On Optimum Conventional Quantization for Source Coding with Side Information at the Decoder
Bibliographic record
Abstract
LetXandYdenote two jointly memoryless sources with finite alphabets. Suppose thatXis to be encoded in a lossy manner withYas the side information available only at the decoder. A common approach to this lossy source coding problem is to apply conventional vector quantization followed by Slepian-Wolf coding. In this paper we are interested in the rate-distortion performance achievable asymptotically by this approach. Given an arbitrary single letter distortion measured, it is shown that the best rate achievable asymptotically under the constraint that X is recovered with distortion level no greater thanD ≥ 0isR̂wz(D) = mintimes[I(X;X̂)-I(Y; X̂)], where the minimum is taken over all auxiliary random variablesXsuch thatEd(X, X̂) ≤ DandX ̂⟶ X ⟶ Yis a Markov chain. An extended Blahut-Arimoto algorithm is then proposed to calculateR̂wz(D)for any(X,Y)and any distortion measure, and the convergence of the algorithm is also proved. Interestingly, it is observed that the random variableX̂achievingR̂wz(D)is, in general, different from the random variableX̂'achieving the classical rate-distortion functionR(D)ofXat distortionD. In particular, it is shown that in the case of binary sources and Hamming distortion measure, the random variableXachievingRwz(D)is the same as the random variableX'achievingR(D)if and only if the channelPY|XfromXtoYis symmetric. Thus, the design of conventional quantization in the case of side information at the decoder should be different from the case of no side information.
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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 | 0.006 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 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) | 0.003 | 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".