• Title/Summary/Keyword: density approximation

Search Result 285, Processing Time 0.028 seconds

Convergence of Min-Sum Decoding of LDPC codes under a Gaussian Approximation (MIN-SUM 복호화 알고리즘을 이용한 LDPC 오류정정부호의 성능분석)

  • Heo, Jun
    • The Journal of Korean Institute of Communications and Information Sciences
    • /
    • v.28 no.10C
    • /
    • pp.936-941
    • /
    • 2003
  • Density evolution was developed as a method for computing the capacity of low-density parity-check(LDPC) codes under the sum-product algorithm [1]. Based on the assumption that the passed messages on the belief propagation model can be approximated well by Gaussian random variables, a modified and simplified version of density evolution technique was introduced in [2]. Recently, the min-sum algorithm was applied to the density evolution of LDPC codes as an alternative decoding algorithm in [3]. Next question is how the min-sum algorithm is combined with a Gaussian approximation. In this paper, the capacity of various rate LDPC codes is obtained using the min-sum algorithm combined with the Gaussian approximation, which gives a simplest way of LDPC code analysis. Unlike the sum-product algorithm, the symmetry condition [4] is not maintained in the min-sum algorithm. Therefore, the variance as well as the mean of Gaussian distribution are recursively computed in this analysis. It is also shown that the min-sum threshold under a gaussian approximation is well matched to the simulation results.

A Comparison on the Differential Entropy

  • Kim, Dae-Hak
    • Journal of the Korean Data and Information Science Society
    • /
    • v.16 no.3
    • /
    • pp.705-712
    • /
    • 2005
  • Entropy is the basic concept of information theory. It is well defined for random varibles with known probability density function(pdf). For given data with unknown pdf, entropy should be estimated. Usually, estimation of entropy is based on the approximations. In this paper, we consider a kernel based approximation and compare it to the cumulant approximation method for several distributions. Monte carlo simulation for various sample size is conducted.

  • PDF

Asymptotic Approximation of Kernel-Type Estimators with Its Application

  • 장유선;김성래;김성균
    • Proceedings of the Korean Society of Computational and Applied Mathematics Conference
    • /
    • 2003.09a
    • /
    • pp.12.1-12
    • /
    • 2003
  • Sufficient conditions are given under which a generalized class of kernel-type estimators allows asymptotic approximation On the modulus of continuity This generalized class includes sample distribution function, kernel-type estimator of density function, and an estimator that may apply to the censored case. In addition, an application is given to asymptotic normality of recursive density estimators of density function at an unknown point.

  • PDF

Krawtchouk Polynomial Approximation for Binomial Convolutions

  • Ha, Hyung-Tae
    • Kyungpook Mathematical Journal
    • /
    • v.57 no.3
    • /
    • pp.493-502
    • /
    • 2017
  • We propose an accurate approximation method via discrete Krawtchouk orthogonal polynomials to the distribution of a sum of independent but non-identically distributed binomial random variables. This approximation is a weighted binomial distribution with no need for continuity correction unlike commonly used density approximation methods such as saddlepoint, Gram-Charlier A type(GC), and Gaussian approximation methods. The accuracy obtained from the proposed approximation is compared with saddlepoint approximations applied by Eisinga et al. [4], which are the most accurate method among higher order asymptotic approximation methods. The numerical results show that the proposed approximation in general provide more accurate estimates over the entire range for the target probability mass function including the right-tail probabilities. In addition, the method is mathematically tractable and computationally easy to program.

Numerical Comparisons for the Null Distribution of the Bagai Statistic

  • Ha, Hyung-Tae
    • Communications for Statistical Applications and Methods
    • /
    • v.19 no.2
    • /
    • pp.267-276
    • /
    • 2012
  • Bagai et al. (1989) proposed a distribution-free test for stochastic ordering in the competing risk model, and recently Murakami (2009) utilized a standard saddlepoint approximation to provide tail probabilities for the Bagai statistic under finite sample sizes. In the present paper, we consider the Gaussian-polynomial approximation proposed in Ha and Provost (2007) and compare it to the saddlepoint approximation in terms of approximating the percentiles of the Bagai statistic. We make numerical comparisons of these approximations for moderate sample sizes as was done in Murakami (2009). From the numerical results, it was observed that the Gaussianpolynomial approximation provides comparable or greater accuracy in the tail probabilities than the saddlepoint approximation. Unlike saddlepoint approximation, the Gaussian-polynomial approximation provides a simple explicit representation of the approximated density function. We also discuss the details of computations.

