AI 中文总结
该研究针对二元对称信道上的确定性识别，引入最小误差参数刻画误差衰减对可实现速率的影响，推导了不同偏差机制下的界，揭示了其渐近行为的几何规律，为有限码长行为提供了见解。
AI 中文摘要
本文研究了在误差约束趋于消失的情况下，二元对称信道（BSCs）上确定性识别（DID）的渐近行为。通过引入最小误差参数，我们刻画了不同的误差衰减机制如何影响可实现的DID速率。推导了通用可达性界和反向界，并给出了大偏差、中偏差和中心极限机制下的显式渐近刻画。可达性分析结合了编码理论构造与概率集中技术，而反向界则通过总变差和汉明型界将统计可区分性与DID码的最小距离结构关联起来。我们的结果表明，BSC上DID的渐近行为由信道输出的汉明壳集中几何所支配，为离散输出信道上确定性识别的有限码长行为提供了见解。
英文摘要
In this paper, we study the asymptotic behavior of deterministic identification (DID) over binary symmetric channels (BSCs) under vanishing error constraints. By introducing a minimum error parameter, we characterize how different error-decay regimes affect the achievable DID rate. General achievability and converse bounds are derived, with explicit asymptotic characterizations in the large-deviation, moderate-deviation, and central-limit regimes. The achievability analysis combines coding-theoretic constructions with probabilistic concentration techniques, while the converse links statistical distinguishability to the minimum-distance structure of DID codes via total variation and Hamming-type bounds. Our results show that the asymptotic behavior of DID over BSCs is governed by a Hamming-shell concentration geometry of channel outputs, offering insights into the finite-blocklength behavior of deterministic identification over discrete-output channels.
CommentsThis work has been accepted by Information Theory Workshop 2026
