Bit-Error Resilient Index Assignment for Multiple Description Scalar Quantizers
Bibliographic record
Abstract
This paper addresses the problem of increasing the robustness to bit errors for two description scalar quantizers. Our approach is to start with an m-diagonal index assignment and further apply a permutation to the indexes of each description to increase the minimum Hamming distance d <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">min</sub> of the set of valid index pairs. In particular, we show how to construct linear permutation pairs achieving d <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">min</sub> 3, and establish a lower bound in terms of the description rate R, for the highest value of m for which such permutations exist. For the case when one description is known to be correct, we propose a new performance measure, denoted by dside,min. This represents the minimum Hamming distance of the set of indexes of one description, when the index of the other description is fixed. We prove the close connection between the problem of robust permutations design under the new criterion and the anti-bandwidth problem in a certain graph derived from a hypercube. Leveraging this connection, we settle the problem of existence of permutations achieving d <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">side,min</sub> ≥ 2, respectively d <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">min</sub> ≥ 2, and show their construction. Further, we develop a technique for constructing linear permutation pairs achieving d <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">side,min</sub> ≥ h based on linear (R, ⌈log2 m⌉) channel codes of minimum Hamming distance h + 1. In addition, tight bounds in terms of R, on the maximum achievable value of d <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">side,min</sub> are derived for m = 2, 3, 4.
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How this classification was reachedexpand
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 | 0.001 | 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 | 0.003 |
| 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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, 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".