Comments on successive relaxation for decoding of LDPC codes
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 was proposed by Hemati et al.. The simulation results presented by Hemati et al. for the SR version of belief propagation (BP) in the likelihood ratio (LR) domain and that of min-sum (MS) in the log-likelihood ratio (LLR) domain are based on the assumption of all-zero codeword transmission. This assumption however results in erroneous error rates when SR is applied in the LR domain. Here, we correct the simulation results reported by Hemati et al. for SR-BP in the LR domain. Furthermore, we investigate the performance of SR-BP and SR-MS in the LLR and LR domains, respectively. The results for a binary input additive white Gaussian noise (BIAWGN) channel show that for both BP and MS, the application of SR in the two domains of LR and LLR results in different error correcting performance. In particular, for the tested codes, it is shown that among the four algorithms, SR-MS-LLR has the best performance. It outperforms standard MS and BP by up to about 0.6 dB and 0.3 dB, respectively, offering an attractive solution in terms of performance/complexity tradeoff.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.005 | 0.041 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.001 | 0.003 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.003 | 0.006 |
| Insufficient payload (model declined to judge) | 0.010 | 0.004 |
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 source (direct Gemma or distilled Codex), 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".