Practical throughput analysis for two-hop wireless network coding

Network coding (NC) has been regarded as a promising technology for throughput improvement in wireless networks, so a thorough understanding on the possible throughput gain from using NC is essential for the application of such technology. Available studies of throughput gain from NC, which mainly focus on only coding sub-layer or both MAC layer and coding sub-layer but largely neglect the primary impact of physical-layer, may lead to an inaccurate (or even qualitatively incorrect) estimation of possible coding gain. To have a more thorough understanding on the practical throughput gain of NC, this paper explores the possible coding gain in the typical two-hop wireless relay network with a careful consideration of interactions among physical layer, MAC layer and coding sub-layer. We first develop an embedded Markov chain theoretical framework to capture the complicated interactions among physical layer, MAC layer and coding sub-layer, based on which the close-form expression of throughput is then derived. We further explore the optimal bandwidth allocation problem in relay nodes for throughput maximization, and also provide a coding condition to clarify the scenarios where network coding does improve the throughput. Our analysis indicates that network coding may actually degrade throughput under some scenarios that were misjudged as being beneficial by previous studies without a careful consideration of primary impact of physical-layer.