Recursive method for generating column weight 3 low‐density parity‐check codes based on three‐partite graphs
Bibliographic record
Abstract
In this study, a method is presented to construct column weight 3 (CW3) low‐density parity‐check (LDPC) codes using three‐partite graphs. Let G b be a bipartite graph and N g be the set of all minimum length cycles in G b . Using G b and N g , a three‐partite graph denoted G ( G b , N g ), or simply G t , is formed. Let T be the set of length 3 cycles in G t and T a be the set of three element subsets of vertices in G t such that each of these subsets form a subgraph with no edges in G t and has precisely one element in each section of G t . Furthermore, let H be the binary matrix in which the set of rows represent the set of vertices of G t , the columns represent the elements of V := T ∪ T a , and h ij = 1 if and only if the i th vertex of G t belongs to the j th three element set in V . Then H is a CW3 binary matrix. Using the Tanner graph representing H , a recursive construction for CW3 LDPC codes is provided. Applying a simple restriction on T and T a , codes free of length 4 cycles are generated. Euclidean and finite geometry codes are used as the base codes for generating new CW3 LDPC codes. Results are presented which show that these new codes perform well in an additive white Gaussian noise (AWGN) channel with the iterative sum‐product decoding algorithm.
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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 | 0.002 | 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 | 0.003 | 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".