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Network coding has recently received increasing attention to improve performance and increase capacity in both wired and wireless communication networks. In this paper, we focus on inter-session network coding, where multiple unicast sessions jointly participate in network coding. Wireless links are often unreliable because of varying channel conditions. We consider multi-hop unicast sessions over unreliable links and propose a distributed end-to-end transmission rate adjustment mechanism to maximize the aggregate network utility by taking into account the wireless link reliability information. This includes an elaborate modeling of end-to-end reliability. Simulation results show that by taking into account the reliability information, we can increase the network throughput by up to 100% for some network topologies. We can also increase the aggregate network utility significantly for various choices of utility functions.