Threshold Values and Convergence Properties of Majority-Based Algorithms for Decoding Regular Low-Density Parity-Check Codes
Bibliographic record
Abstract
This work presents a detailed study of a family of binary message-passing decoding algorithms for low-density parity-check (LDPC) codes, referred to as "majority-based algorithms." Both Gallager's algorithm A (G/sub A/) and the standard majority decoding algorithm belong to this family. These algorithms, which are, in fact, the building blocks of Gallager's algorithm B (G/sub B/), work based on a generalized majority-decision rule and are particularly attractive for their remarkably simple implementation. We investigate the dynamics of these algorithms using density evolution and compute their (noise) threshold values for regular LDPC codes over the binary symmetric channel. For certain ensembles of codes and certain orders of majority-based algorithms, we show that the threshold value can be characterized as the smallest positive root of a polynomial, and thus can be determined analytically. We also study the convergence properties of majority-based algorithms, including their (convergence) speed. Our analysis shows that the stand-alone version of some of these algorithms provides significantly better performance and/or convergence speed compared with G/sub A/. In particular, it is shown that for channel parameters below threshold, while for G/sub A/ the error probability converges to zero exponentially with iteration number, this convergence for other majority-based algorithms is super-exponential.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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 | 0.002 | 0.018 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.001 | 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 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".