of calculating the error probabilities using these asymptotics demonstrate good agreement with measured data.

A NOTE ON THE OPTIMAL CUTOFF POINT IN BANKRUPTCY PREDICTION MODELS

A modified Bayesian decision model is derived in the study to systematically estimate an optimal cutoff point for bankruptcy prediction models. In addition, a loss function is implemented in the model so that the total error costs instead of the total error probability is minimized. Any dichotomous classification problem with unequal error costs would find this decision model useful.

Error-rate floor in optical ASK heterodyne systems caused by nonzero (semiconductor) laser linewidth

Using a simple model to account for the effects of non-negligible linewidths for the transmitter and local oscillator lasers in a heterodyne ASK system, we show that there is an error probability floor which is a function of the IF bandwidth and the relative decision threshold level. We describe the physical reason for this behaviour and present some calculated results for total error probability in terms of signal power, IF linewidth and bandwidth, and threshold setting. The implications of this ‘floor’ for practical receiver design are discussed.

Influence of (semiconductor) laser linewidth on the error-rate floor in dual-filter optical FSK receivers

We discuss an error-rate floor in dual-filter optical FSK receivers in terms of the IF linewidth and the frequency shift between 0s and 1s, using a comprehensive model for the receiver which takes into account nonzero laser linewidth, noise correlation and signal overlap between the filters. We present calculated results for total error probability in terms of signal power, IF linewidth and frequency shift, illustrating the effect of the floor on receiver sensitivity, and we contrast it with a related effect in heterodyne ASK systems.

EXCLUSIVE OR processing (binary image subtraction) using thick Fourier holograms

Theoretical and experimental results are presented for parallel EXCLUSIVE OR processing using thick Fourier holograms. The data pages used contained 1024 bits in a 32 × 32 format. A holographically stored data page is reconstructed together with an input data page that is imaged through the system. The amplitudes of the two wave fronts are adjusted to be equal, and their relative phase is adjusted to be 180°, thus producing the bit-by-bit EXCLUSIVE OR operation between the pages. Using an expanded reference beam for the geometrical configuration treated, it is calculated that the average dynamic range between a 0 and a 1 in the output power would be 17.4 dB. Experimentally, it is shown that excellent EXCLUSIVE OR results are obtainable. Photographs of these results are presented. An average dynamic range of 7.7 dB was measured, the decrease from the calculated value being primarily due to noise in the video method of detection used in the measurements. The probabilities of miss and false alarm and the total probability of error were also measured. The use of a small diameter reference beam, necessary in some applications, causes a large mismatch in the shapes of the two wave fronts, thus degrading the EXCLUSIVE OR results. It is shown theoretically and experimentally that using an aperture at the recording material produces partial compensation of the wave fronts, thus improving the EXCLUSIVE OR results.

AMF phasing—A precise control of the ignition timing of AKM for reduction of the injection error

This paper deals with a new concept, named “AMF Phasing”, which intends to minimize the effect of injection error that would result during apogee motor firing (AMF) of the spinning spacecraft. The characteristic of velocity increment error is derived analytically, based on the disturbed spinning motion during AMF. In order to precisely estimate the amount of fuel required for post-AMF orbital correction maneuvers, a probability model is proposed which estimates the total injection error probability combining the dominant error factors, i.e. pre-AMF attitude determination error and velocity increment error during AMF. It is shown that a substantial saving in fuel normally consumed for post-AMF can be expected, when the resultant velocity increment error contribution, which otherwise would be randomly directed in inertial space, is controlled so that it appears in the direction of local right ascension by igniting AKM at the proper instant (AMF Phasing). The procedure for AMF phasing, using a Sun pulse as a reference signal for the ignition timing is described in this paper. It was actually applied for GMS-2, Japan's second Geostationary Meteorological Satellite (HIMAWARI-II). The HIMAWARI-II post-AMF orbit determination shows that AMF Phasing worked successfully and it is concluded that a substantial fuel saving was achieved.

Image Registration Using Material Information

In studying the performance of any matching technique for image registration it is important to select an appropriate reference image. In this paper a set of a priori probabilities of detection based on explicit information about the materials which surround the edges is used in a strategy for reference selection. This set of a priori probabilities of detection is obtained by finding the frequency of occurrence of material edges. The correlation results for three edges, each belonging to a different material class, are presented. The results of two criteria for optimum reference selection, namely the Neyman-Pearson and the ideal observer, are used to show that the best choice appears to be a compromise. This minimizes the total probability of error while giving a higher probability of correct acquisition for a fixed probability of false alarm.

Resultant forecasts

This article presents 1) the definition of a resultant forecasting function for a stochastic case, 2) construction of a function forecasting a stochastic process, and 3) construction, therefore, of a resultant forecasting function for two criteria and associated operations: minimum of the total probability of error and minimum risk function. The applicational significance of a resultant forecast is discussed in view of hierarchical systems design.

Chernoff bounds for discriminating between two markov processes

We study a statistical hypothesis testing problem, where a sample function of a Markov process with one of two sets of known parameters is observed over a finite time interval. When a log likelihood ratio test is used to discriminate between the two sets of parameters, we give bounds on the probability of choosing an incorrect hypothesis, and on the total probability of error, for both discrete and continuous time parameter, and discrete and continuous state space. The asymptotic behavior of the bounds is examined as the observation interval becomes infinite.

Non-linear filter for rejection of an unknown frequency sine wave interference in an ‘ask system’

This paper presents an analysis and description of the implementation of a Function Elimination Filter (FEF) of the integral type which could be used to reject a sine-wave interference (SWI) in an Amplitude Shift Keying System (ASK). One structure of this filter is expressed by the second-order determinant; its elements are inner products of the observed process and certain coordinate functions. It is sufficient that this FET rejects a sine-wave interference in spite of the absence of any a priori knowledge about its parameters (including frequency). It is shown here that there exist some situations when use of FEF is preferable to a conventional Matched Filter (MF) in order to achieve a minimum total probability of error. The experimental results of testing this filter for detecting a signal in the presence of both SWI and Gaussian noise are given.

A Note on Hoeffding's Inequality

Abstract A lower bound is derived concerning a special form of the entropy function of information theory. It is applied to Hoeffding's bound for the probability of the deviation of the sample mean from its expected value and for the corresponding problem concerning the sample variance. Furthermore, applying the bound one can obtain a discard function for a binary symmetric channel, a lower bound for the total error probability in testing two simple hypotheses, given the number of observations, and a lower bound for the deviation of the empirical distribution from the true distribution.

A Note on Hoeffding's Inequality

Abstract A lower bound is derived concerning a special form of the entropy function of information theory. It is applied to Hoeffding's bound for the probability of the deviation of the sample mean from its expected value and for the corresponding problem concerning the sample variance. Furthermore, applying the bound one can obtain a discard function for a binary symmetric channel, a lower bound for the total error probability in testing two simple hypotheses, given the number of observations, and a lower bound for the deviation of the empirical distribution from the true distribution.