鞍点逼近误差的上界--在信息论中的应用
An Upper Bound on the Error Induced by Saddlepoint Approximations -- Applications to Information Theory
摘要：
本文介绍了一个上限之间的绝对差异：（a）累积分布函数（CDF）的总和有限数量的独立和同分布的随机变量与有限的绝对三阶矩;（b）鞍点近似这样的CDF。这个上界，这是特别精确的制度的大偏差，是用来研究的依赖性测试（DT）界和Meta逆（MC）界上的解码错误概率（DEP）在点对点无记忆信道。通常，这些界限不能解析计算，因此下限和上限变得特别有用。在此背景下，主要结果包括，分别新的上限和下限的DT和MC界限。在二进制对称信道、加性高斯白噪声信道和加性对称$α$ -稳定噪声信道的情况下，给出了这些界的数值实验。
英文摘要：
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.
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