Locally Repairable Convolutional Codes with Sliding Window Repair
Bibliographic record
Abstract
Locally repairable convolutional codes (LRCCs) for distributed storage systems (DSSs) are introduced in this work. They enable local repair, for a single node erasure, and sliding-window global repair, which can correct up to djc-1 node erasures in a window of j+1 consecutive blocks of n nodes, where djcis the jth column distance of the code. The parameter j can be adjusted, for a fixed LRCC, according to different catastrophic erasure patterns, requiring only to contact n(j+1)-djc+1 nodes, plus less than μn other nodes, in the storage system, where μ is the memory of the code. A Singleton-type bound is provided for djc. If it attains such a bound, an LRCC can correct the same number of catastrophic erasures in a window of length n(j + 1) as an optimal locally repairable block code of the same rate and locality, and with block length n(j + 1), but being able to perform the flexible and somehow local sliding-window repair by adjusting j. Furthermore, by sliding the window to consider previous or consequent nodes without erasures, or by increasing the window size, the LRCC can potentially correct more erasures in the original window of n(j + 1) nodes than the optimal locally repairable block code. Finally, an explicit construction of LRCCs whose column distances attain the provided Singleton-type bound, up to certain parameter j = L, is obtained based on known maximum sum-rank distance convolutional codes.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.003 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.004 | 0.001 |
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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".