Tight error bounds for nonuniform signaling over AWGN channels
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Bibliographic record
Abstract
We consider a Bonferroni-type lower bound due to Kounias (1968) on the probability of a finite union. The bound is expressed in terms of only the individual and pairwise event probabilities; however, it suffers from requiring an exponentially complex search for its direct implementation. We address this problem by presenting a practical algorithm for its evaluation. This bound is applied together with two other bounds, a recent lower bound (the KAT bound) and a greedy algorithm implementation of an upper bound due to Hunter (1976), to examine the symbol error (P/sub a/) and bit error (P/sub b/) probabilities of an uncoded communication system used in conjunction with M-ary phase-shift keying (PSK)/quadrature amplitude (QAM) (PSK/QAM) modulations and maximum a posteriori (MAP) decoding over additive white Gaussian noise (AWGN) channels. It is shown that the bounds-which can be efficiently computed-provide an excellent estimate of the error probabilities over the entire range of the signal-to-noise ratio (SNR) E/sub b//N/sub 0/. The new algorithmic bound and the greedy bound are particularly impressive as they agree with the simulation results even during very severe channel conditions.
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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 | 0.002 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.001 | 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