{
  "abstract": "Capacity-approaching quantum error correction faces a fundamental tension: the required parity-check matrices need to become increasingly dense, while practical decoding and syndrome extraction favor sparse, bounded-degree structures. Reconciling these competing requirements remains an important open problem in quantum code design. We construct Calderbank-Shor-Steane (CSS) code ensembles that approach the CSS rate over memoryless Pauli channels under maximum-likelihood decoding while retaining sparse, bounded-degree graphical representations. The construction separates parity-check density from graphical complexity: although capacity-approaching components may require dense parity-check matrices, they are represented by sparse concatenated factor graphs. We first study a construction combining low-density parity-check (LDPC) and low-density generator-matrix (LDGM) component codes and numerically analyze the average weight distributions of the resulting codes. Motivated by these results, we introduce a second construction based on concatenated LDPC and LDGM codes and generalized irregular repeat-accumulate (GIRA) codes. We derive bounds on the average weight distribution of the resulting sum ensemble and use the Miller-Burshtein framework to prove simultaneous reliability of the two CSS decoding components. Consequently, the proposed ensemble achieves rates arbitrarily close to the CSS hashing bound under separate bit- and phase-error correction, while maintaining bounded graphical complexity, thus providing a foundation for future iterative decoders and indirect syndrome-extraction architectures.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.02339",
  "author_total": 3,
  "authors": [
    {
      "name": "Gulnihal Mercanoglu"
    },
    {
      "name": "Achilleas Anastasopoulos"
    },
    {
      "name": "S. Sandeep Pradhan"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/bj9wasd9844ct.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.02339",
  "fulltext_url": null,
  "id": "bj9wasd9844ct",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.02339",
  "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"
    ],
    [
      "arxiv",
      "quant-ph"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.02339",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/bj9wasd9844ct.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:20:59Z",
      "native_id": "2611.02339",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.02339"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.IT",
      "subfield": "general"
    },
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Achievability of CSS codes performance limits over Pauli channels under separate ML decoding with bounded graphical complexity",
  "title_text": "Achievability of CSS codes performance limits over Pauli channels under separate ML decoding with bounded graphical complexity",
  "type": "preprint",
  "updated_at": "2026-11-04T15:21:05Z",
  "url": "https://research.draconitic.com/paper/bj9wasd9844ct",
  "venue": "arXiv",
  "versions": []
}