On the Power Allocation Problem in the Gaussian Interference Channel with Proportional Rate Constraints
Bibliographic record
Abstract
This paper takes an analytical approach to solving the optimization problem of finding the power allocation that maximizes the sum-rate of the Gaussian interference channel with any linear power (interference) constraint and proportional rate constraints. It is proved that the sum-rate of the Gaussian interference channel restricted to proportional rate constraints does not have a critical point and the maximum sum-rate subject to said constraints occurs at the boundary of the domain formed by the plane representing the linear power constraint. This is accomplished by using analytic geometry in higher dimensions to show that the curve of intersection of the sum-rate and the proportional rate constraints is always increasing, and intersects the boundary plane representing the linear power constraint at a unique point. A polynomial time (in the number of users) centralized algorithm that finds this point of optimal power allocation is proposed. This is a significant improvement over existing algorithms for related power allocation problems which have exponential time complexity in the number of users. Two distributed algorithms with linear and constant complexities are also presented. Simulation results supporting the analysis and demonstrating the performances of the algorithms are presented.
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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 | 0.002 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.006 | 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".