Left degree distribution shaping for LT codes over the binary erasure channel
Bibliographic record
Abstract
Fountain codes were introduced to provide higher reliability, lower complexities, and more scalability for networks such as the Internet. Luby-Transform (LT) codes, which are the first realization of Fountain codes, achieve the capacity of the binary erasure channel (BEC) asymptotically and universally. For finite lengths, the search is continued to find codes closer to the capacity limits at even lower encoding and decoding complexities. 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 Poisson to protect the universality. For finite lengths, this is no longer an issue; thus, we focus on the design of better codes for the BEC at practical lengths. Our left degree shaping provides codes outperforming LT and all other competing schemes in the literature. At a bit error rate of 10−7and packet length k = 256, our scheme provides a realized rate of 0.6 which is 23.5% higher than Sorensen et al.'s scheme [1].
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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 | 0.001 | 0.005 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.000 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.001 | 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 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".