Overlapped LT codes over the binary erasure channel: analysis and design
Bibliographic record
Abstract
Fountain codes are promising forward error correction codes suitable for broadcast and multicast applications where many users with different capabilities are involved in the system. Fixed‐rate codes need a priori information about each channel to decide the best code rate and the code rate is usually chosen according to the worst channel to avoid an outage. Fountain codes are agnostic to the channel conditions and rateless. The rate is realised based on the channel conditions for users separately. Overlapped fountain codes were previously invented over the binary erasure channel to provide more degrees of freedom and better trade‐offs for the rateless‐coded system parameters. In this study, the authors show via analysis and simulations that overlapped fountain codes need fewer decoding steps in comparison with the conventional fountain codes. For example, overlapped fountain codes reduce the number of decoding steps/iterations of belief propagation decoder by even at a source length . They optimise the overlap selection probability of the overlapped fountain codes to maximise the code rate and/or minimise the complexity. At source length, , the proposed analytical and simulation studies show that the highest code rate and lowest average complexity are achieved at an overlap selection probability .
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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 | 0.004 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 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".