On optimizing low SNR wireless networks using network coding

TL;DR

This paper investigates rate optimization in low SNR wireless networks employing network coding, demonstrating that the problem simplifies to a linear power minimization and proposing a decentralized algorithm for optimal rate achievement.

Contribution

It introduces a linear programming approach for low SNR network rate optimization with network coding and develops a decentralized primal-dual algorithm for practical implementation.

Findings

The optimization reduces to a linear multi-commodity flow problem.

Network coding simplifies interference issues at low SNR.

The proposed algorithm achieves optimal rates in a decentralized manner.

Abstract

The rate optimization for wireless networks with low SNR is investigated. While the capacity in the limit of disappearing SNR is known to be linear for fading and non-fading channels, we study the problem of operating in low SNR wireless network with given node locations that use network coding over flows. The model we develop for low SNR Gaussian broadcast channel and multiple access channel respectively operates in a non-trivial feasible rate region. We show that the problem reduces to the optimization of total network power which can be casted as standard linear multi-commodity min-cost flow program with no inherent combinatorially difficult structure when network coding is used with non integer constraints (which is a reasonable assumption). This is essentially due to the linearity of the capacity with respect to vanishing SNR which helps avoid the effect of interference for the degraded broadcast channel and multiple access environment in consideration, respectively. We propose a fully decentralized Primal-Dual Subgradient Algorithm for achieving optimal rates on each subgraph (i.e. hyperarcs) of the network to support the set of traffic demands (multicast/unicast connections).