Private Information Retrieval from Locally Repairable Databases with Colluding Servers
Why this work is in the frame
A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.
Bibliographic record
Abstract
Information-theoretical private information retrieval (PIR) is considered from a coded database with colluding servers. The storage code is a locally repairable code (LRC) with maximal recoverability (MR), and in particular, with optimal global minimum distance, for arbitrary code parameters: Number of local groups g, locality r, local distance δ, dimension k ≤ gr and length n = g(r + δ - 1). Servers are identified bijectively with local groups, and only locally non-redundant information is considered and downloaded from each server, that is, only r nodes (out of r + δ - 1) are considered per server. When the remaining MDS code, after removing all locally redundant nodes, is a linearized Reed-Solomon code, a PIR scheme is provided achieving the (download) rate R = (N - k - rt + 1)/N, where N = gr = n - g(δ - 1) is the length of the restricted MDS code, for any t colluding servers such that k + rt ≤ N. The field size is roughly g <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">r</sup> , polynomial in the number of servers g. Assume an arbitrarily large number of stored files. If N - k - rt = 0, the rate R = 1/N is the highest known and coincides with that of previous PIR schemes that work for any MDS storage code. If N - k - rt > 0, the achieved rate R > 1/N coincides with the best known rate of PIR schemes for MDS storage codes (but which do not work for LRCs or linearized Reed-Solomon storage codes) and is always strictly higher than that of known PIR schemes that work for arbitrary MDS storage codes.
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.007 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it