Soft Decision Decoding of Reed-Solomon Codes Using Sphere Decoding
Bibliographic record
Abstract
A new soft decision decoding method for Reed-Solomon (RS) codes is proposed. This method uses sphere decoding in an effort to reduce the decoding complexity. With sphere decoding, instead of considering all of the possible transmitted codewords to determine the most probable one, we only consider the codewords whose distances from the received signal are smaller than a specific search radius. This results in a considerable reduction in the complexity. For an (N,K) RS code, we consider a set of K most reliable and independent positions of a codeword and for each of these positions, an ordered list of most probable transmitted symbols in decreasing order of probability is determined. We start from the hard-decision decoded codeword and we try to find more probable codewords. The search is started by selecting a tentative solution consisting of the K most reliable code symbols whose distance from the corresponding symbols in the received vector is less than the search radius. The acceptable values for each of these K code symbols are determined based of the ordered set of most probable transmitted symbols which means that for each code symbol, we start from the most probable one. We re-encode these K code symbols. If the resulting codeword is within the search radius, we add it to the list of the candidate transmitted codewords. The ordering that was discussed earlier will help finding the candidate codewords quickly. Our method results in considerable improvement of the performance of RS codes compared to hard decision decoding with a moderate increase in complexity.
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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 | 0.000 | 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 | 0.001 |
| Open science | 0.001 | 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".