Second-Order Identification Capacity of AWGN Channels

Abstract

In this paper, we establish the second-order randomized identification capacity (RID capacity) of the Additive White Gaussian Noise Channel (AWGNC). On the one hand, we obtain a refined version of Hayashi's theorem to prove the achievability part. On the other, we investigate the relationship between identification and channel resolvability, then we propose a finer quantization method to prove the converse part. Consequently, the second-order RID capacity of the AWGNC has the same form as the second-order transmission capacity. The only difference is that the maximum number of messages in RID scales double exponentially in the blocklength.

7 pages, 3 figures, 1 table. This paper has been accepted by IEEE ISIT 2024. In response to the reviewer's feedback, we have incorporated additional references and refined the content in the introduction section and we replace some figures as the pdf form