{
  "abstract": "We consider the problem of private information retrieval from MDS-coded databases with $T$ colluding servers, $U$ robust servers, and $B$ Byzantine servers, referred to as U-B-MDS-TPIR. In the U-B-MDS-TPIR setting, $M$ files are stored across $N$ servers, and in this paper each file is independently encoded using an $(N,K)$ GRS code. We characterize the capacity among linear, full support-rank U-B-MDS-TPIR schemes as $C=\\frac{N-U-2B}{N-U}(1+\\frac{K+T-1}{N-U-2B}+\\cdots+(\\frac{K+T-1}{N-U-2B})^{M-1})^{-1}$ when $N-U-2B\\ge KT$. When $K=1$ or $T=1$, the same expression gives the capacity without the linearity and full support-rank restrictions. We further extend the construction to the retrieval of $P$ out of $M$ files. For $P \\ge \\frac{M}{2}$, the resulting multi-file scheme achieves capacity when $K=1$ or $T=1$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.37412",
  "author_total": 2,
  "authors": [
    {
      "name": "Rui Sun"
    },
    {
      "name": "Yiwei Zhang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2na5j0g8sd1dq.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.37412",
  "fulltext_url": null,
  "id": "2na5j0g8sd1dq",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.37412",
  "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",
      "1702|Cryptography and Data Security"
    ]
  ],
  "openalex": "W7224091184",
  "pdf_url": "https://arxiv.org/pdf/2610.37412",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-27",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2na5j0g8sd1dq.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:53Z",
      "native_id": "2610.37412",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.37412"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.IT",
      "subfield": "general"
    }
  ],
  "title": "The Capacity of Private Information Retrieval from Coded Storage Systems with Colluding, Robust and Byzantine Servers",
  "title_text": "The Capacity of Private Information Retrieval from Coded Storage Systems with Colluding, Robust and Byzantine Servers",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:53Z",
  "url": "https://research.draconitic.com/paper/2na5j0g8sd1dq",
  "venue": "arXiv",
  "versions": []
}