Bibliographic record
Abstract
Tensors are multi-way arrays which can be used to model systems spanning many domains. This work proposes to use tensors for characterizing, analyzing, and designing multi-domain communication systems. Most modern day communication systems make use of coding and modulation across different domains such as space, frequency, time. Hence a unified mathematical framework characterizing such a multiple-domain system in an intuitive manner is well needed. In this paper, we present such a unified framework that characterizes a communication system with$N$input domains,$M$output domains and an$M+N$domains multi-linear tensor channel. The proposed framework is generic where the physical interpretation of the domains is system specific. We illustrate a few examples from multi-antenna multi-carrier and multi-user systems that fit the proposed framework. Assuming a fixed tensor channel, we provide an information theoretic analysis by deriving its Shannon capacity and input power allocation under a variety of power constraints. In this paper we show how the tensor framework’s suitability to mathematically describe a family of power constraints can be used to design and analyze various multiple domain communication systems. The tensor based approach extends water-filling from a matrix setting to tensors, encapsulating the effects of multiple domains thereby allowing joint multi-domain precoding. We show that the capacity pre-log for a tensor channel increases exponentially in the number of domains, indicating the potential of tensor based multi-domain communication systems to provide the large information transmission rates envisaged for 5G and beyond systems. We also show the application of the tensor framework in characterizing the capacity and rate regions of multi-user MIMO channels. Both multiple access and interference channels are considered where the tensor based approach leads to a coordinated users transmission scheme. Such a scheme ensures higher achievable sum rates as compared to independent user transmissions.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.005 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.002 | 0.003 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.004 | 0.001 |
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 source (direct Gemma or distilled Codex), 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".