On Optimal Power Allocation for Modulation-Constrained Gaussian Channels
Bibliographic record
Abstract
The problem of optimal power allocation for parallel Gaussian channels under modulation order constrains, in addition to the total transmit power constraint, is considered. It is motivated by coded-modulation systems using powerful capacity-approaching codes. While only analytically-intractable solution is known to this problem, an explicit closed-form solution is obtained here using a sphere-packing-based approximation for modulation-constrained rates. It can be interpreted as waterfilling with variable water level, which is also expressed in a closed-form. The obtained power allocation also solves the dual problem of minimizing the total transmit power subject to the sum rate and modulation order constraints. More insightful analytical solutions are obtained in some special cases. While the new power allocation is similar to the well-known waterfilling procedure at low SNR, it is dramatically different at moderate to high SNR. Proportional cardinality allocation is shown to be optimal at high SNR under the uniform power allocation.
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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 | 0.005 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.002 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.003 | 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".