Outer Bound of the Capacity Region for Identification via Multiple Access Channels

TL;DR

This paper establishes that for multiple access channels with the strong converse property, the identification capacity region equals the transmission capacity region, using a new resolvability approach and a novel converse coding method.

Contribution

It introduces a new resolvability problem and a method to convert direct coding theorems into converse theorems for identification over MACs.

Findings

ID capacity equals transmission capacity for MACs with strong converse.

A new lower bound function for error probabilities tends to zero for noisy channels.

Development of a novel method linking resolvability to converse coding theorems.

Abstract

In this paper we consider the identification (ID) via multiple access channels (MACs). In the general MAC the ID capacity region includes the ordinary transmission (TR) capacity region. In this paper we discuss the converse coding theorem. We estimate two types of error probabilities of identification for rates outside capacity region, deriving some function which serves as a lower bound of the sum of two error probabilities of identification. This function has a property that it tends to zero as $n\to \infty$ for noisy channels satisfying the strong converse property. Using this property, we establish that the transmission capacity region is equal to the ID capacity for the MAC satisfying the strong converse property. To derive the result we introduce a new resolvability problem on the output from the MAC. We further develop a new method of converting the direct coding theorem for the above MAC resolvability problem into the converse coding theorem for the ID via MACs.