Maximum Likelihood Detection in a Four-Dimensional Stokes-Space Receiver
Bibliographic record
Abstract
The maximum likelihood detection rule for a four-dimensional direct-detection optical front-end is derived. The four dimensions are two intensities and two differential phases. Three different signal processing algorithms, composed of symbol-by-symbol, sequence, and successive detection, are discussed. To remedy dealing with special functions in the detection rules, an approximation for high signal-to-noise ratios (SNRs) is provided. Simulation results show that, despite the simpler structure of the successive algorithm, the resulting performance loss, in comparison with the other two algorithms, is negligible. For example, for an 8-ring/8-ary phase constellation, the complexity of detection reduces by a factor of 8, while the performance, in terms of the symbol error rate, degrades by 0.5 dB. It is shown that the high-SNR approximation is very accurate, even at low SNRs. The achievable rates for different constellations are computed and compared by the Monte Carlo method. For example, for a 4-ring/8-ary phase constellation, the achievable rate is 10 bits per channel use at an SNR of 25 dB, while by using an 8-ring/8-ary phase constellation and an error correcting code of rate 5/6, this rate is achieved at an SNR of 20 dB.
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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 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.000 | 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 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".