Memory-Rate Tradeoff for Caching With Uncoded Placement Under Nonuniform Random Demands
Bibliographic record
Abstract
This paper considers a caching system of a single server and multiple users. We aim to characterize the memory-rate tradeoff for caching with uncoded cache placement, under nonuniform file popularity. Focusing on the modified coded caching scheme (MCCS) recently proposed by Yu,etal., we formulate the cache placement optimization problem for the MCCS to minimize the average delivery rate under nonuniform file popularity, restricting to a class of popularity-first placements. We then present two information-theoretic lower bounds on the average rate for caching with uncoded placement, one for general cache placements and the other restricted to the popularity-first placements. By comparing the average rate of the optimized MCCS with the lower bounds, we prove that the optimized MCCS attains the general lower bound for the two-user case, providing the exact memory-rate tradeoff. Furthermore, it attains the popularity-first-based lower bound for the case of general$K$users with distinct file requests. In these two cases, our results also reveal that the popularity-first placement is optimal for the MCCS, and zero-padding used in coded delivery incurs no loss of optimality. For the case of$K$users with redundant file requests, our analysis shows that there may exist a gap between the optimized MCCS and the lower bounds due to zero-padding. We next fully characterize the optimal popularity-first cache placement for the MCCS, which is shown to possess a simple file-grouping structure and can be computed via an efficient algorithm using closed-form expressions. Finally, we extend our study to accommodate nonuniformity in both file popularity and size, where we show that the optimized MCCS attains the lower bound for the two-user case, providing the exact memory-rate tradeoff. Numerical results show that, for general settings, the gap between the optimized MCCS and the lower bound only exists in limited cases and is very small.
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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 | 0.003 | 0.021 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.001 | 0.002 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.002 | 0.004 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.001 | 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 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".