Matrix reordering for efficient list sphere decoding of polar codes
Bibliographic record
Abstract
The Successive-Cancellation List (SCL) algorithm is one of the best polar code decoding algorithms in terms of trade-offs between complexity and error correction performance. The List-Sphere Decoding (List-SD) algorithm has been recently proposed: it yields a better complexity/performance trade-off than SCL in the decoding of short polar codes, that can be used as component codes for larger polar codes. We exploit the structure of the generator matrix of polar codes to propose a matrix reordering technique which allows to significantly reduce the List-SD complexity without degrading its error correction performance, further improving the aforementioned trade-off. The proposed technique is implemented on hardware and it is shown that at the same Frame Error Rate (FER) and Bit Error Rate (BER), the matrix reordering can reduce the resource requirements of List-SD of up to 73%. Furthermore, FER and BER curves are plotted for case studies, showing that at the same complexity cost, matrix reordering improves the performance of List-SD of up to 0.75 dB at FER=10-2.
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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 | 0.002 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.000 | 0.001 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.003 | 0.002 |
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".