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arXiv · 2609.27519

Block Erasure Channel and Block z-Channel with Bounded Decoders and Finite Blocklength

Bin Han·Yao Zhu·Rafael F. Schaefer·Wenwen Chen·Giuseppe Caire·Anke Schmeink·H. Vincent Poor·Hans D. Schotten
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Abstract

Block error rate is a standard metric in finite blocklength (FBL) communication, yet it conflates two qualitatively different failure modes: block confusions, where the decoder selects a wrong codeword, and block erasures, where it declares a loss. Higher-layer protocols treat physical-layer failures as erasures, but this cross-layer assumption lacks FBL justification. We derive a rigorous upper bound and a companion lower-side estimate on the block confusion probability (BLCP) and block erasure probability (BLEP) for bounded-distance decoders over additive white Gaussian noise (AWGN) channels at finite blocklength, recasting the coding problem as a geometric sphere packing one. We analyze the sensitivity of these bounds to blocklength and signalto-noise ratio, characterize the envelope of the upper bound, and derive closed-form Chernoff approximations. Extending the model to idle transmission blocks, we bound the false alarm probability (FAP) and show that a block z-channel abstraction emerges from the bounded-decoding geometry. Numerical results confirm that confusion and false alarm probabilities lie far below the error rate constraint, providing quantitative physicallayer support for the block erasure channel and block z-channel abstractions assumed in protocol design.

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Bin Han, Yao Zhu, Rafael F. Schaefer, Wenwen Chen, Giuseppe Caire, Anke Schmeink, H. Vincent Poor, Hans D. Schotten. 2026-09-23. Block Erasure Channel and Block z-Channel with Bounded Decoders and Finite Blocklength. https://arxiv.org/abs/2609.27519

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