Vol. 12, No. 8, 2019

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Multicast triangular semilattice network

Angelina Grosso, Felice Manganiello, Shiwani Varal and Emily Zhu

Vol. 12 (2019), No. 8, 1307–1328
Abstract

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
Mathematical Subject Classification 2010
Primary: 68P30, 68R10
Secondary: 11T06
Milestones
Received: 14 January 2019
Revised: 3 July 2019
Accepted: 31 August 2019
Published: 25 October 2019

Communicated by Nigel Boston
Authors
Angelina Grosso
Division of Applied Mathematics
Brown University
Providence, RI
United States
Felice Manganiello
School of Mathematical and Statistical Sciences
Clemson University
Clemson, SC
United States
Shiwani Varal
Faculty of Business, Law and Politics
University of Hull
Hull
United Kingdom
Emily Zhu
Department of Mathematics
University of California at San Diego
La Jolla, CA
United States