Asymptotic capacity and optimal precoding strategy of multi-level precode & forward in correlated channels
Bibliographic record
Abstract
We analyze a multi-level MIMO relaying system where a multiple-antenna transmitter sends data to a multiple-antenna receiver through several relay levels, also equipped with multiple antennas. Assuming correlated fading in each hop, each relay receives a faded version of the signal transmitted by the previous level, performs precoding on the received signal and retransmits it to the next level. Using free probability theory and assuming that the noise power at the relay levels - but not at the receiver - is negligible, a closed-form expression of the end-to-end asymptotic instantaneous mutual information is derived as the number of antennas in all levels grow large with the same rate. This asymptotic expression is shown to be independent from the channel realizations, to only depend on the channel statistics and to also serve as the asymptotic value of the end-to-end average mutual information. We also provide the optimal singular vectors of the precoding matrices that maximize the asymptotic mutual information : the optimal transmit directions represented by the singular vectors of the precoding matrices are aligned on the eigenvectors of the channel correlation matrices, therefore they can be determined only using the known statistics of the channel matrices and do not depend on a particular channel realization.
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How this classification was reachedexpand
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 | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.003 |
| Research integrity | 0.000 | 0.001 |
| 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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, 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".