Graph-Based Message-Passing Schedules for Decoding LDPC Codes
Bibliographic record
Abstract
We study a wide range of graph-based message-passing schedules for iterative decoding of low-density parity-check (LDPC) codes. Using the Tanner graph (TG) of the code and for different nodes and edges of the graph, we relate the first iteration in which the corresponding messages deviate from their optimal value (corresponding to a cycle-free graph) to the girths and the lengths of the shortest closed walks in the graph. Using this result, we propose schedules, which are designed based on the distribution of girths and closed walks in the TG of the code, and categorize them as node based versus edge based, unidirectional versus bidirectional, and deterministic versus probabilistic. These schedules, in some cases, outperform the previously known schedules, and in other cases, provide less complex alternatives with more or less the same performance. The performance/complexity tradeoff and the best choice of schedule appear to depend not only on the girth and closed-walk distributions of the TG, but also on the iterative decoding algorithm and channel characteristics. We examine the application of schedules to belief propagation (sum-product) over additive white Gaussian noise (AWGN) and Rayleigh fading channels, min-sum (max-sum) over an AWGN channel, and Gallager's algorithm A over a binary symmetric channel.
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 | 0.001 | 0.008 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.000 |
| 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".