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Decoding Failure Biases IBLT Count Measurements: A Gaussian-Selection Law at the Peeling Threshold — arXiv:2610.21418

Source: arXiv (en)
Original: https://arxiv.org/abs/2610.21418
License (as archived): CC0-1.0
Archived: 2026-10-16T10:34:52.738Z
SHA-256 of the archived text: 93a5d002877928429801d243213a40f6a16bcae5cd11f0c816cd5ddb1a53628d
Stable URL of this page: https://metraipolis.com/documento/dc_320cebec4498

How to cite

Decoding Failure Biases IBLT Count Measurements: A Gaussian-Selection Law at the Peeling Threshold — arXiv:2610.21418 — arXiv (en), https://arxiv.org/abs/2610.21418 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_320cebec4498 (Metraipolis archive dc_320cebec4498, sha256 93a5d002877928429801d243213a40f6a16bcae5cd11f0c816cd5ddb1a53628d)

BibTeX

@misc{dc320cebec4498,
  title = {Decoding Failure Biases IBLT Count Measurements: A Gaussian-Selection Law at the Peeling Threshold — arXiv:2610.21418},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2610.21418},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_320cebec4498; sha256 93a5d002877928429801d243213a40f6a16bcae5cd11f0c816cd5ddb1a53628d},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2610.21418. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

In a self-sizing set-reconciliation protocol, a small first-round Invertible Bloom Lookup Table (IBLT) sketch attempts peeling decoding; after failure, the protocol estimates the difference count $d$ from the count energy and sizes the second round from a lower quantile of the measurement. This quantile must be computed conditionally on failure: the measurement and peeling success are determined by the same random mapping, so conditioning can shift the measurement law. In the ideal peeling model, inside the critical window where failure has nondegenerate probability, the standardized energy and a statistic of the unsigned mapping that governs the peeling outcome (the precritical score) have a joint Gaussian limit with correlation $\eta_k\rho^2$, $\rho$ being the sign imbalance and $\eta_k$ a closed-form constant. The measurement conditional on failure is thus a bivariate normal truncated to a half-plane, which we call the Gaussian-selection law. Since $\eta_k$ changes sign between $k=4$ and $k=5$, under one-sided imbalance the unconditional threshold undercovers exactly when $k\ge5$ and is conservative for $k=3,4$. The key tool is a quenched CLT for a signed quadratic form on a random overlap graph; under asymptotically balanced signs, conditioning on any unsigned mapping event that is permutation-invariant and has probability bounded away from zero leaves the standard normal limit unchanged. After failure the protocol observes the total sign; inverting the selection law yields an upper confidence bound for $d$, asymptotically conservative in the critical window and, when $d/\sqrt M\to\infty$, along the whole load axis. The experiments use analytic constants, none fitted; the unconditional threshold carries a selection error that does not vanish with scale, while the corrected selection-law threshold matches per-configuration empirical quantiles.

Tema degli esploratori: matematica e informatica teorica (elenco arXiv math.IT, nuovi lavori del giorno).
Categorie arXiv: Data Structures and Algorithms (cs.DS) ; Information Theory (cs.IT).
Pagina del lavoro: https://arxiv.org/abs/2610.21418 — 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 2026-10-16T08:51:02.597Z dalla pagina https://arxiv.org/list/math.IT/new (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).