{
  "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.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.27519",
  "author_total": 8,
  "authors": [
    {
      "name": "Bin Han"
    },
    {
      "name": "Yao Zhu"
    },
    {
      "name": "Rafael F. Schaefer"
    },
    {
      "name": "Wenwen Chen"
    },
    {
      "name": "Giuseppe Caire"
    },
    {
      "name": "Anke Schmeink"
    },
    {
      "name": "H. Vincent Poor"
    },
    {
      "name": "Hans D. Schotten"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2g8xz04z70cn4.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.27519",
  "fulltext_url": null,
  "id": "2g8xz04z70cn4",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.27519",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.IT"
    ],
    [
      "arxiv",
      "math.IT"
    ],
    [
      "openalex",
      "1705|Error Correcting Code Techniques"
    ]
  ],
  "openalex": "W7214181651",
  "pdf_url": "https://arxiv.org/pdf/2609.27519",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-23",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2g8xz04z70cn4.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:00Z",
      "native_id": "2609.27519",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.27519"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.IT",
      "subfield": "general"
    }
  ],
  "title": "Block Erasure Channel and Block z-Channel with Bounded Decoders and Finite Blocklength",
  "title_text": "Block Erasure Channel and Block z-Channel with Bounded Decoders and Finite Blocklength",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:00Z",
  "url": "https://research.draconitic.com/paper/2g8xz04z70cn4",
  "venue": "arXiv",
  "versions": []
}