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We present a system for collaborative video streaming in wired overlay networks. We propose a scheme that builds on both rateless codes and network coding in order to improve the system throughput and the video quality at clients. Our hybrid coding algorithm permits to efficiently exploit the available source and path diversity without the need for expensive routing nor scheduling algorithms. We consider specifically an architecture where multiple streaming servers simultaneously deliver video information to a set of clients. The servers apply Raptor coding on the video packets for error resiliency, and the overlay nodes selectively combine the Raptor coded video packets in order to increase the packet diversity in the system. We analyze the performance of selective network coding and describe its application to practical video streaming systems. We further compute an effective source and channel rate allocation in our collaborative streaming system. We estimate the expected symbol diversity at clients with respect to the coding choices. Then we cast a minmax quality optimization problem that is solved by a low-cost bisection based method. The experimental evaluation demonstrates that our system typically outperforms Raptor video streaming systems that do not use network coding as well as systems that perform decoding and encoding in the network nodes. Finally, our solution has a low complexity and only requires small buffers in the network coding nodes, which are certainly two important advantages toward deployment in practical streaming systems.