An analysis of packet loss correlation in FEC-enhanced multicast trees

We study group loss probabilities of forward error correction (FEC) codes in shared loss multicast communication. We present a new analysis model with explicit state equations using recursive formulae. Our method looks at an FEC group as a whole, rather than analyze the number of transmissions of a particular packet. Our work applies to C(n,k) erasure codes, where any k out of n packets may decode the entire group. We find the cumulative distribution function that all leaf nodes in a shared loss tree successfully decode a C(n,k) FEC group, the probability mass function (p.m.f.) for the number of leaf nodes that successfully decode a transmission group, the expected number of packets received on successful decode and the expected number of missing packets on decode failure for a particular leaf node of the multicast tree, the p.m.f. that all leaf nodes hold the same packets in common, and the expected height of packet loss. Most of our findings generalize to arbitrary trees with non-uniform link loss. Our results also apply to non-FEC trees. We illustrate applications of our work with examples.