Sum-Networks from Undirected Graphs: Construction and Capacity Analysis
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 for constructing sum-networks with arbitrary capacities. Specifically, we answer an open question in prior work by demonstrating sum-networks with significantly fewer number of sources and terminals.
A. S. Tripathy and A. Ramamoorthy, "Sum-Networks from Undirected Graphs: Construction and Capacity Analysis," 2014 52nd Annual Allerton Conference on Communication, Control, and Computing, Allerton 2014, pp. 651 - 658, Institute of Electrical and Electronics Engineers (IEEE), Oct 2014.
The definitive version is available at https://doi.org/10.1109/ALLERTON.2014.7028517
52nd Allerton Conference on Communication, Control, and Computing (2014: Sep. 30-Oct. 3, Monticello, IL)
International Standard Book Number (ISBN)
Article - Conference proceedings
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03 Oct 2014