Gaussian Z-Interference Channel With a Relay Link: Achievability Region and Asymptotic Sum Capacity
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Bibliographic record
Abstract
This paper studies a Gaussian Z-interference channel with a rate-limited digital relay link from one receiver to another. Achievable rate regions are derived based on a combination of a Han–Kobayashi common-private power-splitting technique and either a compress-and-forward relay strategy or a decode-and-forward strategy for interference subtraction at the other end. For the Gaussian Z-interference channel with a digital link from the interference-free receiver to the interfered receiver, the capacity region is established in the strong interference regime; an achievable rate region is established in the weak interference regime. In the weak interference regime, the decode-and-forward strategy is shown to be asymptotically sum-capacity achieving in the high signal-to-noise ratio and high interference-to-noise ratio limit. In this case, each relay bit asymptotically improves the sum capacity by one bit. For the Gaussian Z-interference channel with a digital link from the interfered receiver to the interference-free receiver, the capacity region is established in the strong interference regime; achievable rate regions are established in the moderately strong and weak interference regimes. In addition, the asymptotic sum capacity is established in the limit of a large relay link rate. In this case, the sum capacity improvement due to the digital link is bounded by half a bit when the interference link is weaker than a certain threshold, but the sum capacity improvement becomes unbounded when the interference link is strong.
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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) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.003 |
| 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)
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Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
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