{
  "abstract": "We develop a theory of universal decoding built on the pairwise error probability (PEP) primitive of a companion paper. The PEP and its error spectrum are defined for an arbitrary decoding metric, and while raw metric values across a family share no common scale, the PEP supplies one. Universal decoding -- decoding well simultaneously against a whole family of metrics or channels -- becomes the problem of merging the per-metric spectra into a single rule, which we construct from a clipped inverse-PEP statistic. The construction rests on a Kraft-type inequality for decoding, valid for any input prior: per output, every metric canonicalizes into a conditional probability assignment on the codewords, and the merge is the normalized-maximum-likelihood envelope of the induced family. We prove the rule is random-coding universal (it loses only a vanishing rate relative to the best metric in the family, against every channel), show it is an asymptotic minimax/equalizer rule, and derandomize it: over a subexponential channel family a single deterministic code inherits the guarantee. For discrete memoryless channels the construction reduces to types and recovers the maximum-mutual-information decoder, its tilted variant for non-uniform memoryless input, and finite-state universal decoders. It extends to decoding with an erasure option (deterministically, uniformly over erasure margins) and, via a discretization of separable metric families, to continuous alphabets: for AWGN with deterministic interference it attains the matched-ML exponent up to an explicit typical-set cap, and for ISI channels the best exponent in a family of equalize-and-decode rules, under explicit assumptions on the equalizers and the channel spectrum and the same cap. Throughout, universality is a corollary of the PEP analysis rather than a separate theory.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.27887",
  "author_total": 2,
  "authors": [
    {
      "name": "Nir Elkayam"
    },
    {
      "name": "Meir Feder"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1khdtf5h1xmwm.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.27887",
  "fulltext_url": null,
  "id": "1khdtf5h1xmwm",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.27887",
  "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": "W7214239502",
  "pdf_url": "https://arxiv.org/pdf/2609.27887",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1khdtf5h1xmwm.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:00Z",
      "native_id": "2609.27887",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.27887"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.IT",
      "subfield": "general"
    }
  ],
  "title": "Universal Decoding via the Pairwise Error Probability",
  "title_text": "Universal Decoding via the Pairwise Error Probability",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:00Z",
  "url": "https://research.draconitic.com/paper/1khdtf5h1xmwm",
  "venue": "arXiv",
  "versions": []
}