Second-Order Identification Capacity of AWGN Channels

TL;DR

This paper determines the second-order randomized identification capacity of AWGN channels, showing it enjoys the same second-order form as transmission capacity while the RID code size scales double-exponentially with blocklength. The authors extend Hayashi's achievability via an auxiliary output distribution and introduce a refined power-shell quantization for the converse, yielding a tight n^{-1/2} dispersion term. Specifically, for δ\to 0, log\log N^{*}(\varepsilon,δ|W^{n})= nC(P)-\sqrt{nV(P)}\,Q^{-1}(\varepsilon)+O(\log n), with C(P)=\frac{1}{2}\log(1+P) and V(P)=\log^{2}e\frac{P(P+2)}{2(P+1)^{2}}. This advances understanding of finite-length RID performance on continuous-input channels and suggests practical implications for ultra-reliable, low-latency identification tasks in wireless networks.

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.

Figures (5)

• Figure 1: Research status of the Randomized Identification Problems.
• Figure 2: Problem formulation of the channel resolvability.
• Figure 3: The dual relation between the identification and the resolvability.
• Figure 4: Intuition behind the quantization method.
• Figure 5: A finer quantization method.

Theorems & Definitions (1)

• proof