On the capacity region of parallel Gaussian broadcast channels with common information
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Bibliographic record
Abstract
We consider a broadcast scenario in which a single transmitter wishes to send common, partially common and particular messages to several receivers over the product of unmatched parallel scalar Gaussian subchannels with a total power constraint. This scenario is a generalization of the 2-user 2-subchannel scenario that was studied earlier in the literature. In order to expose the signal structure and the difficulties that arise in generalizing the results on the 2-user 2-subchannel case to the case of K users and N subchannels, we consider a representative scenario with 3 users and 2 subchannels. For this case, we characterize the achievable rate region, and express the boundary points thereof as the solution of an optimization problem. This problem is not convex in the general case, but it provides insight that leads to tight inner and outer bounds on the capacity region that can be obtained efficiently via the solution of a convex Geometric Program (GP). (The GP also generates the corresponding power loads and partitions.) In addition to these bounds, we provide a (precise) GP formulation for the optimal power allocation problem for the 2-user 2-subchannel case.
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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 | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| 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 it