Opportunistic network coding: Competitive analysis

It was recently shown that the reverse carpooling technique can realize the benefits of network coding while requiring only a simple coding scheme that can be efficiently implemented in practice. However, when no opportunity for coding exists at an intermediate (relay) node, it needs to decide whether to transmit an uncoded packet or wait for the next opportunity to create a coded packet. While the decision to wait for the next coding opportunity can reduce the number of transmissions, it incurs a penalty in terms of packet delay. In this paper we present an on-line algorithm for making transmit/wait decisions at the relay nodes. The algorithm minimizes the total system cost that includes both the number of transmissions as well as packet delay. Our algorithm is based on the primal-dual approach and achieves the competitive ratio of e/(e - 1).