Deterministic identification (DI) has emerged as a promising paradigm for large-scale and goal-oriented communication systems. Despite significant progress, a fundamental open problem has remained unresolved: a persistent gap between the best known lower and upper bounds on the DI capacity, as well as on the corresponding rate-reliability tradeoff bounds. In this paper, we finally close this gap for Gaussian channels $\mathcal{G}$ by constructing an optimised code that achieves the known upper bound. This allows us to establish that the linearithmic capacity for deterministic identification is $\dot{C}_{\text{DI}}(\mathcal{G})=\frac{1}{2}$. Furthermore, we analyse the rate-reliability tradeoff and show that the proposed scheme matches the known upper bounds to first order, thereby closing the existing gap in reliability performance for all admissible error decay regimes. Finally, we demonstrate the existence of an optimum universal code, which does not require knowledge of the channel parameters and yet achieves capacity.

翻译：确定性识别（DI）已成为大规模与目标导向通信系统的一种有前景的范式。尽管取得了显著进展，但仍存在一个基本开放问题：DI容量的已知下界与上界之间，以及相应的速率-可靠性权衡边界之间，始终存在持续差距。本文通过构建达到已知上界的优化编码，最终填补了高斯信道 $\mathcal{G}$ 下的这一缺口。由此我们确定，确定性识别的线性对数容量为 $\dot{C}_{\text{DI}}(\mathcal{G})=\frac{1}{2}$。此外，我们分析了速率-可靠性权衡，并证明所提方案在一阶意义上匹配已知上界，从而在所有可容许的错误衰减 regime 中填补了可靠性性能的现有差距。最后，我们证明了最优通用编码的存在性，该编码无需知晓信道参数即可达到容量。