On the Redundancy of Slepian–Wolf Coding
Bibliographic record
Abstract
In this paper, the redundancy of both variable and fixed rate Slepian–Wolf coding is considered. Given any jointly memoryless source-side information pair$\{(X_i, Y_i)\}_{i=1}^{\infty}$with finite alphabet, the redundancy$R^n(\epsilon_n)$of variable rate Slepian–Wolf coding of$X_1^n$with decoder only side information$Y_1^n$depends on both the block length$n$and the decoding block error probability$\epsilon_n$, and is defined as the difference between the minimum average compression rate of order$n$variable rate Slepian–Wolf codes having the decoding block error probability less than or equal to$\epsilon_n$, and the conditional entropy$H(X\vert Y)$, where$H(X\vert Y)$is the conditional entropy rate of the source given the side information. The redundancy of fixed rate Slepian–Wolf coding of$X_1^n$with decoder only side information$Y_1^n$is defined similarly and denoted by$R^n_F(\epsilon_n)$. It is proved that under mild assumptions about$\epsilon_n,$$R^n(\epsilon_n) = d_v \sqrt{-\log\epsilon_n/n} + o(\sqrt{-\log \epsilon_n/n})$and$R^n_{F}(\epsilon_n) = d_f \sqrt{- \log \epsilon_n / n} + o(\sqrt{-\log \epsilon_n/n})$, where$d_f$and$d_v$are two constants completely determined by the joint distribution of the source-side information pair. Since$d_v$is generally smaller than$d_f$, our results show that variable rate Slepian–Wolf coding is indeed more efficient than fixed rate Slepian–Wolf coding.
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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 | 0.009 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.003 | 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".