发表机构
Graduate School of Informatics, Chiba University（千叶大学信息学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文针对有限块长 regime 下埃奇沃思展开的负概率问题，提出 q-变形框架，通过动态缩放 q-对数参数实现三阶偏度的精确吸收，为超可靠通信提供稳健基础。
AI 中文摘要
本文研究有限块长（FBL） regime 下埃奇沃思展开的结构崩溃问题，该 regime 中传统渐近近似在深尾区域会产生非物理的负概率。我们提出一种 q-变形框架，通过用信息密度空间的几何变形替代加性多项式扰动来解决该不一致性。受非线性动力学线性化的启发，我们证明动态缩放 q-对数参数可精确吸收三阶偏度，同时保持全局非负性。我们建立了通用渐近匹配，表明该框架可包含高阶渐近尺度。数值结果证实，所提方法达到了最先进的 Cornish-Fisher 界精度，且无负概率风险。该框架为评估 6G、URLLC 等超可靠通信的运行极限提供了稳健且计算稳定的基础。
英文摘要
This paper addresses the structural breakdown of the Edgeworth expansion in the finite-blocklength (FBL) regime, where conventional asymptotic approximations yield unphysical negative probabilities in the deep-tail region. We propose a $q$-deformed framework that resolves this inconsistency by replacing additive polynomial perturbations with a geometric deformation of the information density space. Motivated by the linearization of nonlinear dynamics, we prove that dynamically scaling the $q$-logarithmic parameter exactly absorbs the third-order skewness while preserving global nonnegativity. We establish a universal asymptotic matching, demonstrating that the framework encapsulates higher-order asymptotic scales. Numerical results confirm that the proposed method matches the state-of-the-art precision of the Cornish-Fisher bound without the risk of negative probabilities. The framework offers a robust and computationally stable foundation for evaluating operational limits in ultra-reliable communications such as 6G and URLLC.
Comments7 pages, 4 figures. Extended version of the paper accepted for ISITA 2026 (the concise version will appear in IEEE Xplore). Updated figures and added discussions
