On the construction of space-time Hamiltonian constellations from group codes
Bibliographic record
Abstract
Full diversity signal constellations for any numbers of transmitter antennas and for any orders which are constructed from 2/spl times/2 Hamiltonian matrices are investigated in this paper. The diversity product of a 2/spl times/2 Hamiltonian constellation equals one half of the Euclidean distance between two points in C/sup 2/. By considering the transformation from R/sup 4/ to C/sup 2/, the idea of group codes is used to construct a high diversity product constellation for any order L. The (L,4) cyclic group codes are considered to obtain L 4-dimensional codewords for group codes. We show that our 2/spl times/2 Hamiltonian constellations have higher diversity product than orthogonal and diagonal constellation designs. We extend our construction to the general case for any numbers of transmitter antennas M>2 by using a direct sum of 2/spl times/2 Hamiltonian matrices for M even, and a direct sum of 2/spl times/2 Hamiltonian matrices with the L/sup th/ roots of unity for M odd. It is shown that these constellations outperform cyclic groups and some of those obtained using fixed-point free groups.
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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 | 0.002 |
| 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 | 0.000 | 0.001 |
| Open science | 0.000 | 0.001 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 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".