{
  "abstract": "Theory for distribution matchers (DMs) is extended to distributions with memory. The divergence-minimizing DM is shown to select the sequences with the highest target probability, as in the memoryless case. A scaling law for divergence is extended to distributions driven by innovation processes. The theory is applied to parallel additive white Gaussian noise channels. A modified enumerative sphere-shaping (ESS) method with a weighted energy constraint is used in implementations. An illustrative example with three channels shows that joint ESS across channels reduces the rate loss by a large factor compared to product DMs at short blocklengths. The gains are confirmed by simulations with probabilistic amplitude shaping and a 5G-NR low-density parity-check code.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.34779",
  "author_total": 2,
  "authors": [
    {
      "name": "Francesca Diedolo"
    },
    {
      "name": "Gerhard Kramer"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/cnxjva4zxcd4m.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.34779",
  "fulltext_url": null,
  "id": "cnxjva4zxcd4m",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.34779",
  "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": "W7214746783",
  "pdf_url": "https://arxiv.org/pdf/2609.34779",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-28",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/cnxjva4zxcd4m.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:17Z",
      "native_id": "2609.34779",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.34779"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.IT",
      "subfield": "general"
    }
  ],
  "title": "Divergence-Minimizing Distribution Matching for Parallel Channels and Channels with Memory",
  "title_text": "Divergence-Minimizing Distribution Matching for Parallel Channels and Channels with Memory",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:17Z",
  "url": "https://research.draconitic.com/paper/cnxjva4zxcd4m",
  "venue": "arXiv",
  "versions": []
}