Comparison of Split-Step Fourier Schemes for Simulating Fiber Optic Communication Systems
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Bibliographic record
Abstract
This paper mainly focuses on efficient schemes for simulating propagation in optical fibers. Various schemes based on split-step Fourier techniques to solve the nonlinear Schrödinger equation (NLSE), which describes the propagation in optical fibers, are compared. In general, the schemes in which the loss operator is combined with nonlinearity operator are found to be more computationally efficient than the schemes in which the loss is combined with dispersion. When the global error is large, the schemes with variable step size outperform the ones with uniform step size. The schemes based on local error and/or minimum area mismatch (MAM) further improve the computational efficiency. In this scheme, by minimizing the area mismatch between the exponential profile and its stepwise approximation, an optimal step size distribution is found. The optimization problem is solved by the steepest descent algorithm. The number of steps to get the desired accuracy is determined by the local error method. The proposed scheme is found to have higher computational efficiency than the other schemes studied in this paper. For QPSK systems, when the global error is <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="TeX">$10^{-8}$</tex-math></inline-formula> , the number of fast Fourier transforms (FFTs) needed for the conventional scheme (loss combined with dispersion and uniform step size) is 5.8 times that of the proposed scheme. When the global error is <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="TeX">$10^{-6}$</tex-math></inline-formula> , the number of FFTs needed for the conventional scheme is 3.7 times that of the proposed scheme.
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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 | 0.001 | 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 it