Closed-form CRLBs for SNR estimation from turbo-coded square-QAM-modulated signals
Bibliographic record
Abstract
In this contribution, we derive for the first time the closed-form expressions for the Cramér-Rao lower bounds (CRLBs) of the signal-to-noise ratio (SNR) estimates from turbo-coded square-QAM transmissions. By exploiting the structure of the Gray mapping, we are able to factorize the likelihood function thereby linearizing all the derivation steps for the FIM elements. The analytical CRLBs coincide exactly with their empirical counterparts validating thereby our new analytical expressions. Numerical results suggest that the CLRBs for code-aided (CA) SNR estimates range between the CRLBs for non-data-aided (NDA) SNR estimates and those for data-aided (DA) ones, thereby highlighting the effect of the coding gain. At sufficiently high SNR levels, the three CRLBs coincide. The derived bounds are also valid for LDPC-coded systems and they can be evaluated in the same way when the latter are decoded using the turbo principal.
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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 | 0.004 | 0.037 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.003 | 0.003 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.004 | 0.003 |
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".