{
  "abstract": "Soft-input detection over a discrete constellation \\(\\mathcal{M}\\) of cardinality \\(M\\) requires computing a posterior whose mean and mode are respectively given by the minimum mean square error (MMSE) and maximum a posteriori (MAP) estimates, both of which incur a computational cost of order \\(\\mathcal{O}(M)\\) per symbol. We show that this cost is reduced to \\(\\mathcal{O}(L)\\), where \\(L \\le M\\) is the number of distinct amplitudes (rings), once the discrete prior is replaced by its maximum-entropy counterpart subject to the same radial marginal. This orbital prior, which is a mixture of uniform circular shells, is obtained by maximizing a mixed discrete-continuous entropy. We prove in this paper that such a distribution is the only distribution on \\(\\mathbb{C}\\) that preserves the amplitude statistics of \\(\\mathcal{M}\\) exactly while remaining maximally noncommittal in phase. Under the additive white Gaussian noise (AWGN) channel, the orbital prior induces a closed-form posterior that factors into a softmax over the \\(L\\) rings and a von Mises phase distribution whose concentration is supplied entirely by the observation, yielding closed-form orbital MMSE and MAP detectors of the discrete symbol at \\(\\mathcal{O}(L)\\) cost. The resulting hierarchical rule selects the ring by posterior mass and the phase by conditional mode. We compare the pairwise ring boundary with that of the joint posterior-density and quantify the leading-order outward shift at high signal-to-noise ratio (SNR). Numerical results using standard constellations confirm that the orbital detectors maintain similar symbol error rate (SER) performance to optimal detectors, at a fraction of the complexity.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.21466",
  "author_total": 3,
  "authors": [
    {
      "name": "Kuranage Roche Rayan Ranasinghe"
    },
    {
      "name": "Takumi Takahashi"
    },
    {
      "name": "Giuseppe Thadeu Freitas de Abreu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5hr5b4f8b1emt.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.21466",
  "fulltext_url": null,
  "id": "5hr5b4f8b1emt",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.21466",
  "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",
      "2208|Advanced Wireless Communication Techniques"
    ]
  ],
  "openalex": "W7213927645",
  "pdf_url": "https://arxiv.org/pdf/2609.21466",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-18",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5hr5b4f8b1emt.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:07Z",
      "native_id": "2609.21466",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.21466"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.IT",
      "subfield": "general"
    }
  ],
  "title": "Orbital Detection: On Maximum-Entropy Priors",
  "title_text": "Orbital Detection: On Maximum-Entropy Priors",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:07Z",
  "url": "https://research.draconitic.com/paper/5hr5b4f8b1emt",
  "venue": "arXiv",
  "versions": []
}