{
  "abstract": "We develop design methodologies for the rate profile of polarization-adjusted convolutional (PAC) codes tailored to successive cancellation list (SCL) decoding. The crux of our approach is two-fold: first is the creation of a modified density evolution Gaussian approximation (DEGA), called conditional DEGA (CDEGA), to analyze the decoding process in the presence of errors; second is the creation of a dangerous-path occupancy metric to find the conditional occupancy of bit-errors in a finite list. Our approach not only illuminates the role of rate-one precoding, but also provides insight into why certain information sets are particularly well suited to PAC codes. We demonstrate the usefulness of CDEGA and dangerous-path metrics with algorithms that create new information sets, as well as precoders that are extremely sparse yet competitive. In particular, we design codes of length $N \\leq 512$ with various rates and list sizes, all of which offer at least half a dB gain over traditional PAC codes at an FER of $10^{-3}$ and improve upon state-of-the-art results.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.40512",
  "author_total": 3,
  "authors": [
    {
      "name": "Tyler Kann"
    },
    {
      "name": "Shrinivas Kudekar"
    },
    {
      "name": "Matthieu R. Bloch"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2v7zs9xtkygc4.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.40512",
  "fulltext_url": null,
  "id": "2v7zs9xtkygc4",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.40512",
  "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": null,
  "pdf_url": "https://arxiv.org/pdf/2610.40512",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2v7zs9xtkygc4.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:35Z",
      "native_id": "2610.40512",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.40512"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.IT",
      "subfield": "general"
    }
  ],
  "title": "An SCL-Aware Design of PAC Codes",
  "title_text": "An SCL-Aware Design of PAC Codes",
  "type": "preprint",
  "updated_at": "2026-11-01T12:20:53Z",
  "url": "https://research.draconitic.com/paper/2v7zs9xtkygc4",
  "venue": "arXiv",
  "versions": []
}