Deterministic Identification Over Fading Channels

TL;DR

This paper investigates deterministic identification over fading Gaussian channels with channel side information, establishing capacity bounds and revealing that capacity is infinite in one scale and zero in another, regardless of noise.

Contribution

It provides the first capacity bounds for deterministic identification over fading channels, highlighting the scale-dependent nature of capacity.

Findings

Capacity scales as $2^{n ext{log}(n)R}$ with block length

DI capacity is infinite in exponential scale

DI capacity is zero in double-exponential scale

Abstract

Deterministic identification (DI) is addressed for Gaussian channels with fast and slow fading, where channel side information is available at the decoder. In particular, it is established that the number of messages scales as $2^{n\log(n)R}$, where $n$ is the block length and $R$ is the coding rate. Lower and upper bounds on the DI capacity are developed in this scale for fast and slow fading. Consequently, the DI capacity is infinite in the exponential scale and zero in the double-exponential scale, regardless of the channel noise.