{
  "abstract": "We study the design of linear time-invariant (LTI) encoder-decoder pairs for transmitting the state of a discrete-time LTI vector source over power-constrained parallel Gaussian channels with feedback. Two types of power constraints are considered. Under individual subchannel power constraints, a necessary and sufficient condition for designing an encoder-decoder pair that achieves bounded estimation error covariance (EEC) is established via two coupled majorization inequalities involving the subchannel signal-to-noise ratios and the antistable poles of the source. Under total channel power constraint, we derive the minimum total power required for a feasible encoder-decoder design by exploiting partial-order progamming under majorization order. An analytical optimal power allocation is obtained for the case of equal noise variances, which admits a water-filling interpretation; for general noise case, a sequential water-filling algorithm is developed. Our results reveal that the difficulty of transmitting a discrete-time LTI source via LTI coding is governed not only by its topological entropy, but also by the evenness of the log-magnitudes of its antistable poles. The design methods for feasible encoder-decoder pairs are also provided.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.29511",
  "author_total": 4,
  "authors": [
    {
      "name": "Shihao Jin"
    },
    {
      "name": "Junhui Li"
    },
    {
      "name": "Shinji Hara"
    },
    {
      "name": "Wei Chen"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5x8q8h5v4ywk7.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.29511",
  "fulltext_url": null,
  "id": "5x8q8h5v4ywk7",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.29511",
  "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",
      "cs.SY"
    ],
    [
      "arxiv",
      "eess.SY"
    ],
    [
      "arxiv",
      "math.IT"
    ],
    [
      "arxiv",
      "math.OC"
    ],
    [
      "openalex",
      "2207|Stability and Control of Uncertain Systems"
    ]
  ],
  "openalex": "W7204887255",
  "pdf_url": "https://arxiv.org/pdf/2608.29511",
  "pmcid": null,
  "pmid": null,
  "published": "2026-08-30",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5x8q8h5v4ywk7.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:48Z",
      "native_id": "2608.29511",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.29511"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "Linear Coding of LTI Sources Over Vector Gaussian Channels: A Majorization Approach",
  "title_text": "Linear Coding of LTI Sources Over Vector Gaussian Channels: A Majorization Approach",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:48Z",
  "url": "https://research.draconitic.com/paper/5x8q8h5v4ywk7",
  "venue": "arXiv",
  "versions": []
}