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Multicast
triangular semilattice network
Angelina Grosso, Felice Manganiello, Shiwani Varal and Emily Zhu
Vol. 12 (2019), No. 8, 1307–1328
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Abstract |
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We investigate the structure of the code graph of a multicast network that has a characteristic shape of an inverted equilateral triangle. We provide a criterion that determines the validity of a receiver placement within the code graph, present invariance properties of the determinants corresponding to receiver placements under symmetries, and provide a complete study of these networks’ receivers and required field sizes up to a network of four sources. We also improve on various definitions related to code graphs. |
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Keywords
multicast network, triangular semilattice, determinantal
condition, finite field, multivariate polynomial, linear
network coding, multicast communication, code graph
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Mathematical Subject Classification 2010
Primary: 68P30, 68R10
Secondary: 11T06
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Milestones
Received: 14 January 2019
Revised: 3 July 2019
Accepted: 31 August 2019
Published: 25 October 2019
Communicated by Nigel Boston
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Authors |
| Angelina Grosso | |
| Division of Applied
Mathematics Brown University Providence, RI United States |
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| Felice Manganiello | |
| School of Mathematical and
Statistical Sciences Clemson University Clemson, SC United States |
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| Shiwani Varal | |
| Faculty of Business, Law and
Politics University of Hull Hull United Kingdom |
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| Emily Zhu | |
| Department of Mathematics University of California at San Diego La Jolla, CA United States |
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