标题： 快速衰落高斯信道的秘密容量的算术复杂度表征 显示英文标题

标题： Characterization of the Arithmetic Complexity of the Secrecy Capacity of Fast-Fading Gaussian Channels

摘要： 本文从算法的角度研究了快速衰落窃听信道的保密容量的可计算性，探讨其是否能够以算法方式计算。 为了解决这个问题，采用了图灵机的概念，该概念建立了数字计算机的基本性能限制。 结果表明，某些可计算的连续衰落概率分布函数所对应的保密容量是非可计算数。 此外，我们评估了保密容量在算术谱系中的分类，揭示了不存在可计算的可达性和反向界。 显示英文摘要

摘要： This paper studies the computability of the secrecy capacity of fast-fading wiretap channels from an algorithmic perspective, examining whether it can be computed algorithmically or not. To address this question, the concept of Turing machines is used, which establishes fundamental performance limits of digital computers. It is shown that certain computable continuous fading probability distribution functions yield secrecy capacities that are non-computable numbers. Additionally, we assess the secrecy capacity's classification within the arithmetical hierarchy, revealing the absence of computable achievability and converse bounds.