A degree-matched check node approximation for LDPC decoding
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Bibliographic record
Abstract
This paper examines ways to recoup the performance loss incurred when using the min-sum approximation instead of the exact sum-product algorithm for decoding low-density parity check codes (LDPCs). Approximations to the correction factor exactly expressing the difference between these two decoding algorithms exist for degree 3 check nodes, and can be applied to higher degree nodes by subdividing them into component degree 3 nodes. However, this results in replication of the approximation. An asymptotic expression for the correction factor at a check node of any degree is derived in this paper, and used to develop two simple approximations to the correction factor, matched to the check node degree. One has very low complexity, and both only need be applied once per check node extrinsic message. Simulation results are presented for each check node approximation when decoding a regular and an irregular LDPC. Both degree-matched check node approximations achieve sum-product decoding performance
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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 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| 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.
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