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Capacity Of Sum-Networks For Different Message Alphabets, Ardhendu Tripathy, Aditya Ramamoorthy
Capacity Of Sum-Networks For Different Message Alphabets, Ardhendu Tripathy, Aditya Ramamoorthy
Ardhendu Tripathy
A sum-network is a directed acyclic network in which all terminal nodes demand the `sum' of the independent information observed at the source nodes. Many characteristics of the well-studied multiple-unicast network communication problem also hold for sum-networks due to a known reduction between instances of these two problems. Our main result is that unlike a multiple unicast network, the coding capacity of a sum-network is dependent on the message alphabet. We demonstrate this using a construction procedure and show that the choice of a message alphabet can reduce the coding capacity of a sum-network from 1 to close to 0.
Sum-Networks From Undirected Graphs: Construction And Capacity Analysis View Document, Ardhendu Tripathy, Aditya Ramamoorthy
Sum-Networks From Undirected Graphs: Construction And Capacity Analysis View Document, Ardhendu Tripathy, Aditya Ramamoorthy
Ardhendu Tripathy
We consider a directed acyclic network with multiple sources and multiple terminals where each terminal is interested in decoding the sum of independent sources generated at the source nodes. We describe a procedure whereby a simple undirected graph can be used to construct such a sum-network and demonstrate an upper bound on its computation rate. Furthermore, we show sufficient conditions for the construction of a linear network code that achieves this upper bound. Our procedure allows us to construct sum-networks that have any arbitrary computation rate p/q (where p, q are non-negative integers). Our work significantly generalizes a previous approach …