Capacity-Achieving Distributions for the Discrete-Time Poisson Channel—Part I: General Properties and Numerical Techniques
Bibliographic record
Abstract
Despite being an accepted model for a wide variety of optical channels, few general results on optimal signalling for discrete-time Poisson (DTP) channels are known. Among the most significant is that under simultaneous peak and average constraints, the capacity-achieving distributions are discrete with a finite number of mass points. In this paper, several fundamental properties of capacity-achieving distributions for DTP channels are established. In particular, we demonstrate that all capacity-achieving distributions of the DTP channel have zero as a mass point. In the case of only a peak constraint, it is further shown that the optimal distribution always has a mass point at the maximum amplitude. Finally, under solely an average power constraint, it is shown that a finite number of mass points are insufficient to achieve the capacity. In addition to these analytical results, a numerical algorithm based on deterministic annealing is presented which can efficiently compute both the channel capacity and the associated optimal input distribution under peak and average power constraints. Numerical lower bounds based on the envelope of information rates induced by the maxentropic distributions are also shown to be extremely close to the capacity, especially in the low power regime.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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 | 0.013 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.004 | 0.001 |
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".