  Random linear network coding is a particularly decentralized approach to the
multicast problem. Use of random network codes introduces a non-zero
probability however that some sinks will not be able to successfully decode the
required sources. One of the main theoretical motivations for random network
codes stems from the lower bound on the probability of successful decoding
reported by Ho et. al. (2003). This result demonstrates that all sinks in a
linearly solvable network can successfully decode all sources provided that the
random code field size is large enough. This paper develops a new bound on the
probability of successful decoding.
