How much feedback is required in MIMO Broadcast Channels?
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Bibliographic record
Abstract
In this paper, a downlink communication system, in which a base station (BS) equipped with M antennas communicates with N users each equipped with K receive antennas is considered. We study the minimum required amount of feedback at the BS, in order to achieve the maximum sum-rate capacity. First, we define the amount of feedback as the average number of users who send information to the BS. In the asymptotic case of N rarr infin, we show that with finite amount of feedback, it is not possible to achieve the maximum sum-rate. Indeed, in order to reduce the gap between the achieve sum-rate and the optimum value to zero, a minimum feedback of ln ln ln N is asymptotically necessary. Then, we consider a practical scenario, in which the amount of feedback is defined as the average number of bits which is sent to the BS. We show that to achieve the maximum sum-rate, infinite amount of feedback is required. Moreover, the minimum amount of feedback, in order to reduce the gap to the optimum sum-rate to zero, scales as otimes(ln ln ln N), which is achievable by the random beam-forming scheme proposed in M. Sharif and B. Hassibi, (2005)
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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