FPGA implementation of variants of min-sum algorithm
Bibliographic record
Abstract
This paper presents the FPGA implementation of a number of popular decoding algorithms for a regular rate-1/2 low density parity check code with block length 504 bits. The so-called min-sum (MS) algorithm and two of its variants, known as MS with successive relaxation (SR-MS) and MS with unconditional correction (MS-UC), are implemented. We implement the algorithms on a Xilinx XC2VP100 FPGA device with 4-bit quantization. We show that for MS-UC, the circuit utilization increases by about 2% compared to standard MS and that the throughput is the same as that of MS. For SR-MS, the device utilization is increased by about 26% and the throughput is decreased by approximately 20% compared to standard MS. While the throughput and the area and power consumption of our implementation is comparable to the most recent FPGA implementations of LDPC decoders, ours is the first attempt at implementing an iterative decoding algorithm with memory (SR-MS).
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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 | 0.001 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.004 | 0.001 |
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".