Minimax Converse for Identification via Channels

TL;DR

This paper establishes a minimax converse for identification via channels, deriving a general capacity formula that matches transmission capacity without requiring the strong converse, and characterizes the optimal second-order coding rate.

Contribution

It introduces a novel minimax converse approach based on partial channel resolvability, overcoming previous limitations and providing new capacity and rate characterizations.

Findings

Identification capacity equals transmission capacity.

Derived the general formula for identification capacity.

Characterized the optimal second-order coding rate.

Abstract

A minimax converse for the identification via channels is derived. By this converse, a general formula for the identification capacity, which coincides with the transmission capacity, is proved without the assumption of the strong converse property. Furthermore, the optimal second-order coding rate of the identification via channels is characterized when the type I error probability is non-vanishing and the type II error probability is vanishing. Our converse is built upon the so-called partial channel resolvability approach; however, the minimax argument enables us to circumvent a flaw reported in the literature.