On Characterization of Elementary Trapping Sets of Variable-Regular LDPC\n Codes
Bibliographic record
Abstract
In this paper, we study the graphical structure of elementary trapping sets\n(ETS) of variable-regular low-density parity-check (LDPC) codes. ETSs are known\nto be the main cause of error floor in LDPC coding schemes. For the set of LDPC\ncodes with a given variable node degree $d_l$ and girth $g$, we identify all\nthe non-isomorphic structures of an arbitrary class of $(a,b)$ ETSs, where $a$\nis the number of variable nodes and $b$ is the number of odd-degree check nodes\nin the induced subgraph of the ETS. Our study leads to a simple\ncharacterization of dominant classes of ETSs (those with relatively small\nvalues of $a$ and $b$) based on short cycles in the Tanner graph of the code.\nFor such classes of ETSs, we prove that any set ${\\cal S}$ in the class is a\nlayered superset (LSS) of a short cycle, where the term "layered" is used to\nindicate that there is a nested sequence of ETSs that starts from the cycle and\ngrows, one variable node at a time, to generate ${\\cal S}$. This\ncharacterization corresponds to a simple search algorithm that starts from the\nshort cycles of the graph and finds all the ETSs with LSS property in a\nguaranteed fashion. Specific results on the structure of ETSs are presented for\n$d_l = 3, 4, 5, 6$, $g = 6, 8$ and $a, b \\leq 10$ in this paper. The results of\nthis paper can be used for the error floor analysis and for the design of LDPC\ncodes with low error floors.\n
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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) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.001 | 0.002 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.003 | 0.002 |
| Research integrity | 0.001 | 0.001 |
| 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".