On Characterization and Efficient Exhaustive Search of Elementary Trapping Sets of Variable-Regular LDPC Codes
Bibliographic record
Abstract
Recently, Karimi and Banihashemi demonstrated that a large majority of the elementary trapping set (ETS) structures of variable-regular low-density parity-check (LDPC) codes are layered supersets (LSS) of short cycles. The LSS property corresponds to a simple search algorithm that can find all ETSs with LSS structure starting from short cycles in a guaranteed fashion. In this letter, we complement this characterization by demonstrating that the remaining structures of ETSs, that are not LSS of short cycles, are all LSS of a small number of other graphical structures within the Tanner graph of the code, and thus can also be found efficiently. This together with the results of Karimi and Banihashemi provides a simple search algorithm that can find all the (a,b) ETSs of any variable-regular LDPC code for any size a and any number of unsatisfied check nodes b in a guaranteed fashion.
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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 | 0.000 | 0.004 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.000 | 0.000 |
| 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".