A one-session multicast network, on which a coding scheme with networkcoding is defined, was implemented with a maximum common flow of $r$ -packets arriving simultaneously at $\vert T\vert $ sink nodes. Determining h...
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A one-session multicast network, on which a coding scheme with networkcoding is defined, was implemented with a maximum common flow of $r$ -packets arriving simultaneously at $\vert T\vert $ sink nodes. Determining how to order the $r$ -packets that emerge from the source node $s$ through their output $n$ -links, constitutes a combinatorial problem. In this work, the set of all the possible output configurations is constructed, where each configuration is a vector of packets tags of length equal to $n$ . Each tag has a length equal to $r$ . Through a combinatorial algorithm on the set of possible output configurations, a path is carried out on the graph representing the one-session multicast network. The path is based on a topological ordering of the multicast graph that allowed us finding all possible ways to order the output of the $r$ -packets from $s$ to the sink nodes in $T$ . An ordering configuration based on networkcoding is valid, if the coding of packets is achieved through a linear combination in the coding nodes and the decoding of packets in the sink nodes. This validation verifies, then, a one-session multicast solution. The proposal of this work is independent of the network topology, the maximum flow value, and the size of the packets.
This work proposes a model to solve the problem of networkcoding over a one-session multicast network. The model is based on a system of restrictions that defines the packet flows received in the sink nodes as functi...
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This work proposes a model to solve the problem of networkcoding over a one-session multicast network. The model is based on a system of restrictions that defines the packet flows received in the sink nodes as functions of the outgoing flows from the source node. A multicast network graph is used to derive a directed labeled line graph (DLLG). The successive powers of the DLLG adjacency matrix to the convergence in the null matrix permits the construction of the jump matrix Source-Sinks. In its reduced form, this shows the dependency of the incoming flows in the sink nodes as a function of the outgoing flows in the source node. The emerging packets for each outgoing link from the source node are marked with a tag that is a linear combination of variables that corresponds to powers of two. Restrictions are built based on the dependence of the outgoing and incoming flows and the packet tags as variables. The linear independence of the incoming flows to the sink nodes is mandatory. The method is novel because the solution is independent of the Galois field size where the packet contents are defined.
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