Quasi‐cyclic low‐density parity‐check codes based on finite set systems
Bibliographic record
Abstract
A finite set system (FSS) is a pair ( V , ℬ) where V is a finite set whose members are called points, equipped with a finite collection of its subsets ℬ whose members are called blocks. In this paper, FSSs are used to define a class of quasi‐cyclic low‐density parity‐check (LDPC) codes, called FSS codes, such that the constructed codes possess large girth and arbitrary column‐weight distributions. Especially, the constructed column weight‐2 FSS codes have higher rates than the column weight‐2 geometric and cylinder‐type codes with the same girths. To find the maximum girth of FSS codes based on ( V , ℬ), inevitable walks are defined in ℬ such that the maximum girth is determined by the smallest length of the inevitable walks in ℬ. Simulation results show that the constructed FSS codes have very good performance over the additive white Gaussian noise channel with iterative decoding and achieve significantly large coding gains compared with the random‐like LDPC codes of the same lengths and rates.
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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 | 0.001 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.004 | 0.001 |
| 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".