• Journal of Korean Society of Industrial and Systems Engineering
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• v.41 no.2
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• pp.117-132
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• 2018

There always exist nonzero inspection errors whether inspectors are humans or automatic inspection machines. Inspection errors can be categorized by two types, type I error and type II error, and they can be regarded as either a constant or a random variable. Under the assumption that two types of random inspection errors are distributed with the "uniform" distribution on a half-open interval starting from zero, it was proved that inspectors overestimate any given fraction defective with the probability more than 50%, if and only if the given fraction defective is smaller than a critical value, which depends upon only the ratio of a type II error over a type I error. In addition, it was also proved that the probability of overestimation approaches one hundred percent as a given fraction defective approaches zero. If these critical phenomena hold true for any error distribution, then it might have great economic impact on commercial inspection plans due to the unfair overestimation and the recent trend of decreasing fraction defectives in industry. In this paper, we deal with the same overestimation problem, but assume a "symmetrical triangular" distribution expecting better results since our triangular distribution is closer to a normal distribution than the uniform distribution. It turns out that the overestimation phenomenon still holds true even for the triangular error distribution.

• Communications of the Korean Mathematical Society
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• v.38 no.2
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• pp.431-450
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• 2023

The basic goal of quantization for probability distribution is to reduce the number of values, which is typically uncountable, describing a probability distribution to some finite set and thus to make an approximation of a continuous probability distribution by a discrete distribution. It has broad application in signal processing and data compression. In this paper, first we define the uniform distributions on different curves such as a line segment, a circle, and the boundary of an equilateral triangle. Then, we give the exact formulas to determine the optimal sets of n-means and the nth quantization errors for different values of n with respect to the uniform distributions defined on the curves. In each case, we further calculate the quantization dimension and show that it is equal to the dimension of the object; and the quantization coefficient exists as a finite positive number. This supports the well-known result of Bucklew and Wise [2], which says that for a Borel probability measure P with non-vanishing absolutely continuous part the quantization coefficient exists as a finite positive number.

• Journal of the Institute of Electronics Engineers of Korea TC
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• v.43 no.8 s.350
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• pp.59-68
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• 2006

The study on the uniform error property of codes has been restricted to additive white Gaussian noise (AWGN) channel, which is generally referred to as geometrical uniformity. In this paper, we extend the uniform error property to space-time codes in multiple-input multiple-output (MIMO) channel by directly treating the probability density functions fully describing the transmission channel and the receiver. Moreover, we provide the code construction procedure for the geometrically uniform space-time trellis codes in fast MIMO channels, which consider the distance spectrum. Due to the uniform error property, the complexity of code search is extensively reduced. Such reduction makes it possible to obtain the optimal space-time trellis codes with high order states. Simulation results show that new codes offer a better performance in fast MIMO channels than other known codes.

• Proceedings of the IEEK Conference
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• 2003.07a
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• pp.89-92
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• 2003

A geometrically uniform code in AWGN channel has strong symmetry properties such as a) the distance profiles form codewords On C to all other codewords are all the same, and b) all Voronoi regions of codewords in C have the same shape. Such properties make the word error probability of geometrically uniform codes be transparent to the transmitted codeword. In this paper, we extend the geometrically uniform codes in AWGN channel to the geometrical uniform codes in fading channel with multiple transmit antennas.

• Journal of Communications and Networks
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• v.7 no.4
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• pp.450-461
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• 2005

In this paper, we derive analytical expressions for the exact pairwise error probability (PEP) of a space-time coded system operating over spatially correlated fast (constant over the duration of a symbol) and slow (constant over the length of a code word) fad­ing channels using a moment-generating function-based approach. We discuss two analytical techniques that can be used to evaluate the exact-PEPs (and therefore, approximate the average bit error probability (BEP)) in closed form. These analytical expressions are more realistic than previously published PEP expressions as they fully account for antenna spacing, antenna geometries (uniform linear array, uniform grid array, uniform circular array, etc.) and scattering models (uniform, Gaussian, Laplacian, Von-mises, etc.). Inclusion of spatial information in these expressions provides valuable insights into the physical factors determining the performance of a space-time code. Using these new PEP expressions, we investigate the effect of antenna spacing, antenna geometries and azimuth power distribution parameters (angle of arrival/departure and angular spread) on the performance of a four-state QPSK space-time trellis code proposed by Tarokh et al. for two transmit antennas.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.25 no.1A
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• pp.48-55
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• 2000

