Piecewise linear LLR approximation for non-binary modulations over Gaussian channels with unknown noise variance
Bibliographic record
Abstract
Channel log-likelihood ratio (LLR) calculation on many communication channels is a challenging task especially when non-binary modulations are used. This is because LLRs are usually complicated functions of the channel output and their calculation also requires knowledge of the channel parameters. In this paper, we consider the problem of finding good approximate LLRs for the additive white Gaussian noise channel under non-binary modulations when the noise variance is unknown at the receiver. To this end, we propose piecewise linear LLR approximating functions and we use the LLR accuracy measure of to optimize the parameters. First, we assume that the noise variance is known at the receiver and later we generalize the method to the case of unknown noise variance. It is shown in the latter case that the optimum piecewise linear approximate LLRs depend on the code used on the channel. We observe that the optimized piecewise linear LLRs perform extremely close to exact LLRs.
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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 | 0.008 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.001 | 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".