Collaborative algebraic decoding of interleaved Reed–Solomon codes
Bibliographic record
Abstract
ABSTRACT We derive and analyse an algorithm for collaborative decoding of heterogeneous interleaved Reed–Solomon (IRS) codes. They are generated by interleaving several codewords from different Reed–Solomon codes with the same length over the same Galois field. The basis of the decoding algorithm is similar to the Guruswami–Sudan (GS) decoding method. However, here multivariate interpolation is used to decode all the codewords of the interleaved scheme simultaneously. In the presence of burst errors, we show that the error‐correction capability of this algorithm is larger than that of independent decoding of each codeword using the standard GS method. In the latter case, the error‐correction capability is equal to the decoding radius of the GS algorithm for the Reed–Solomon code with the largest dimension. Also, concatenated codes using IRS codes as their outer codes and binary linear block codes as their inner codes are considered. Assuming maximum likelihood decoding of the inner code, we derive upper and lower bounds for the word error probability of concatenated codes over additive white Gaussian noise channel with binary phase‐shift keying modulation for both cases of independent and collaborative decoding of the outer IRS codes. We show that collaborative decoding provides considerable coding gain compared with independent decoding. Copyright © 2011 John Wiley & Sons, Ltd.
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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 | 0.002 | 0.009 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.001 | 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".