Bibliographic record
Abstract
Fountain codes are used in many applications where the channels are time varying and it is difficult at the transmitter to predict the appropriate code rate. In this situation, fixed-rate codes are not suitable. Despite the good performance of fountain codes, universally optimal codes do not exist in the finite-length regime. In this paper, we design new fountain codes that are robust to the communication system's parameters such as erasure probability as well as the source length. We employ density evolution together with linear programming to design robust fountain codes offering some of the attractive properties of universally optimal codes. Different objectives are used in the analysis such as minimizing the erasure probability and maximizing the code rate. Analytically, results indicate that fountain codes can decrease the failure probability to the level of 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-12</sup> using the optimized parameters at source length k = 128, code rate R = 1/2 and erasure probability ε = 0. Further, simulation results show that the code rate can be improved significantly. For example, at a source length k = 512, Shokrollahi distribution achieves code rate R = 0.7268 while our novel design provides a code rate R = 0.76331, that is an improvement of 5%.
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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 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.002 | 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".