Relay-aided interference alignment for the quasi-static X channel
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Bibliographic record
Abstract
In this paper, we first introduce a simple procedure for aligning interference directions in an M×N user MIMO X channel. The scheme is then modified for an M×2 user X channel in which each user is equipped with M + 1 antennas. Next we investigate the degrees of freedom (DOF) for a single antenna X channel in slow fading environments with the help of a simple relay. The relay stores all the received signals and sends their linear combination in subsequent transmissions. Using this scheme, it is shown that adding a relay can help the system to achieve all the available DOF. It is also proved that if the relay's output power scales with P/(log P) <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">s</sup> , there is no loss in the achieved DOF as long as s > 0. In other words, in a network with quasi-static channels, it is possible to achieve a higher DOF through the use of randomizing relays whose powers grow at a much slower rate than the main transmitters. Similarly, when there are stricter constraints on the output power scaling of the transmitters, all the DOF can still be utilized, if the relay power can grow with P/(log P) <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">t</sup> for any t > 0. These results suggest that adding relays to a network can be beneficial in terms of simultaneously acquiring higher DOF.
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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