Author
Kumar K. R. Dinesh
Bio: Kumar K. R. Dinesh is an academic researcher from Indian Institute of Technology Madras. The author has contributed to research in topics: System of polynomial equations & Air cooling. The author has an hindex of 1, co-authored 2 publications receiving 3 citations.
Papers
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28 Jun 2009TL;DR: This article provides an alternative derivation of the information flow tree approach that results in two further extensions to networks with cycles, which are to flow acyclic solutions on any directed cyclic network and to cyclic networks where all strongly connected components are simple cycles.
Abstract: Algebraic criteria for existence of scalar linear network codes to satisfy a set of connection requirements has been discussed extensively by Koetter and Medard. Solving for a network code is now known to be equivalent to solving a system of polynomial equations obtained by assigning variables to edges in the line graph of the network and computing a suitable transfer function. An alternative formulation for arriving at an equivalent system of polynomial equations is given in this paper based on the decomposition of the original network into trees, which we call “information flow trees”. The basic idea is to exploit the graph structure and assign variables suitably. Interestingly, the information flow tree approach results in only linear and degree-2 equations that can be simplified considerably in directed acyclic networks as shown in prior work. In this article, we provide an alternative derivation of the information flow tree approach that results in two further extensions to networks with cycles. The first extension is to flow acyclic solutions on any directed cyclic network. The second extension is to cyclic networks where all strongly connected components are simple cycles. Here the degree of the equations we are left to solve is limited to 4.
3 citations
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Cited by
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01 Jan 2014
TL;DR: A particular binding is found for the variables sets of these streaming high level Petri graphs in such a way the sink places in the net graph which models the acyclic communication network can be marked with the requested marking.
Abstract: In this paper, we model an acyclic communication network as a net graph, and we use this net graph to define inter session-network coding as high level Petri graph. We then model inter-session network coding as a set of streaming high level Petri net graphs. Finally, we find a particular binding for the variables sets of these streaming high level Petri graphs in such a way the sink places in the net graph which models the acyclic communication network can be marked with the requested marking.
1 citations
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TL;DR: In this paper, the authors consider a two-unicast-Z$ network over a directed acyclic graph of unit capacitated edges, and show that vector linear codes outperform scalar linear codes and non-linear codes in general, and develop a commutative algebraic approach to derive linear network coding achievability results.
Abstract: We consider a two-unicast-$Z$ network over a directed acyclic graph of unit capacitated edges; the two-unicast-$Z$ network is a special case of two-unicast networks where one of the destinations has apriori side information of the unwanted (interfering) message. In this paper, we settle open questions on the limits of network coding for two-unicast-$Z$ networks by showing that the generalized network sharing bound is not tight, vector linear codes outperform scalar linear codes, and non-linear codes outperform linear codes in general. We also develop a commutative algebraic approach to deriving linear network coding achievability results, and demonstrate our approach by providing an alternate proof to the previous results of C. Wang et. al., I. Wang et. al. and Shenvi et. al. regarding feasibility of rate $(1,1)$ in the network.
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01 Jun 2017TL;DR: Open questions on the limits of network coding for two-unicast-Z networks are settled by showing that the generalized network sharing bound is not tight, vector linear codes outperform scalar linear codes, and nonlinear codes outperforms linear codes in general.
Abstract: We consider a two-unicast-Z network over a directed acyclic graph of unit capacitated edges; the two-unicast-Z network is a special case of two-unicast networks where one of the destinations has apriori side information of the unwanted (interfering) message. In this paper, we settle open questions on the limits of network coding for two-unicast-Z networks by showing that the generalized network sharing bound is not tight, vector linear codes outperform scalar linear codes, and nonlinear codes outperform linear codes in general. We also develop a commutative algebraic approach to deriving linear network coding achievability results, and demonstrate our approach by providing an alternate proof to the previous result of Wang et. al. regarding feasibility of rate (1,1) in the network.