In this paper, an assumption to design a quantizer, is proposed that if one small region of a probability density function is represented larger probability and bigger total error than another neighbour region, then the quantizer is not optimal. It is tested when the probability functions are Gaussian, Laplacian and uniform density function by the computer simulations. A new LBG algorithm which originates from this assumption in addition to LBG algorithm, is designed for the vector quantizer. The new LBG algorithm presents better performance than the original LBG algorithm in the average error and the variance of the error.

• The Journal of Korea Institute of Information, Electronics, and Communication Technology
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• v.9 no.2
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• pp.190-195
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• 2016

In this paper, we are comparative analysis both class method and proposal method in order to estimation of incident signal direction on uniform array antenna system. Proposal method of this paper decrease error probability for a signal direction of arrival estimation using maximum posterior probability estimator. If it decrease to signal estimation direction error probability, signal direction of arrival can correctly estimate. Through simulation, we were comparative analysis proposed method and class method. Also, we were comparative analysis about signal estimation error probability with increasing array antenna element. We show the superior performance of the proposed method relative to the class method to decrease of signal estimation error probability about 12%.

• Nuclear Engineering and Technology
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• v.54 no.5
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• pp.1606-1615
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• 2022

For investigating whether the MARSSIM nonparametric test has sufficient statistical power when a site has a specific contamination distribution before conducting a final status survey (FSS), a novel approach was proposed to predict the release probability of the site. Five distributions were assumed: lognormal distribution, normal distribution, maximum extreme value distribution, minimum extreme value distribution, and uniform distribution. Hypothetical radioactivity populations were generated for each distribution, and Sign tests were performed to predict the release probabilities after extracting samples using Monte Carlo simulations. The designed Type I error (0.01, 0.05, and 0.1) was always satisfied for all distributions, while the designed Type II error (0.01, 0.05, and 0.1) was not always met for the uniform, maximum extreme value, and lognormal distributions. Through detailed analyses for lognormal and normal distributions which are often found for contaminants in actual environmental or soil samples, it was found that a greater statistical power was obtained from survey units with normal distribution than with lognormal distribution. This study is expected to contribute to achieving the designed decision error when the contamination distribution of a survey unit is identified, by predicting whether the survey unit passes the statistical test before undertaking the FSS according to MARSSIM.

• Communications for Statistical Applications and Methods
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• v.10 no.1
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• pp.233-237
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• 2003

An asymptotic property of the ordinary least squares estimator of the disturbance variance is considered in the regression model with correlated errors. It is shown that the convergence in probability of S$^2$ is equivalent to the asymptotic unbiasedness. Beyond the assumption on the design matrix or the variance-covariance matrix of disturbances error, the result is quite general and simplify the earlier results.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.29 no.6C
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• pp.857-864
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• 2004

Many image compression standards such as JPEG, MPEG or H.263 are based on the discrete cosine transform (DCT) and quantization method. Quantization error. is the major source of image quality degradation. The current dequantization method assumes the uniform distribution of the DCT coefficients. Therefore the dequantization value is the center of each quantization interval. However DCT coefficients are regarded to follow Laplacian probability density function (pdf). The center value of each interval is not optimal in reducing squared error. We use mean of the quantization interval assuming Laplacian pdf, and show the effect of correction on image quality. Also, we compare existing quantization error to corrected quantization error in closed form. The effect of PSNR improvements due to the compensation to the real image is in the range of 0.2 ∼0.4 ㏈. The maximum correction value is 1.66 ㏈.