Minimum Feedback for Collision-Free Scheduling in Massive Random Access
Why this work is in the frame
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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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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 | 0.000 |
| 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 it