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Generalized Mm,r-Network: A Case for Fixed Message Dimensions
Journal article   Peer reviewed

Generalized Mm,r-Network: A Case for Fixed Message Dimensions

Vikrant Singh, Behrouz Zolfaghari, Chunduri Venkata Dheeraj Kumar, Brijesh Kumar Rai, Khodakhast Bibak, Gautam Srivastava, Swapnoneel Roy and Takeshi Koshiba
IEEE communications letters, Vol.24(1), pp.38-42
01/2020
DOI: https://doi.org/10.1109/LCOMM.2019.2950193
Web of Science ID: WOS:000508630200009

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Abstract

In this letter, we first present a class of networks named Generalized M-m,M- r-Network for every integer m >= 2 and for all r is an element of {0, 1, ..., 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-m,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-m,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-m,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-m,M- r-Network, our studies pose some open problems which make the Generalized M-m,M- r-Network an attractive topic for further research.

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