Spatially-coupled Split-component Codes with Iterative Algebraic\n Decoding
Bibliographic record
Abstract
We analyze a class of high performance, low decoding-data-flow\nerror-correcting codes suitable for high bit-rate optical-fiber communication\nsystems. A spatially-coupled split-component ensemble is defined, generalizing\nfrom the most important codes of this class, staircase codes and braided block\ncodes, and preserving a deterministic partitioning of component-code bits over\ncode blocks. Our analysis focuses on low-complexity iterative algebraic\ndecoding, which, for the binary erasure channel, is equivalent to a\ngeneralization of the peeling decoder. Using the differential equation method,\nwe derive a vector recursion that tracks the expected residual graph evolution\nthroughout the decoding process. The threshold of the recursion is found using\npotential function analysis. We generalize the analysis to mixture ensembles\nconsisting of more than one type of component code, which provide increased\nflexibility of ensemble parameters and can improve performance. The analysis\nextends to the binary symmetric channel by assuming mis-correction-free\ncomponent-code decoding. Simple upper-bounds on the number of errors\ncorrectable by the ensemble are derived. Finally, we analyze the threshold of\nspatially-coupled split-component ensembles under beyond bounded-distance\ncomponent decoding.\n
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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 | 0.001 | 0.003 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 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 | 0.001 |
| 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".