Block Erasure Channel and Block z-Channel with Bounded Decoders and Finite Blocklength
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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BibTeX
@misc{han2026block,
title = {{Block Erasure Channel and Block z-Channel with Bounded Decoders and Finite Blocklength}},
author = {Bin Han and Yao Zhu and Rafael F. Schaefer and Wenwen Chen and Giuseppe Caire and Anke Schmeink and H. Vincent Poor and Hans D. Schotten},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.27519},
eprint = {2609.27519},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.27519},
}
RIS
TY - UNPB
TI - Block Erasure Channel and Block z-Channel with Bounded Decoders and Finite Blocklength
AU - Bin Han
AU - Yao Zhu
AU - Rafael F. Schaefer
AU - Wenwen Chen
AU - Giuseppe Caire
AU - Anke Schmeink
AU - H. Vincent Poor
AU - Hans D. Schotten
PY - 2026
DA - 2026/09/23
PB - arXiv
DO - 10.48550/arxiv.2609.27519
UR - https://arxiv.org/abs/2609.27519
AB - 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.
ER -