Automorphism Ensemble Decoding of Polar Codes with Reduced Number of Routes
Bibliographic record
Abstract
Automorphism ensemble decoding (AED) with the successive cancellation (SC) constituent decoder (AED-SC) can achieve similar decoding performance to the successive cancellation list (SCL) decoder when decoding short-to-medium-length polar codes. However, implementing automorphisms requires additional hardware for routing, leading to significant area overhead, especially with a large number of automorphisms. We propose methods for selecting automorphisms in SC decoders to reduce routing overhead. We establish the equivalence between automorphism selection and the NP-hard minimum K-union (MKU) problem. To maintain decoding performance under the selected automorphisms, we formulate the equivalence class property of AED-SC as a quadratic constraint. Compared to the state-of-the-art, our method achieves up to a 2.9× reduction in the number of routes needed to implement all automorphisms.
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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 | 0.000 | 0.003 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.000 | 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".