Acyclic Tanner graphs and maximum-likelihood decoding of linear block codes
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Bibliographic record
Abstract
The maximum-likelihood decoding of linear block codes by Wagner rule decoding is discussed. In this approach, the Wagner rule decoding, which has been primarily applied to single parity check codes, is employed on acyclic Tanner graphs. Accordingly, a coset decoding equipped with Wagner rule decoding is applied to the decoding of a code C having a Tanner graph with cycles. A subcode C1 of C with acyclic Tanner graph is chosen as the base subcode. All cosets of C1 have the same Tanner graph and are distinguished by their values of parity nodes in the graph. The acyclic Tanner graph of C1, together with a trellis representation of the space of the parity sequences, represent the code C. This graphical representation provides a unified and systematic approach to search for an efficient method for the maximum-likelihood decoding of a given linear block code. It is shown that the proposed method covers the most efficient techniques known for the decoding of some important block codes, including the hexacode H6, extended Golay codes, Reed–Muller codes, Hamming code and (32, 16, 8) quadratic residue codes. The generalisation to the decoding of lattices is briefly explained.
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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 | 0.000 | 0.000 |
| 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 | 0.001 |
| Open science | 0.002 | 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