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鞍点近似法引起的误差的上界——在信息论中的应用

An Upper Bound on the Error Induced by Saddlepoint Approximations-Applications to Information Theory.

作者信息

Anade Dadja, Gorce Jean-Marie, Mary Philippe, Perlaza Samir M

机构信息

Laboratoire CITI, a Joint Laboratory between INRIA, the Université de Lyon and the Institut National de Sciences Appliquées (INSA) de Lyon. 6 Av. des Arts, 69621 Villeurbanne, France.

IETR and the Institut National de Sciences Appliquées (INSA) de Rennes, 20 Avenue des Buttes de Coësmes, CS 70839, 35708 Rennes, France.

出版信息

Entropy (Basel). 2020 Jun 20;22(6):690. doi: 10.3390/e22060690.

DOI:10.3390/e22060690
PMID:33286462
原文链接:https://pmc.ncbi.nlm.nih.gov/articles/PMC7517223/
Abstract

This paper introduces an upper bound on the absolute difference between: ( a ) the cumulative distribution function (CDF) of the sum of a finite number of independent and identically distributed random variables with finite absolute third moment; and ( b ) a saddlepoint approximation of such CDF. This upper bound, which is particularly precise in the regime of large deviations, is used to study the dependence testing (DT) bound and the meta converse (MC) bound on the decoding error probability (DEP) in point-to-point memoryless channels. Often, these bounds cannot be analytically calculated and thus lower and upper bounds become particularly useful. Within this context, the main results include, respectively, new upper and lower bounds on the DT and MC bounds. A numerical experimentation of these bounds is presented in the case of the binary symmetric channel, the additive white Gaussian noise channel, and the additive symmetric α -stable noise channel.

摘要

本文介绍了以下两者之间绝对差的一个上界

(a) 具有有限绝对三阶矩的有限个独立同分布随机变量之和的累积分布函数(CDF)；以及(b) 此类CDF的鞍点近似。这个上界在大偏差情况下特别精确，用于研究点对点无记忆信道中解码错误概率(DEP)的相关性检验(DT)界和元逆(MC)界。通常，这些界无法通过解析计算得出，因此上下界变得尤为有用。在此背景下，主要结果分别包括DT界和MC界的新上界和下界。针对二元对称信道、加性高斯白噪声信道和加性对称α稳定噪声信道的情况，给出了这些界的数值实验。

https://cdn.ncbi.nlm.nih.gov/pmc/blobs/6476/7517223/9dd00e05fa51/entropy-22-00690-g005.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/6476/7517223/edc0ff99987b/entropy-22-00690-g001.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/6476/7517223/a68cc1548b52/entropy-22-00690-g002.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/6476/7517223/fe95aecb05e0/entropy-22-00690-g003.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/6476/7517223/e5bc685f2a52/entropy-22-00690-g004.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/6476/7517223/9dd00e05fa51/entropy-22-00690-g005.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/6476/7517223/edc0ff99987b/entropy-22-00690-g001.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/6476/7517223/a68cc1548b52/entropy-22-00690-g002.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/6476/7517223/fe95aecb05e0/entropy-22-00690-g003.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/6476/7517223/e5bc685f2a52/entropy-22-00690-g004.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/6476/7517223/9dd00e05fa51/entropy-22-00690-g005.jpg

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