发表机构
Eindhoven University of Technology; National University of Singapore（埃因霍温理工大学; 新加坡国立大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文纠正了 Omura 与 Dueck-Körner 强逆指数在所有速率下重合的错误论断，证明在容量以上存在临界速率，两指数在第二阈值前重合、之后严格不同，并给出模加信道与二元擦除信道的闭式结果。
AI 中文摘要
Omura 在容量以上速率下正确解码概率的下界具有球堆积形式的指数。Dueck 和 Körner 通过码本扩展步骤改进了 Omura 的论证，并得到了精确的强逆指数。文献中曾声称这两个指数在所有速率下都重合，但该论证包含一个错误。为解决此问题，我们首先证明在某个阈值速率以上，强逆指数遵循由无穷阶 Rényi 容量决定的单位斜率直线。该阈值速率充当容量以上的临界速率，而无穷阶容量则充当截止速率。然后我们证明这两个指数在第二个阈值速率（位于第一个阈值速率之上）之前重合，并在其之后严格不同。例子包括模加信道，其中不存在间隙；以及二元擦除信道，其中阈值和间隙以闭式形式计算得出。
英文摘要
Omura's lower bound on the probability of correct decoding at rates above capacity has an exponent of sphere packing form. Dueck and Körner refined Omura's argument through a codebook extension step and obtained the exact strong converse exponent. It has been claimed in the literature that the two exponents coincide at all rates, but the argument contains an error. To settle this question, we first show that above a threshold rate, the strong converse exponent follows a straight line of unit slope determined by the Rényi capacity of order infinity. This threshold rate plays the role of a critical rate above capacity, while the order-infinity capacity plays that of a cutoff rate. We then show that the two exponents coincide up to a second threshold rate, which lies above the first, and differ strictly beyond it. Examples include modulo-additive channels, where there is no gap; and the binary erasure channel, where the thresholds and the gap are computed in closed form.
Comments6 pages, 2 figures. To be submitted to ITW 2027
