Generalized and Extended Subspace Algorithms for Error Correction with Quantized DFT Codes
Bibliographic record
Abstract
Discrete Fourier transform (DFT) codes have been used to provide robustness against errors and erasures in various applications. This paper focuses on improving error localization of the Bose-Chaudhuri-Hocquenghem (BCH) DFT codes. First, we analyze how the subspace-based error localization outperforms the coding-theoretic one. Then, we propose an extension of the subspace-based error localization, based on additional syndrome, that improves the existing one and is naturally suitable for rate-adaptive distributed source coding (DSC). Further, we propose a new generic subspace-based algorithm to decode BCH-DFT codes. The proposed approach generalizes the encoding and decoding of this important class of DFT codes. It introduces many different decoding matrices for a DFT code; this diversity is then used to diminish the effect of the quantization noise and thus to improve the decoding. Finally, the extended and generalized approaches are combined to maximize the decoding gain. Simulation results demonstrate the capability of the proposed algorithms to perform significantly better than the existing subspace-based error localization, in the presence of quantization noise.
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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 | 0.004 |
| 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 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 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 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".