论文标题
在小型到中度偏差方面的通道编码的三阶分析
Third-order Analysis of Channel Coding in the Small-to-Moderate Deviations Regime
论文作者
论文摘要
本文研究了具有最大功率限制的非主流无内存通道和高斯通道的三阶特征。我们扩展中的三阶项在这里采用了一个新数量，称为通道偏度，随着误差概率降低，它会更明显地影响近似准确性。对于高斯通道，评估香农的1959年随机编码结合和Vazquez-Vilar在中心极限定理（CLT）方向上的2021键键键结合，使通道偏度的精确计算。对于离散的无内存通道，这项工作概括了Moulin的2017年界限，该界限是从CLT制度的非介绍通道的最大可实现消息集大小的渐近扩展，以包括中度偏差（MD）制度，从而完善Altuğ和Wagner的2014年MD结果。示例二进制对称频道和最重要的$（n，ε）$对，包括[100，500] $中的$ n \ in [10^{ - 10}，10^{ - 1}] $，在文献中，在频道偏斜的几个扩展中，频道最准确的近似值是最准确的。还包括在MD制度中二进制假设检验的II型误差指数中的三阶项的推导。由此产生的三阶项与通道偏度相似。
This paper studies the third-order characteristic of nonsingular discrete memoryless channels and the Gaussian channel with a maximal-power constraint. The third-order term in our expansions employs a new quantity here called the channel skewness, which affects the approximation accuracy more significantly as the error probability decreases. For the Gaussian channel, evaluating Shannon's 1959 random coding bound and Vazquez-Vilar's 2021 meta-converse bound in the central limit theorem (CLT) regime enables exact computation of the channel skewness. For discrete memoryless channels, this work generalizes Moulin's 2017 bounds on the asymptotic expansion of the maximum achievable message set size for nonsingular channels from the CLT regime to include the moderate deviations (MD) regime, thereby refining Altuğ and Wagner's 2014 MD result. For an example binary symmetric channel and most practically important $(n, ε)$ pairs, including $n \in [100, 500]$ and $ε\in [10^{-10}, 10^{-1}]$, an approximation up to the channel skewness is the most accurate among several expansions in the literature. A derivation of the third-order term in the type-II error exponent of binary hypothesis testing in the MD regime is also included; the resulting third-order term is similar to the channel skewness.
