Open AccessOn characteristics dependent linear coding capacity of sum‐networks
Author(s) -
Rai Brijesh Kumar,
Das Niladri
Publication year - 2017
Publication title -
iet networks
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.466
H-Index - 21
eISSN - 2047-4962
pISSN - 2047-4954
DOI - 10.1049/iet-net.2016.0099
Subject(s) - linear network coding , finite field , coding (social sciences) , finite set , mathematics , field size , computer science , multicast , discrete mathematics , theoretical computer science , statistics , computer network , physics , mathematical analysis , network packet , imaging phantom , optics
It is known that the linear coding capacity of non‐multicast networks may depend on the characteristic of the finite field. Such a dependence has been demonstrated in several examples presented in the literature. However, in all such examples, the number of distinct values that the linear coding capacity can take over different characteristics of the finite field is two. For example, the Fano network has linear coding capacity equal to one over even characteristic, and has linear coding capacity equal to 4/5 over odd characteristics. It is a natural question that whether a network can have arbitrarily many different characteristics dependent linear coding capacities. In this study, the authors answer the question for sum‐networks, which are networks where the terminals demand the sum of the messages generated by the sources. Specifically, they show that given a set of characteristics (prime numbers) { p 1 ,p 2 , … ,p n } , indeed there exists a sum‐network such that for each different value of the characteristic of the finite field, the linear coding capacity of the sum‐network is different.