Capacity-achieving signals of non-coherent rayleigh fading channels with additive gaussian mixture noise
Bibliographic record
Abstract
This paper investigates the detailed characterization of the capacity-achieving input signals for a non-coherent Rayleigh fading channel with Gaussian mixture noise where neither the transmitter nor the receiver has the knowledge of fading coefficients. The considered model is suited for wireless networks having multi-tier heterogeneous architectures in which the channel conditions change rapidly. By first establishing an integrable upper bound on the absolute function of the integrand in the output entropy equation, we demonstrate that there exists a unique input distribution that achieves the channel capacity. By formulating the Kuhn-Tucker condition (KTC), we then examine in detail the number of mass points in the optimal input distribution. Specifically, by establishing a diverging lower bound on the KTC, we show that it is not possible for the optimal input distribution to have an infinite number of mass points. As a result, the capacity-achieving input distribution is discrete having a finite number of mass points. Finally, we develop a simple numerical method to evaluate the optimal input and compute the capacity.
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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 | 0.000 | 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 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".