Non-Asymptotic Achievable Rates for Gaussian Energy-Harvesting Channels: Save-and-Transmit and Best-Effort
Bibliographic record
Abstract
An additive white Gaussian noise energy-harvesting channel with an infinite-sized battery is considered. The energy arrival process is modeled as a sequence of independent and identically distributed random variables. The channel capacity 1/2 log(1 + P) is achievable by the so-called best-effort and save-and-transmit schemes where P denotes the battery recharge rate. This paper analyzes the save-and-transmit scheme whose transmit power is strictly less than P and the best-effort scheme as a special case of save-and-transmit without a saving phase. In the finite blocklength regime, we obtain new nonasymptotic achievable rates for these schemes that approach the capacity with gaps vanishing at rates proportional to 1/√n and ((log n)/n) <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1/2</sup> respectively where n denotes the blocklength. The proof technique involves analyzing the escape probability of a Markov process. When P is sufficiently large, we show that allowing the transmit power to back off from P can improve the performance for save-and-transmit. The results are extended to a block energy arrival model where the length of each energy block L grows sublinearly in n. We show that the save-and-transmit and best-effort schemes achieve coding rates that approach the capacity with gaps vanishing at rates proportional to √(L/n) and (max{log n, L}/n) <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1/2</sup> , respectively.
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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 | 0.001 |
| 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".