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Bibliographic record
Abstract
<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> In this paper, the redundancy of both variable and fixed rate Slepian–Wolf coding is considered. Given any jointly memoryless source-side information pair <emphasis emphasistype="italic"><formula formulatype="inline"><tex Notation="TeX">$\{(X_i, Y_i)\}_{i=1}^{\infty}$</tex></formula></emphasis> with finite alphabet, the redundancy <emphasis emphasistype="italic"><formula formulatype="inline"> <tex Notation="TeX">$R^n(\epsilon_n)$</tex></formula></emphasis> of variable rate Slepian–Wolf coding of <emphasis emphasistype="italic"><formula formulatype="inline"><tex Notation="TeX">$X_1^n$</tex></formula></emphasis> with decoder only side information <emphasis emphasistype="italic"><formula formulatype="inline"> <tex Notation="TeX">$Y_1^n$</tex></formula></emphasis> depends on both the block length <emphasis emphasistype="italic"><formula formulatype="inline"> <tex Notation="TeX">$n$</tex></formula></emphasis> and the decoding block error probability <emphasis emphasistype="italic"><formula formulatype="inline"> <tex Notation="TeX">$\epsilon_n$</tex></formula></emphasis>, and is defined as the difference between the minimum average compression rate of order <emphasis emphasistype="italic"><formula formulatype="inline"><tex Notation="TeX">$n$</tex> </formula></emphasis> variable rate Slepian–Wolf codes having the decoding block error probability less than or equal to <emphasis emphasistype="italic"><formula formulatype="inline"><tex Notation="TeX">$\epsilon_n$</tex></formula></emphasis>, and the conditional entropy <emphasis emphasistype="italic"><formula formulatype="inline"> <tex Notation="TeX">$H(X\vert Y)$</tex></formula></emphasis>, where <emphasis emphasistype="italic"><formula formulatype="inline"><tex Notation="TeX">$H(X\vert Y)$</tex></formula></emphasis> is the conditional entropy rate of the source given the side information. The redundancy of fixed rate Slepian–Wolf coding of <emphasis emphasistype="italic"><formula formulatype="inline"><tex Notation="TeX">$X_1^n$</tex></formula></emphasis> with decoder only side information <emphasis emphasistype="italic"><formula formulatype="inline"><tex Notation="TeX">$Y_1^n$</tex> </formula></emphasis> is defined similarly and denoted by <emphasis emphasistype="italic"><formula formulatype="inline"><tex Notation="TeX">$R^n_F(\epsilon_n)$</tex></formula></emphasis>. It is proved that under mild assumptions about <emphasis emphasistype="italic"><formula formulatype="inline"><tex Notation="TeX">$\epsilon_n,$</tex></formula></emphasis> <emphasis emphasistype="italic"><formula formulatype="inline"><tex Notation="TeX">$R^n(\epsilon_n) = d_v \sqrt{-\log\epsilon_n/n} + o(\sqrt{-\log \epsilon_n/n})$</tex></formula></emphasis> and <emphasis emphasistype="italic"><formula formulatype="inline"><tex Notation="TeX">$R^n_{F}(\epsilon_n) = d_f \sqrt{- \log \epsilon_n / n} + o(\sqrt{-\log \epsilon_n/n})$</tex></formula></emphasis>, where <emphasis emphasistype="italic"><formula formulatype="inline"><tex Notation="TeX">$d_f$</tex> </formula></emphasis> and <emphasis emphasistype="italic"><formula formulatype="inline"> <tex Notation="TeX">$d_v$</tex></formula></emphasis> are two constants completely determined by the joint distribution of the source-side information pair. Since <emphasis emphasistype="italic"><formula formulatype="inline"><tex Notation="TeX">$d_v$</tex> </formula></emphasis> is generally smaller than <emphasis emphasistype="italic"><formula formulatype="inline"><tex Notation="TeX">$d_f$</tex></formula></emphasis>, our results show that variable rate Slepian–Wolf coding is indeed more efficient than fixed rate Slepian–Wolf coding. </para>
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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 | 0.001 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 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