Multi-Resolution Multicasting Over the Grassmann and Stiefel Manifolds
Bibliographic record
Abstract
We consider the design of space-time codes for the multiple-input multiple-output multicast communication systems with two classes of receivers. The first class comprises high-resolution (HR) receivers which have access to reliable channel state information (CSI) and can perform coherent detection, and the second class comprises low-resolution (LR) receivers which do not have access to CSI and can only perform non-coherent detection. We propose a layered encoding structure in which LR information available to both classes of receivers is encoded using Grassmannian constellations, and an incremental component, which is available only to the HR receivers, is encoded in the particular bases of the transmitted Grassmannian constellation points, thereby giving rise to constellations on the Stiefel manifold. The proposed structure enables reliable coherent communication of the HR information without compromising the reliability with which the basic LR information is non-coherently communicated. To effect rate-efficient communication of the incremental, HR layer, we use optimization methods on the Stiefel manifold to develop a novel technique for designing the unitary constellations directly. This approach alleviates the restriction imposed by the traditional techniques in which unitary space-time codes are constructed from scalar constellations. As such, this approach enables better control of the distance spectrum of the developed constellations and more effective utilization of the degrees of freedom that underlie the Stiefel manifold. For the LR receivers, we use maximum likelihood detection, whereas for the HR receivers, we develop a computationally-efficient two-step sequential detector which detects the LR information prior to detecting the incremental component superimposed on it. The detectors and the layered structure with the aforementioned constellations enable full diversity and maximum degrees of freedom to be achieved on the Grassmann and Stiefel manifolds.
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How this classification was reachedexpand
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 | 0.000 |
| Science and technology studies | 0.003 | 0.001 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.002 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| 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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, 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".