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Exact Dynamic Range--Robustness Tradeoff for Chinese Remainder Theorem under Non-Uniformly Bounded Remainder Errors — arXiv:2609.22615

Source: arXiv (en)
Original: https://arxiv.org/abs/2609.22615
License (as archived): CC0-1.0
Archived: 2026-10-10T00:58:03.763Z
SHA-256 of the archived text: 9ed589f588ba42ca70697787af4d0484cfe4fda4adbea6795942285399fe8d3e
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How to cite

Exact Dynamic Range--Robustness Tradeoff for Chinese Remainder Theorem under Non-Uniformly Bounded Remainder Errors — arXiv:2609.22615 — arXiv (en), https://arxiv.org/abs/2609.22615 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_44f74e804eca (Metraipolis archive dc_44f74e804eca, sha256 9ed589f588ba42ca70697787af4d0484cfe4fda4adbea6795942285399fe8d3e)

BibTeX

@misc{dc44f74e804eca,
  title = {Exact Dynamic Range--Robustness Tradeoff for Chinese Remainder Theorem under Non-Uniformly Bounded Remainder Errors — arXiv:2609.22615},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2609.22615},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_44f74e804eca; sha256 9ed589f588ba42ca70697787af4d0484cfe4fda4adbea6795942285399fe8d3e},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2609.22615. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

The Chinese remainder theorem (CRT) is highly sensitive to remainder errors. Robust CRT addresses this problem by recovering the folding integers correctly from erroneous remainders, so that the final reconstruction error is bounded by the remainder error level. The existing dynamic range--robustness tradeoff results mainly assume a uniform remainder error bound, where all remainders share one scalar error bound. This paper studies the exact tradeoff when the remainder error bound is a vector in the sense that different remainders may have different error bounds. For any fixed candidate range length, which specifies the integer interval over which an unknown integer is to be determined from its erroneous remainders, and any fixed remainder error bound vector, we derive a scalar necessary and sufficient condition for robust determination. Based on this condition, we characterize the largest admissible range length, called the dynamic range, for a given remainder error bound vector. Conversely, for a given range length, we characterize all remainder error bound vectors under which remainder errors can be tolerated. We also give an exact folding integer vector decoding algorithm. We show that the proposed results reduce to the classical CRT in the error-free case and coincide with the known result when all remainder error bounds are equal. Numerical results show that the dynamic range depends on the full remainder error bound vector. They also show that the remainders are coupled in the robustness, which cannot be captured by a single uniform error bound.

Tema degli esploratori: statistica e scienza dei dati (retro-catalogo arXiv: annunci del 2026-09-22 in eess.SP).
Categorie arXiv: Signal Processing (eess.SP).
Pagina del lavoro: https://arxiv.org/abs/2609.22615 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-10-09T23:57:50.921Z dalla pagina https://arxiv.org/catchup/eess.SP/2026-09-22?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).