Optimal quantization for noisy channels with random index assignment
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Bibliographic record
Abstract
This paper studies the design of vector quantization (VQ) on noisy channels and its asymptotic performance analysis. Given a tandem source-channel coding system with VQ and block channel coding, we derive a closed-form formula of the average end-to-end distortion (EED), which reveals a structural factor called the scatter factor for noisy channel quantizers. Based on this formula, an iterative algorithm is developed for jointly designing optimal quantizers with channel conditions. Simulations show that quantizers that are jointly designed with channel conditions significantly reduce the EED when compared with quantizers that are designed separately from channel conditions. Indeed, our asymptotic analyses show that the infimum of the mean squared EED over all possible quantizers with joint quantization design is p <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">err</sub> sigma <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> , where p <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">err</sub> is the average transmission error probability of the channel and sigma <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> is the component variance of the source. This is 4.77dB better than that with separate quantization design for an i.i.d. Guassian source.
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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 | 0.000 | 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 | 0.001 | 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