TY - JOUR

T1 - GeneralizedMm,r-Network

T2 - A Case for Fixed Message Dimensions

AU - Singh, Vikrant

AU - Zolfaghari, Behrouz

AU - Kumar, Chunduri Venkata Dheeraj

AU - Rai, Brijesh Kumar

AU - Bibak, Khodakhast

AU - Srivastava, Gautam

AU - Roy, Swapnoneel

AU - Koshiba, Takeshi

N1 - Publisher Copyright:
© 1997-2012 IEEE.
Copyright:
Copyright 2020 Elsevier B.V., All rights reserved.

PY - 2020/1

Y1 - 2020/1

N2 - 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.

AB - 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.

KW - Generalized M-Networks

KW - Network coding

KW - fixed message dimension

KW - linear coding capacity

UR - http://www.scopus.com/inward/record.url?scp=85078536163&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85078536163&partnerID=8YFLogxK

U2 - 10.1109/LCOMM.2019.2950193

DO - 10.1109/LCOMM.2019.2950193

M3 - Article

AN - SCOPUS:85078536163

VL - 24

SP - 38

EP - 42

JO - IEEE Communications Letters

JF - IEEE Communications Letters

SN - 1089-7798

IS - 1

M1 - 8886606

ER -