Galaxy Codes: Advancing Achievability for Deterministic Identification via Gaussian Channels

TL;DR

This paper introduces galaxy codes for deterministic identification over Gaussian channels, significantly improving the achievable bounds and enabling more efficient communication in scenarios where full message decoding is unnecessary.

Contribution

The paper presents a novel construction called galaxy codes, advancing the achievability bounds for deterministic identification capacity in Gaussian channels.

Findings

Achieved an improvement in the achievability bound from 1/4 to 3/8.

Demonstrated that deterministic identification capacity grows superexponentially in Gaussian channels.

Provided a new coding scheme that surpasses previous bounds for deterministic identification.

Abstract

Deterministic identification offers an efficient solution for scenarios where decoding entire messages is unnecessary. It is commonly used in alarm systems and control systems. A key advantage of this approach is that the capacity for deterministic identification in Gaussian channels with power constraints grows superexponentially, unlike Shannon's transmission capacity. This allows for a significantly higher number of messages to be transmitted using this event-driven method. So far, only upper and lower bounds for deterministic identification capacity have been established. Our work introduces a novel construction: galaxy codes for deterministic identification. Using these codes, we demonstrate an improvement in the achievability bound of 1/4 to 3/8, representing a previously unknown advance that opens new possibilities for efficient communication.