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Forward error correction (FEC) coding is the preferred error correction technique for interactive video streaming applications on the Internet. Because its performance is impaired by the burstiness of packet loss of Internet links, peer-to-peer (P2P) networks are often proposed to provide multiple paths between a sender and a receiver. However, peers may leave abruptly and the number of disjoint paths may be limited; it is unclear whether or when the use of P2P networks for path diversity can be justified. In this paper, we study the packet loss ratio after FEC correction when using P2P networks to provide multiple paths. We examine two situations: a sender can find enough disjoint paths, or uses a limited number of disjoint paths. We model Internet links using Markov chains, provide numerical analysis of the performance of systematic FEC codes, and verify the results by simulation. We find that although using P2P networks for path diversity often results in a lower post-FEC loss ratio, conditions apply. There exist guidelines but no simple formula to determine when to use P2P networks for path diversity and coding parameters. An application should carefully evaluate the performance gain before taking actions.