CRC-Based Correction of Multiple Errors Using an Optimized Lookup Table
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Bibliographic record
Abstract
In this paper, we propose a new approach to perform multiple error correction in wireless communications over error-prone networks. It is based on the cyclic redundancy check syndrome, using an optimized lookup table that avoids performing arithmetic operations. This method is able to achieve the same correction performance as the state-of-the-art approaches while significantly reducing the computational complexity. The table is designed to allow multiple bit error correction simply by navigating within it. Its size is constant when considering more than two errors, which represents a tremendous advantage over earlier lookup table-based approaches. Simulation results of a C implementation performed on a Raspberry Pi 4 show that the proposed method is able to process single and double error corrections of large payloads in 100ns and 642<inline-formula> <tex-math notation="LaTeX">$\mu \text{s}$ </tex-math></inline-formula>, respectively, while it would take 300<inline-formula> <tex-math notation="LaTeX">$\mu \text{s}$ </tex-math></inline-formula> and 1.5s, respectively, with the state-of-the-art CRC multiple error correction technique. This represents a speedup of nearly <inline-formula> <tex-math notation="LaTeX">$3000\pmb {\times }$ </tex-math></inline-formula> for single error and <inline-formula> <tex-math notation="LaTeX">$2300\pmb {\times }$ </tex-math></inline-formula> for double error correction, respectively. Compared to table-based approaches, the proposed method offers a speedup of nearly <inline-formula> <tex-math notation="LaTeX">$1200\pmb {\times }$ </tex-math></inline-formula> for single error and <inline-formula> <tex-math notation="LaTeX">$2300\pmb {\times }$ </tex-math></inline-formula> for double error correction under the same conditions. We also show that when multiple candidate error patterns are present, numerous errors can be corrected by adding a checksum cross-validation step.
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| 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) | 0.000 | 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 it