GeneralizedMm,r-Network: A Case for Fixed Message Dimensions
Document Type
Article
Publication Date
1-1-2020
Abstract
In this letter, we first present a class of networks named Generalized {{M}}_{{ \textit {m, r}}} -Network for every integer {m} \geq 2 and \forall {r} \in \{0, 1,\ldots, {m}-1\} and we show that every network of this class admits a vector linear solution if and only if the message dimension is an integer multiple of {m}. We show that the Generalized {M} -Network presented in the work of Das and Rai and the Dim- {m} Network introduced in the work of Connelly and Zeger which are generalizations to the {M} -Network can be considered as special cases of Generalized {M}_{\textit {m, r}} -Network for {r}=1 and {r}={m}-1 respectively. Then we focus on a problem induced by depending on integer multiples of {m} as message dimensions to achieve the linear coding capacity in the class of Generalized {M}_{\textit {m, r}} (proven to be equal to 1). We note that for large values of {m} , packet sizes will grow beyond feasible thresholds in real-world networks. This motivates us to examine the capacity of the network in the case of fixed message dimensions. A study on the contrast among the impacts of fixed message dimensions in different networks of class {M}_{\textit {m, r}} -Network highlights the importance of the examined problem. In addition to complete/partial solutions obtained for different networks of the class Generalized {M}_{\textit {m, r}} -Network, our studies pose some open problems which make the Generalized {M}_{\textit {m, r}} -Network an attractive topic for further research.
Publication Title
IEEE Communications Letters
Volume
24
Issue
1
First Page
38
Last Page
42
Digital Object Identifier (DOI)
10.1109/LCOMM.2019.2950193
ISSN
10897798
E-ISSN
15582558
Citation Information
V. Singh et al., "Generalized $M_{m,r}$ -Network: A Case for Fixed Message Dimensions," in IEEE Communications Letters, vol. 24, no. 1, pp. 38-42, Jan. 2020, doi: 10.1109/LCOMM.2019.2950193.