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Record W4225656449 · doi:10.1109/access.2022.3160187

The Tensor Multi-Linear Channel and Its Shannon Capacity

2022· article· en· W4225656449 on OpenAlex
Divyanshu Pandey, H. Leib

Why this work is in the frame

A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.

affAt least one author lists a Canadian institution in the pinned OpenAlex snapshot.
fundA Canadian funder is recorded on the work.

Bibliographic record

VenueIEEE Access · 2022
Typearticle
Languageen
FieldMathematics
TopicTensor decomposition and applications
Canadian institutionsMcGill University
FundersNatural Sciences and Engineering Research Council of Canada
KeywordsTensor (intrinsic definition)NotationChannel (broadcasting)PrecodingDomain (mathematical analysis)Computer scienceMathematicsTheoretical computer scienceTopology (electrical circuits)Pure mathematicsMIMOMathematical analysis

Abstract

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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 <inline-formula> <tex-math notation="LaTeX">$N$ </tex-math></inline-formula> input domains, <inline-formula> <tex-math notation="LaTeX">$M$ </tex-math></inline-formula> output domains and an <inline-formula> <tex-math notation="LaTeX">$M+N$ </tex-math></inline-formula> 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&#x2019;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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Full frame distilled prediction

Teacher imitation

Not 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.

metaresearch head score (Codex)0.000
metaresearch head score (Gemma)0.000
Version: codex-gemma-dda1882f352aValidation status: machine_predicted_unvalidated
Candidate categoriesnone
Consensus categoriesnone
DomainCandidate signal: none · Consensus signal: none
Study designCandidate signal: Theoretical or conceptual · Consensus signal: none
GenreCandidate signal: Empirical · Consensus signal: Empirical
Teacher disagreement score0.425
Threshold uncertainty score0.648

Codex and Gemma teacher scores by category

CategoryCodexGemma
Metaresearch0.0000.000
Meta-epidemiology (narrow)0.0000.000
Meta-epidemiology (broad)0.0000.000
Bibliometrics0.0000.000
Science and technology studies0.0010.000
Scholarly communication0.0000.000
Open science0.0000.000
Research integrity0.0000.000
Insufficient payload (model declined to judge)0.0000.000

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.

Opus teacher head0.187
GPT teacher head0.386
Teacher spread0.200 · how far apart the two teachers sit on this one work
Validation statusscore_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it