Network coding has recently attracted attention as a substantial improvement to packet retransmission schemes in wireless multicast broadcast services (MBS). Since the problem of finding the optimal network code maximizing the bandwidth efficiency is hard to solve and hard to approximate, two main network coding heuristic schemes, namely opportunistic and full network coding, were suggested in the literature to improve the MBS bandwidth efficiency. However, each of these two schemes usually outperforms the other in different receiver, demand, and feedback settings. The continuous and rapid change of these settings in wireless networks limits the bandwidth efficiency gains if only one scheme is always employed. In this paper, we propose an adaptive scheme that maintains the highest bandwidth efficiency obtainable by both opportunistic and full network coding schemes in wireless MBS. The proposed scheme adaptively selects, between these two schemes, the one that is expected to achieve the better bandwidth efficiency performance. The core contribution in this adaptive selection scheme lies in our derivation of performance metrics for opportunistic network coding, using random graph theory, which achieves efficient selection when compared to appropriate full network coding parameters. To compare between different complexity levels, we present three approaches to compute the performance metric for opportunistic coding using different levels of knowledge about the opportunistic coding graph. For the three considered approaches, simulation results show that our proposed scheme almost achieves the bandwidth efficiency performance that could be obtained by the optimal selection between the opportunistic and full coding schemes.
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