An algebraic number theoretic framework for space-time coding
Bibliographic record
Abstract
In this paper, we develop a novel framework for constructing full rate, full diversity, and polynomial complexity space-time codes for systems with arbitrary numbers of transmit and receive antennas. The proposed framework combines space-time layering concepts with algebraic number theoretic constellations to construct universal codes for scenarios where the channel state information (CSI) is known a-priori at the transmitter and receiver (TR-CSI), receiver only (R-CSI), and neither one of them (N-CSI). For a coherent system (i.e., R-CSI) with M transmit and N receive antennas in quasi-static fading, the proposed codes are constructed over T = M symbol periods by properly assigning algebraic number theoretic constellations to the different layers. The proposed codes are delay-optimal and achieve the maximum diversity advantage MN over quasi-static fading channels for arbitrary numbers of antennas and arbitrary transmission rates. The lattice structure of the proposed codes allows for polynomial complexity maximum likelihood decoding using the sphere decoder. The proposed framework subsumes many of the existing codes in the literature, extends naturally to time-selective and frequency-selective channels, and allows for more flexibility in the trade-off between power efficiency, bandwidth efficiency, and receiver complexity.
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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 | 0.002 | 0.004 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.004 |
| Scholarly communication | 0.002 | 0.004 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.003 |
| Insufficient payload (model declined to judge) | 0.003 | 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".