Improved finite‐length Luby‐transform codes in the binary erasure channel
Why this work is in the frame
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Bibliographic record
Abstract
Fountain codes were introduced to provide high reliability and scalability and low complexities for networks such as the Internet. Luby‐transform (LT) codes, which are the first realisation of Fountain codes, achieve the capacity of the binary erasure channel (BEC) asymptotically and universally. Most previous work on single‐layer Fountain coding targets the design via the right degree distribution. The left degree distribution of an LT code is left as a Poisson to protect the universality. For finite lengths, this is no longer an issue; thus, the author's focus is on designing better codes for the BEC at practical lengths. Their left degree shaping provides codes outperforming LT codes and all other competing schemes in the literature. At a bit error rate of 10 −7 and packet length k = 256, their scheme provides a realised rate of 0.6 which is 23.5% higher than that of Sorensen et al. ’s decreasing‐ripple‐size scheme.
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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 | 0.006 | 0.001 |
| 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 it