{
  "abstract": "Function-correcting codes (FCCs) protect specified function evaluations of messages against errors while reducing the redundancy required for reliable communication. We study FCCs for symbol-pair read channels, motivated by high-density storage systems that read overlapping symbol pairs. Phase-shift keying (PSK) modulation is well-suited to such systems due to its bandwidth efficiency and noise robustness. While FCCs for symbol-pair read channels have been studied under the Hamming metric, the Lee metric is a more appropriate error model for $q$-ary PSK and, hence for $q$-ary symbol-pair read channels. We generalize the symbol-pair Lee distance, previously defined only over $\\mathbb{Z}_4$, to $\\mathbb{Z}_q$, $q\\ge2$, and introduce function-correcting symbol-pair Lee-distance codes (FCSPLCs) over $\\mathbb{Z}_q$, specializing to $q=2^m$, $m\\ge1$, for $2^m$-ary PSK constellations. We investigate their redundancy requirements by introducing irregular-pair Lee-distance codes and relating the optimal redundancy of FCSPLCs to the shortest length of such codes. We derive Plotkin-type and Gilbert--Varshamov-type bounds on the optimal redundancy through lower and upper bounds on the shortest length of irregular-pair Lee-distance codes. For bijective functions, we obtain corresponding Plotkin-type and Gilbert--Varshamov-type bounds for classical Lee metric codes for symbol-pair read channels over $\\mathbb{Z}_q$, which, to the best of our knowledge, are the first such bounds for the Lee metric symbol-pair setting. We then specialize the FCSPLC framework to pair-locally bounded functions, the Pair-Lee weight function, and the Pair-Lee weight distribution function, giving explicit constructions and corresponding bounds on the optimal redundancy. Finally, for linear functions, we derive a Plotkin-type lower bound on the optimal redundancy.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.09491",
  "author_total": 2,
  "authors": [
    {
      "name": "Hareesh K."
    },
    {
      "name": "B. Sundar Rajan"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/e56540vab120f.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.09491",
  "fulltext_url": null,
  "id": "e56540vab120f",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.09491",
  "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|Coding theory and cryptography"
    ]
  ],
  "openalex": "W7220894373",
  "pdf_url": "https://arxiv.org/pdf/2610.09491",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-07",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/e56540vab120f.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:42Z",
      "native_id": "2610.09491",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.09491"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.IT",
      "subfield": "general"
    }
  ],
  "title": "Function-Correcting Lee-distance Codes for Symbol-Pair Read Channels",
  "title_text": "Function-Correcting Lee-distance Codes for Symbol-Pair Read Channels",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:42Z",
  "url": "https://research.draconitic.com/paper/e56540vab120f",
  "venue": "arXiv",
  "versions": []
}