A probabilistic model for optical fiber channels with zero dispersion
Bibliographic record
Abstract
Signal evolution in optical fibers with zero dispersion and distributed Raman amplification is modeled by a stochastic nonlinear ordinary differential equation (ODE) which includes the effects of the Kerr nonlinearity and amplified spontaneous emission noise. Such a mathematical model in the form of a stochastic nonlinear ODE is not initially suitable for information-theoretic analysis. In this paper we provide a simple framework to probabilistically model signal propagation in optical fibers. The analysis is based on discretizing the fiber as a cascade of an infinite number of infinitesimal pieces of fiber in the distance dimension, while at the same time quantizing the signal into a large number of small bins in the complex plane. This can be understood in the context of the sum-product algorithm, known in coding theory. Though the method can be also applied to fibers with dispersion, in this paper it is illustrated for the special case of zero dispersion. In particular, for this case we find the conditional probability density function of the output signal given the input signal. We further show that the capacity of the dispersion-free optical channel as a function of signal-to-noise ratio (SNR) goes to infinity with SNR → ∞.
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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 | 0.005 |
| 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 | 0.003 |
| Scholarly communication | 0.002 | 0.004 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.002 | 0.002 |
| Insufficient payload (model declined to judge) | 0.002 | 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 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".