Deterministic Identification Over Poisson Channels

TL;DR

This paper investigates deterministic identification over Poisson channels with power constraints, revealing that the code size grows super-exponentially and the capacity is infinite in the exponential scale, extending previous Gaussian channel results.

Contribution

It establishes the super-exponential scaling of code size and bounds the DI capacity for Poisson channels, demonstrating infinite capacity in the exponential scale regardless of noise.

Findings

Code size scales as 2^{(n log n) R}

DI capacity is infinite in the exponential scale

Results extend Gaussian channel findings to Poisson channels

Abstract

Deterministic identification (DI) for the discrete-time Poisson channel, subject to an average and a peak power constraint, is considered. It is established that the code size scales as $2^{(n\log n)R}$, where $n$ and $R$ are the block length and coding rate, respectively. The authors have recently shown a similar property for Gaussian channels [1]. Lower and upper bounds on the DI capacity of the Poisson channel are developed in this scale. Those imply that the DI capacity is infinite in the exponential scale, regardless of the dark current, i.e., the channel noise parameter.