Efficient soft decoding of Reed–Solomon codes based on sphere decoding
Bibliographic record
Abstract
A novel soft-decision decoding method motivated by the idea of sphere decoding is proposed for Reed–Solomon (RS) codes. Sphere decoding reduces the complexity of finding the closest lattice point to a given point by confining the search to points that fall inside a sphere around the given point. In the authors’ proposed scheme, in order to reduce the search even further, the search effort is concentrated on the most probable lattice points. To do so, they first find the most reliable positions of the codeword. Then a sphere decoder is used to select symbol values for these positions. The proposed sphere decoder chooses the acceptable symbol values for each position from a pre-determined ordered set of most probable transmitted symbols. Each time the most reliable code symbols are selected, they are used to find the rest of RS symbols. If the resulting codeword is within the search radius, it is saved as a candidate transmitted codeword. The ordering used in the algorithm helps finding the candidate codewords quickly resulting in an efficient decoding method. Simulation results indicate considerable coding gains over hard decision decoding with a feasible complexity. The performance is also superior to the soft decision Koetter–Vardy method.
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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 | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.003 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| 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".