Computing Vector-Linear Functions on Diamond Network

Network function computation is investigated in the letter. In the model, a target function, of which the inputs are generated at multiple source nodes, is required to be computed with zero error at a sink node over a network. Toward this end, distributed coding by integrating communication and comp...

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Veröffentlicht in:	IEEE communications letters Jg. 26; H. 7; S. 1519 - 1523
Hauptverfasser:	Li, Dan, Xu, Yinfei
Format:	Journal Article
Sprache:	Englisch
Veröffentlicht:	New York IEEE 01.07.2022 The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Schlagworte:	Codes Combinatorial analysis Computational modeling computing capacity Diamond diamond network Diamonds Encoding Function computation Information theory integration of communication and computation Linear functions Relays Symbols Topology Upper bound
ISSN:	1089-7798, 1558-2558
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Abstract	Network function computation is investigated in the letter. In the model, a target function, of which the inputs are generated at multiple source nodes, is required to be computed with zero error at a sink node over a network. Toward this end, distributed coding by integrating communication and computation in networks is regarded as an efficient solution. We are interested in its fundamental computing capacity of importance in theory and applications. In the letter, we explicitly characterize the capacities of computing all the vector-linear functions over the diamond network. The diamond network has an important topology structure which not only is typical for many multi-terminal information-theoretic problems but also illustrates the combinatorial nature of the computing problem. By applying the computing capacities thus obtained, we solve the solvability problem of vector-linear functions over the diamond network. We determine all the solvable vector-linear functions and obtain an enhanced result that the remaining vector-linear functions are not only linearly non-solvable but also non-linearly non-solvable.
AbstractList	Network function computation is investigated in the letter. In the model, a target function, of which the inputs are generated at multiple source nodes, is required to be computed with zero error at a sink node over a network. Toward this end, distributed coding by integrating communication and computation in networks is regarded as an efficient solution. We are interested in its fundamental computing capacity of importance in theory and applications. In the letter, we explicitly characterize the capacities of computing all the vector-linear functions over the diamond network. The diamond network has an important topology structure which not only is typical for many multi-terminal information-theoretic problems but also illustrates the combinatorial nature of the computing problem. By applying the computing capacities thus obtained, we solve the solvability problem of vector-linear functions over the diamond network. We determine all the solvable vector-linear functions and obtain an enhanced result that the remaining vector-linear functions are not only linearly non-solvable but also non-linearly non-solvable.
Author	Li, Dan Xu, Yinfei
Author_xml	– sequence: 1 givenname: Dan orcidid: 0000-0001-8744-1041 surname: Li fullname: Li, Dan email: lidaneileen@163.com organization: Department of Mathematics, Tianjin University of Technology, Tianjin, China – sequence: 2 givenname: Yinfei orcidid: 0000-0003-3191-6903 surname: Xu fullname: Xu, Yinfei email: yinfeixu@seu.edu.cn organization: School of Information Science and Engineering, Southeast University, Nanjing, China
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SubjectTerms	Codes Combinatorial analysis Computational modeling computing capacity Diamond diamond network Diamonds Encoding Function computation Information theory integration of communication and computation Linear functions Relays Symbols Topology Upper bound
Title	Computing Vector-Linear Functions on Diamond Network
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