A Performance Metric for Codes With a High-Order Spectral Null at Zero Frequency
Bibliographic record
Abstract
Sum-variance is a well-known metric for assessing the performance of dc-free codes (first-order spectral-null codes), however, as we show in this paper, it is unsuitable for comparing the magnitude of spectral components of high-order spectral-null (HOSN) codes at low frequencies. In this paper, we introduce a new performance metric for evaluating the spectrum compression of arbitrarily HOSN codes around zero frequency; we call this metric the low-frequency spectrum weight (LFSW). We show that the asymptotic low-frequency spectral components of Kth-order spectral-null codes (K/spl ges/1) are exclusively determined by the order K and the LFSW, and that the LFSW equals the zero-frequency value in the spectrum of the corresponding sequence of Kth-order running digital sum values. We derive this result for symbol-by-symbol encoding, and then extend it to block HOSN codes. We then derive a closed-form expression for the LFSW of HOSN codes constructed through state-independent encoding. Closed-form expressions for LFSW of first-order zero-disparity codes and for the asymptotic LSFW of maxentropic dc-free sequences are also given.
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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 | 0.003 | 0.021 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.001 | 0.002 |
| 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".