Adaptive Multiset Stochastic Decoding of Non-Binary LDPC Codes
Bibliographic record
Abstract
We propose a non-binary stochastic decoding algorithm for low-density parity-check (LDPC) codes over GF(q) with degree two variable nodes, called Adaptive Multiset Stochastic Algorithm (AMSA). The algorithm uses multisets, an extension of sets that allows multiple occurrences of an element, to represent probability mass functions that simplifies the structure of the variable nodes. The run-time complexity of one decoding cycle using AMSA is O(q) for conventional memory architectures, and O(1) if a custom memory architecture is used. Two fully-parallel AMSA decoders are implemented on FPGA for two (192,96) (2,4)-regular codes over GF(64) and GF(256), both achieving a maximum clock frequency of 108 MHz. The GF(64) decoder has a coded throughput of 65 Mb/s at Eb/N0=2.4 dB when using conventional memory, while a decoder using the custom memory version can achieve 698 Mb/s at the same Eb/N0. At a frame error rate (FER) of 2×10-6the GF(64) version of the algorithm is only 0.04 dB away from the floating-point SPA performance, and for the GF(256) code the difference is 0.2 dB. To the best of our knowledge, this is the first fully parallel non-binary LDPC decoder over GF(256) reported in the literature.
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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 | 0.000 | 0.001 |
| 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 | 0.001 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| 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".