Performance Variation of Gray Codes for Cropped Gaussian 16PAM Constellations
Bibliographic record
Abstract
There are many ways to label symbols in a constellation. We investigate the performance impact of the Gray code choice both in the case of uniformly-spaced symbol constellations and cropped Gaussian constellations, with the BICM (bit-interleaved coded modulation) mutual information as a performance measure. We exhaustively search and find all 131 Gray codes, including cyclic and acyclic Gray codes, each representing a class of codes resulting in the same performance, that can be used with a symmetric 16PAM. Our results show that Gray codes having a bit position with only a single transition tend to outper-form codes where all bit positions have multiple transitions. The ranking of Gray code performance was similar when using both square PAM and optimized cropped Gaussian PAM, with only minor differences in the rankings of Gray codes. This indicates that joint selection of the cropped Gaussian constellation and the Gray code is not significantly important in designing a system. These results in the present paper can be applied to 256-symbol QAM constellations with in-phase/quadrature symmetry.
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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 | 0.012 |
| Meta-epidemiology (narrow) | 0.000 | 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 | 0.000 | 0.001 |
| Research integrity | 0.001 | 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".