On the Accuracy of the High-SNR Approximation of the Differential Entropy of Signals in Additive Gaussian Noise: Real and Complex Cases
Bibliographic record
Abstract
One approach to the analysis of the high signal-to-noise ratio (SNR) capacity of noncoherent wireless communication systems is to ignore the noise component of the received signal in the computation of its differential entropy. In this paper, we consider the error incurred by this approximation when the transmitter and the receiver have one antenna each and when the noise has a Gaussian distribution. We consider the complex and real cases, and we show that when the probability density function (pdf) of the signal component of the received signal is piecewise differentiable, the approximation error decays as 1/SNR, which tightens the available result that the error decays as o(1). In addition, we consider the special instance in which the signal component of the received signal corresponds to a signal transmitted over a channel with a Gaussian fading coefficient. For that case, we provide explicit expressions for the first nonconstant term of the Taylor expansion of the differential entropy, and we invoke Schwartz's inequality to obtain an efficiently computable bound on it. Our results are supported by numerical examples.
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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".