论文标题
鞍点近似引起的误差的上限 - 信息理论的应用
An Upper Bound on the Error Induced by Saddlepoint Approximations -- Applications to Information Theory
论文作者
论文摘要
本文引入了上限，这是关于：（a）有限数量的独立变量和相同分布的随机变量的累积分布函数（CDF）之间的绝对差异； （b）这种CDF的鞍点近似。该上限在大偏差的状态中特别精确，用于研究依赖性测试（DT）结合，并且在无数无内存通道中绑定在解码误差概率（DEP）上的元逆变（MC）。通常，这些界限不能在分析上计算，因此下限和上限变得特别有用。在这种情况下，主要结果分别包括DT和MC边界上的新上限和下限。这些边界的数值实验在二进制对称通道，加性白色高斯噪声通道和添加剂对称$α$稳定的噪声通道中提出。
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.
