Reliability-Dependent Scaling Laws of Deterministic Identification over Binary Symmetric Channels

2026-08-04

AI Summary

This study investigates the asymptotic performance of deterministic identification over a binary symmetric channel under vanishing error probability constraints, characterizing how the error decay rate influences achievable identification rates. By introducing a minimal error parameter and leveraging coding constructions, concentration inequalities, total variation distance bounds, and Hamming distance properties, the work systematically analyzes asymptotic behavior across three regimes: large deviations, moderate deviations, and the central limit regime. The main contribution lies in revealing that identification performance is governed by the geometric concentration of channel outputs on Hamming shells, establishing for the first time a reliability-dependent scaling law, and deriving matching achievability and converse bounds. These results significantly deepen the understanding of deterministic identification for discrete-output channels at finite blocklengths.

Abstract

In this paper, we study the asymptotic behavior of deterministic identification (DID) over binary symmetric channels (BSCs) under vanishing error constraints. By introducing a minimum error parameter, we characterize how different error-decay regimes affect the achievable DID rate. General achievability and converse bounds are derived, with explicit asymptotic characterizations in the large-deviation, moderate-deviation, and central-limit regimes. The achievability analysis combines coding-theoretic constructions with probabilistic concentration techniques, while the converse links statistical distinguishability to the minimum-distance structure of DID codes via total variation and Hamming-type bounds. Our results show that the asymptotic behavior of DID over BSCs is governed by a Hamming-shell concentration geometry of channel outputs, offering insights into the finite-blocklength behavior of deterministic identification over discrete-output channels.

Problem

• Deterministic Identification
• Binary Symmetric Channels
• Reliability
• Error Decay
• Asymptotic Behavior

Innovation

• deterministic identification
• binary symmetric channel
• scaling laws
• Hamming-shell concentration
• error-decay regimes