An efficient exhaustive search algorithm for elementary trapping sets of variable-regular LDPC codes
Bibliographic record
Abstract
In this paper, we propose an efficient exhaustive search algorithm for elementary trapping sets (ETS) of variable-regular low-density parity-check (LDPC) codes. Recently, Karimi and Banihashemi proposed a characterization of ETSs, which was based on viewing an ETS as a layered superset (LSS) of a short cycle in the code's Tanner graph. A notable advantage of LSS characterization is that it corresponds to a simple LSS-based search algorithm (expansion technique) that starts from short cycles of the graph and finds the ETSs with LSS structure efficiently. Compared to the LSS-based search, which is based on a single LSS expansion technique, the new search algorithm involves two additional expansion techniques. The introduction of the new techniques results in significant improvements in search efficiency compared to the LSS-based search. We prove that using the three expansion techniques, each and every ETS structure can be obtained starting from a simple cycle. We also provide extensive simulation results that show, compared to the LSS-based search, up to three orders of magnitude improvement in search speed and memory requirements can be achieved.
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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 | 0.000 |
| 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 | 0.000 |
| Open science | 0.001 | 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".