Lower bounds on the maximum energy benefit of network coding for wireless multiple unicast

Authors:
Jasper Goseling;Ryutaroh Matsumoto;Tomohiko Uyematsu;Jos H. Weber
Affiliations:
Faculty of Electrical Engineering, Mathematics and Computer Science, Delft University of Technology, Delft, The Netherlands and Faculty of Electrical Engineering, Mathematics and Computer Science, ...;Department of Communication and Integrated System, Tokyo Institute of Technology, Tokyo, Japan;Department of Communication and Integrated System, Tokyo Institute of Technology, Tokyo, Japan;Faculty of Electrical Engineering, Mathematics and Computer Science, Delft University of Technology, Delft, The Netherlands
Venue:
EURASIP Journal on Wireless Communications and Networking - Special issue on network coding for wireless networks
Year:
2010

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Abstract

We consider the energy savings that can be obtained by employing network coding instead of plain routing in wireless multiple unicast problems. We establish lower bounds on the benefit of network coding, defined as the maximum of the ratio of the minimum energy required by routing and network coding solutions, where the maximum is over all configurations. It is shown that if coding and routing solutions are using the same transmission range, the benefit in d-dimensional networks is at least 2d/⌊√d⌋. Moreover, it is shown that if the transmission range can be optimized for routing and coding individually, the benefit in 2-dimensional networks is at least 3. Our results imply that codes following a decode-and-recombine strategy are not always optimal regarding energy efficiency.