Second-Order Identification Capacity of AWGN Channels

TL;DR

This paper determines the second-order randomized identification capacity of AWGN channels, revealing it has the same form as transmission capacity but with a double exponential message scale.

Contribution

It extends the understanding of identification capacity by establishing the second-order capacity for AWGN channels with refined bounds and novel quantization methods.

Findings

Second-order RID capacity matches the form of transmission capacity.

Maximum messages in RID scale double exponentially with blocklength.

Refined achievability and converse proofs for 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.