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arXiv · 2608.03282

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

Zhicheng Liu·Liuquan Yao·Guiying Yan·Zhiming Ma·Zechun Hu
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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.

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Zhicheng Liu, Liuquan Yao, Guiying Yan, Zhiming Ma, Zechun Hu. 2026-08-04. Reliability-Dependent Scaling Laws of Deterministic Identification over Binary Symmetric Channels. https://arxiv.org/abs/2608.03282

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