Network coding performance for reliable multicast

The capacity gain of network coding has been extensively studied in wired and wireless networks. Recently, it has been shown that network coding improves network reliability by reducing the number of packet retransmissions in lossy networks. However, the extent of the reliability benefit of network coding is not known. This paper quantifies the reliability gain of network coding for reliable multicasting in a wireless network where network coding is the most promising. We define the expected number of transmissions per packet as the performance metric for reliability and derive analytical expressions characterizing the performance of network coding. For a tree-based multicast, we derive expressions for the expected number of transmissions at the source of the multicast and inside the multicast free. We also analyze the performance of error control mechanisms based on rateless codes and automatic repeat request (ARQ). We then use the analytical expressions to study the impact of multicast group size on the performance of different error control schemes. Our numerical results show that network coding significantly reduces the number of retransmissions in lossy networks compared to end-to-end ARQ scheme, however, rateless coding and link-by-link ARQ are able to achieve performance results comparable to that of network coding. Interestingly, link-by-link ARQ can outperform rateless coding depending on the network size and loss probability. We conjecture that network coding achieves a logarithmic reliability gain with respect to multicast group size compared to a simple ARQ scheme.