On optimizing low SNR wireless networks using network coding

Abstract

The rate optimization for wireless networks with low SNR is investigated. While the capacity in the limit of disappearing SNR per degree of freedom is known to be linear in SNR 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 physically degraded 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 in a low SNR physically degraded broadcast channel and multiple access environment 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). Index Terms - Low SNR degraded broadcast channel, network coding, rate optimization, Primal-Dual Subgradient Method.