Optimal Codes for Deterministic Identification over Gaussian Channels: Closing the Capacity Gap

2026-04-13

AI Summary

This work resolves a long-standing gap between the upper and lower bounds on the capacity and rate-reliability tradeoff for deterministic identification (DI) over Gaussian channels. By constructing a novel information-theoretic code that requires no prior knowledge of channel parameters, the authors achieve the previously known DI capacity upper bound, thereby fully closing this theoretical gap. The proposed universal coding scheme establishes that the linear-logarithmic DI capacity of the Gaussian channel equals 1/2 and demonstrates optimal rate-reliability tradeoff across all admissible error decay regimes, thus proving joint optimality in both capacity and reliability.

Technology Category

• Machine Learning: Information Theory
• Reasoning under Uncertainty: Relational Probabilistic Models
• Cognitive Modeling & Cognitive Systems: Neural Spike Coding

Application Category

• Economics, Online Markets and Human Computation: Trust and reliance of crowd workers and data experts on GenAI
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Security and Privacy: Large-scale security measurements

Abstract

Deterministic identification (DI) has emerged as a promising paradigm for large-scale and goal-oriented communication systems. Despite significant progress, a fundamental open problem has remained unresolved: a persistent gap between the best known lower and upper bounds on the DI capacity, as well as on the corresponding rate-reliability tradeoff bounds. In this paper, we finally close this gap for Gaussian channels $\mathcal{G}$ by constructing an optimised code that achieves the known upper bound. This allows us to establish that the linearithmic capacity for deterministic identification is $\dot{C}_{\text{DI}}(\mathcal{G})=\frac{1}{2}$. Furthermore, we analyse the rate-reliability tradeoff and show that the proposed scheme matches the known upper bounds to first order, thereby closing the existing gap in reliability performance for all admissible error decay regimes. Finally, we demonstrate the existence of an optimum universal code, which does not require knowledge of the channel parameters and yet achieves capacity.

Problem

• Deterministic Identification
• Gaussian Channels
• Capacity Gap
• Rate-Reliability Tradeoff

Innovation

• deterministic identification
• Gaussian channels
• capacity gap
• rate-reliability tradeoff
• universal code