Reduced-Complexity Projection-Aggregation List Decoder for Reed-Muller Codes
Bibliographic record
Abstract
Projection-aggregation decoders have been used in conjunction with a list structure to achieve near maximum-likelihood decoding for short-length and low-rate Reed-Muller (RM) codes but suffer from high computational complexity. We reduce the worst-case computational complexity of projection-aggregation (PA) decoders by more than 50% using a scheduling scheme compared to PA decoders without the scheduling scheme, and propose a redesigned syndrome check pattern to avoid repeated syndrome computations in the decoder. A latency model based on the existing hardware architecture is proposed. Input distribution aware (IDA) decoding is adopted as a pre-possessing tool, and the average list size when using IDA decoding is analytically derived under additive white Gaussian noise and uncorrelated normalized Rayleigh fading channels. Using IDA, the average list size is reduced by 30% with less than 0.1 dB loss. The proposed list decoders require a smaller computational complexity than the state-of-the-art iterative decoder, automorphism ensemble decoding with the belief propagation constituent decoder (AED-BP) for decoding RM(7, 3) and RM(8, 3) codes. Based on the developed latency models, the PA list decoder has a smaller latency than the AED-BP and the successive cancellation list decoder to reach near maximum-likelihood decoding performance.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.002 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.000 | 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 teacher head, 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".