Hybrid Decoding of LDPC Codes Based on Interior Point Method
Bibliographic record
Abstract
In this paper, a hybrid decoding algorithm for finite-geometry low-density parity-check (FG-LDPC) codes is proposed. The algorithm is based on the interior point method with barrier function introduced by Wadayama. First, an efficient implementation of Wadayama's algorithm is presented. The main idea behind the modification is to approximate the barrier function for the fundamental polytope defining the code so that it contains only one linear constraint for each of the parity-check constraints. A two-stage hybrid decoding which combines the interior point decoding (IPD) and a low-complexity decoding algorithm for FG-LDPC codes is then proposed. In the first stage, the interior point decoding is used to generate a search point. If the first stage decoding fails, the decoding is continued by the low-complexity algorithm that is initialized by the result of the IPD. Compared with a conventional iterative message-passing (IMP) decoder, the proposed hybrid algorithm achieves better bit-error rate (BER) and frame-error rate (FER) for small block lengths at medium to high signal-to-noise ratio (SNR).
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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 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| 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 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".