Stability analysis of an improved min-sum decoder
Bibliographic record
Abstract
It has been shown that under min-sum (MS) decoding, scaling the messages at the output of check nodes can improve the performance of regular low-density parity-check (LDPC) codes. However, for irregular codes designed for the sum-product decoder, linear scaling can hinder the performance. The problem of code design for MS and linear scaling min-sum (LSMS) decoders have been recently investigated. It is shown that the gap to the capacity for LSMS codes is better than MS codes, but compared to sum-product codes the gap is still considerable. In this letter, a modified MS decoding is proposed and studied. We use the stability analysis of density evolution to show that the proposed method allows for a larger fraction of edges connected to degree-2 variable nodes than LSMS codes. Finally, by designing codes based on the modified method, we show that compared to MS and LSMS codes, a smaller gap to the capacity can indeed be achieved while the complexity of decoding remains essentially the same.
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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) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.002 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.004 | 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 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".