Variable LLR Scaling in Min-Sum Decoding for Irregular LDPC Codes
Why this work is in the frame
A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.
Bibliographic record
Abstract
Min-sum decoding is a low-complexity alternative to the so-called belief propagation and consists in simplification of the nonlinear operation on the log likelihood ratios (LLRs) in the check nodes. The resulting suboptimality may be tempered via appropriate scaling of the LLRs, e.g., the fixed optimal scaling in the normalized min-sum algorithm, and variable scaling algorithms gradually appearing in the literature. However, up to now, none of the papers studied variable scaling both as per iteration and as per different check node degree, due to the prohibitive complexity of multioptimization over space of too many parameters. In this paper, we propose a generalized mutual information (GMI) of LLRs as the criterion to search for the scaling factors for different check node degrees in every iteration in a 1-D thus low-complexity manner. This approach is first analyzed via density evolution, and in addition can be extended to practical LLRs based formulas via Monte Carlo tools to cope with the mismatch issue. Bit error rate simulation results on two low-density parity-check codes show that our proposed GMI metrics have a noticeable gain over the variable scaling schemes that appeared in the literature.
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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 | 0.001 |
| 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.
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