Network coding is a promising technique to improve the performance of wireless networks. In this paper, we establish the hexagram polling network model and propose a network coding scheme applied in this network. Based on the fact that one of the lost data blocks in a certain polling round may be recovered by the network coded data block, we establish a group of linear equations. Then we compute the average outage probability of the network coding scheme by solving the group of linear equations. Analytical results show that the network coding scheme outperforms non-network coding scheme when each source broadcasts one data block per polling round. We also study how the location of source nodes influences the performance gain brought by network coding. Results reveal that the performance gain brought by network coding becomes greater when the distances from the sources to the destination become larger.
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