Optimal Design of Multiple Description Lattice Vector Quantizers
Bibliographic record
Abstract
In the design of multiple description lattice vector quantizers (MDLVQ), index assignment plays a critical role. In addition, one also needs to choose the Voronoi cell size of the central lattice v, the sublattice index N, and the number of side descriptions K to minimize the expected MDLVQ distortion, given the total entropy rate of all side descriptions Rt and description loss probability p. In this paper we propose a linear-time MDLVQ index assignment algorithm for any K >= 2 balanced descriptions in any dimensions, based on a new construction of so-called K-fraction lattice. The algorithm is greedy in nature but is proven to be asymptotically (N -> infinity) optimal for any K >= 2 balanced descriptions in any dimensions, given Rt and p. The result is stronger when K = 2: the optimality holds for finite N as well, under some mild conditions. For K > 2, a local adjustment algorithm is developed to augment the greedy index assignment, and conjectured to be optimal for finite N. Our algorithmic study also leads to better understanding of v, N and K in optimal MDLVQ design. For K = 2 we derive, for the first time, a non-asymptotical closed form expression of the expected distortion of optimal MDLVQ in p, Rt, N. For K > 2, we tighten the current asymptotic formula of the expected distortion, relating the optimal values of N and K to p and Rt more precisely.
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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 | 0.000 | 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 | 0.002 | 0.002 |
| Research integrity | 0.000 | 0.001 |
| 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".