Compute-and-Forward: Optimization Over Multisource–Multirelay Networks
Bibliographic record
Abstract
In this paper, we investigate a multisource multicast network with the aid of an arbitrary number of relays, where it is assumed that no direct link is available at each S-D pair. The aim is to find the fundamental limit on the maximal common multicast throughput of all source nodes if resource allocations are available. A transmission protocol employing the relaying strategy, i.e., compute-and-forward (CPF), is proposed. We also adjust the methods in the literature to obtain the integer network-constructed coefficient matrix (i.e., a naive method, a local optimal method, and a global optimal method) to fit the general topology with an arbitrary number of relays. Three transmission scenarios are addressed. The first scenario is delay-stringent transmission, where each message must be delivered within one slot. The second scenario is delay-tolerant transmission where no delay constraint is imposed. The associated optimization problems to maximize the short- and long-term common multicast throughputs are formulated and solved, and the optimal allocation of power and time slots are presented. The third case (a general N-slot-delay-tolerant scenario) is also discussed, and a suboptimal algorithm is presented. Performance comparisons show that the CPF strategy outperforms conventional decode-and-forward (DF) strategy. It is also shown in the simulation that with more relays, the CPF strategy performs even better due to the increased diversity. Finally, by simulation, it is observed that, with CPF, the N-slot-delay-constraint case can perform close to that of the delay-tolerant case in terms of throughput, given that N is relatively large.
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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 | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.000 |
| 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".