On the Energy Benefit of Network Coding for Wireless Multiple Unicast

TL;DR

This paper analyzes the potential energy savings of network coding over routing in wireless multiple unicast scenarios, providing lower bounds on the benefits and highlighting the limitations of decode-and-recombine strategies.

Contribution

It establishes theoretical lower bounds on energy benefits of network coding versus routing in wireless networks, considering fixed and optimized transmission ranges.

Findings

Benefit in d-dimensional networks is at least 2d/⌊√d⌋ with same transmission range.

Benefit in 2D networks is at least 3 with optimized transmission ranges.

Decode-and-recombine codes are not always energy optimal.

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 $2d/\lfloor\sqrt{d}\rfloor$. 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 \emph{decode-and-recombine} strategy are not always optimal regarding energy efficiency.