Construction of Optimal Concatenated Zigzag Codes Using Density Evolution with a Gaussian Approximation

  • Hong Song-Nam;Shin Dong-Joon
    • The Journal of Korean Institute of Communications and Information Sciences
    • /
    • v.31 no.9C
    • /
    • pp.825-830
    • /
    • 2006
  • Capacity-approaching codes using iterative decoding have been the main subject of research activities during past decade. Especially, LDPC codes show the best asymptotic performance and density evolution has been used as a powerful technique to analyze and design good LDPC codes. In this paper, we apply density evolution with a Gaussian approximation to the concatenated zigzag (CZZ) codes by considering both flooding and two-way schedulings. Based on this density evolution analysis, the threshold values are computed for various CZZ codes and the optimal structure of CZZ codes for various code rates are obtained. Also, simulation results are provided to conform the analytical results.

Use of Beta-Polynomial Approximations for Variance Homogeneity Test and a Mixture of Beta Variates

  • Ha, Hyung-Tae;Kim, Chung-Ah
    • Communications for Statistical Applications and Methods
    • /
    • v.16 no.2
    • /
    • pp.389-396
    • /
    • 2009
  • Approximations for the null distribution of a test statistic arising in multivariate analysis to test homogeneity of variances and a mixture of two beta distributions by making use of a product of beta baseline density function and a polynomial adjustment, so called beta-polynomial density approximant, are discussed. Explicit representations of density and distribution approximants of interest in each case can easily be obtained. Beta-polynomial density approximants produce good approximation over the entire range of the test statistic and also accommodate even the bimodal distribution using an artificial example of a mixture of two beta distributions.

2차원 층상 물질인 GaS, GaSe의 Van der Waals 상호작용에 대한 제일원리연구

  • Cha, Seon-Gyeong;An, Da-Bin
    • Proceeding of EDISON Challenge
    • /
    • 2015.03a
    • /
    • pp.400-404
    • /
    • 2015
  • 2차원 물질인 metal mono chalcogenides(MMC) 중 GaS와 GaSe를 대상으로 하여 층과 층 사이의 van der Waals(vdW) 상호작용을 density functional theory(DFT) 계산을 이용해 연구하였다. Local density approximation(LDA)와 generalized gradient approximation (GGA)의 두 가지 다른 exchange correlation functional을 이용하고, 또한 두 개의 층 사이에 작용하는 van der Waals 상호작용을 고려한 LDA-D2, GGA-D2 계산을 수행하였다. 이와 같은 네 가지 방법으로 층간거리를 바꾸어 binding energy curve를 계산하였다. 그 결과 GGA-D2계산이 MMC의 층간 상호 작용을 가장 잘 기술하였다.

  • PDF

The analysis of dependence on the gas number density in $SF_{6}$-Ar mixtures ($SF_{6}$-Ar혼합가스에서의 압력 의존도 해석)

  • 전병훈;하성철
    • Proceedings of the Korean Institute of Electrical and Electronic Material Engineers Conference
    • /
    • 2002.07a
    • /
    • pp.248-251
    • /
    • 2002
  • We measured the electron drift velocity, W, in 0.5% $SF_{6}$-Ar mixture over the E/N range from 30 Td to 300 Td and gas pressure range from 0.1 to 8 Torr by the double shutter drift tube with a variable drift distance. This coefficient in the mixture was calculated over the same E/N and gas pressure range by using the two-term approximation of the Boltzmann equation. And the measured and calculated values at different gas number density at each E/N was appreciable dependence in the results on the gas number density,

  • PDF

Differential non-linearity correction for successive approximation ADC

  • Yamada, Hikaru
    • 제어로봇시스템학회:학술대회논문집
    • /
    • 1987.10a
    • /
    • pp.847-850
    • /
    • 1987
  • In this paper a new method to correct the differential non-linearity(D NL) error for a successive approximation is proposed. The DNL of ADC is very important characteristic in the field of radiation pulse height analysis or measurement of probability density function. The results of computer simulations are shown to demonstrate the feasibility of the proposed correction method.

  • PDF