Trace-Orthonormal Full-Diversity Cyclotomic Space–Time Codes
Bibliographic record
Abstract
In this paper, we consider the design of full-diversity space-time codes for a coherent multiple-input multiple-output (MIMO) communication system. Starting from both the information theoretic and detection error viewpoints, we first establish that a desirable property for general linear dispersion (LD) codes is to have an interunitary as well as an intraunitary structure-a structure we call trace-orthonormality. By imposing the trace-orthonormal structure on an LD code and applying cyclotomic number theory, we establish, for an arbitrary number of transmitter and receiver antennas, a systematic and simple method to jointly design a unitary cyclotomic matrix, the Diophantine number, and the corresponding constellation for an LD code. As a result, this enables us to construct full-diversity rectangular cyclotomic LD codes with any symbol transmission rate less than or equal to the number of transmitter antennas. In addition, for the case when the number of transmitter antennas is greater than the number of receiver antennas, by taking advantage of the delay, we also arrive at the design of a special trace-orthonormal full-diversity cyclotomic space-time block code which, for the number of transmitter antenna being equal to 2m, can be proved to minimize the worst case pairwise error probability of a maximum-likelihood (ML) detector for a q-ary quadrature amplitude modulation (QAM) signal constellation and, therefore, achieves optimal coding gain. Computer simulations show that these codes have bit-error performance advantages over currently available codes
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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 | 0.002 |
| 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 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| 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".