Successive relaxation for decoding of LDPC codes
Why this work is in the frame
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Bibliographic record
Abstract
The application of successive relaxation (SR) to the fixed-point problem associated with the iterative decoding of low-density parity-check (LDPC) codes is studied. We consider finite-length codes decoded by belief propagation (BP) and a well-known approximation of it, referred to as min-sum (MS), over a binary input additive white Gaussian noise (BIAWGN) channel. For both algorithms, we show that the application of SR in different domains results in different error correcting performance. In particular, the performances of SR in log-likelihood ratio (LLR) and LR domains for BP and MS are compared, and it is shown that SR-MS-LLR has the best performance. For the tested codes, SR-MS-LLR outperforms standard BP by up to about 0.5dB, offering an attractive solution in terms of performance/complexity tradeoff. We also investigate the effects of quantization on SR-MS-LLR and demonstrate that at least 6–7 bits of quantization is required to capture close to floating-point 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 | 0.000 |
| Open science | 0.000 | 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