{
  "abstract": "LZ77 coders spend the same number of bits on the distance of every match, although short matches rarely pay off at long distances. With match-length-dependent windows, used in several practical codecs, a match of length $\\ell$ may refer back at most $W(\\ell)$ symbols: short matches get short distance fields, while long matches keep the full window $W$. This breaks the suffix closure that classical LZ77 analyses rely on: the tail of an admissible match need not be admissible. We bound the cost of this loss, and of matches missed by a practical hash search, by the phrase count of a single-window reference parse. Consequently, when the full window starts at length $O(\\log W)$, greedy parsing keeps the convergence rates and the optimal finite-input rates of LZ77 under substring-complexity constraints, and when it starts at length $o(\\log W)$, greedy parsing is universal for stationary ergodic sources. We then delimit what the windows gain. A calibrated schedule never increases the minimum code length and saves a polynomially small rate on some iid sources. The leading redundancy term is set by the length code instead: on uniform iid data, with logarithmic-cost lengths and a fixed full-window threshold, it is at least of order $(\\log\\log W)/\\log W$ whatever windows the short matches use, and a short codeword for a growing longest match reduces it to $O((\\log\\log\\log W)/\\log W)$. We also quantify the gains of coding single-symbol runs by count and of Huffman coding the token fields, and obtain a consistent entropy-rate estimator by selecting the window.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.06530",
  "author_total": 2,
  "authors": [
    {
      "name": "Yingquan"
    },
    {
      "name": "Wu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3r143yy54ybth.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.06530",
  "fulltext_url": null,
  "id": "3r143yy54ybth",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.06530",
  "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|Algorithms and Data Compression"
    ]
  ],
  "openalex": "W7220674067",
  "pdf_url": "https://arxiv.org/pdf/2610.06530",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-22",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3r143yy54ybth.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:19Z",
      "native_id": "2610.06530",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.06530"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.IT",
      "subfield": "general"
    }
  ],
  "title": "Lempel-Ziv Parsing with Match-Length-Dependent Windows: Universality and Limits",
  "title_text": "Lempel-Ziv Parsing with Match-Length-Dependent Windows: Universality and Limits",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:19Z",
  "url": "https://research.draconitic.com/paper/3r143yy54ybth",
  "venue": "arXiv",
  "versions": []
}