We establish non-asymptotic lower and upper bounds for the identification capacity of discrete-time Gaussian channels subject to inter-symbol interference (ISI), a canonical model in wireless communication. Our analysis accounts for deterministic encoders under peak power constraint. A principal finding is that, even when the number of ISI taps scales sub-linearly with the codeword length, \(n\), i.e., \(\sim n^κ\) with \(κ\in [0,1/2),\) the number of messages that can be reliably identified grows super-exponentially in \(n\), i.e., \(\sim 2^{(n \log n)R}\), where \(R\) denotes the coding rate.

翻译：本文针对无线通信中的经典模型——受符号间干扰影响的离散时间高斯信道，建立了其识别容量的非渐近上下界。我们的分析考虑了峰值功率约束下的确定性编码器。一个主要发现是，即使当符号间干扰抽头数量随码字长度 \(n\) 呈亚线性增长，即 \(\sim n^κ\)，其中 \(κ\in [0,1/2)\)，能够被可靠识别的消息数量仍能以超指数方式增长，即 \(\sim 2^{(n \log n)R}\)，其中 \(R\) 表示编码速率。