Multicast Triangular Semilattice Network

TL;DR

This paper analyzes the structure of multicast triangular semilattice networks, providing criteria for receiver placement validity, invariance properties, and a comprehensive study of small network cases.

Contribution

It introduces new criteria and invariance properties for code graphs of multicast triangular networks, extending understanding up to four sources.

Findings

Criteria for receiver placement validity established

Invariance properties under network symmetries demonstrated

Complete analysis of networks with up to four sources

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 4 sources. We also improve on various definitions related to code graphs.