On Characterization and Efficient Exhaustive Search of Elementary Trapping Sets of Variable-Regular LDPC Codes
Why this work is in the frame
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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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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 it