Minimum Feedback for Collision-Free Scheduling in Massive Random Access
Bibliographic record
Abstract
This paper considers a massive random access scenario where a small random set of k active users out of a larger number of n total potential users seek to transmit data to a base station. Specifically, we examine an approach in which the base station first determines the set of active users based on an uplink pilot phase, then broadcasts a common feedback message to all the active users for the scheduling of their subsequent data transmissions. Our main question is: What is the minimum amount of common feedback needed to schedule k users in k slots while completely avoiding collisions? Instead of a naive scheme of using k log(n) feedback bits, this paper presents upper and lower bounds to show that the minimum number of required common feedback bits scales linearly in k, plus an additive term that scales only as Θ(log log(n)). The achievability proof is based on a random coding argument. We further connect the problem of constructing a minimal length feedback code to that of finding a minimal set of complete k-partite subgraphs that form an edge covering of a k-uniform complete hypergraph with n vertices. Moreover, the problem is also equivalent to that of finding a minimal perfect hashing family, thus allowing leveraging the explicit perfect hashing code constructions for achieving collision-free massive random access.
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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 | 0.014 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.002 |
| 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".