Capacity of random network coding under a probabilistic error model

A probabilistic error model for random network coding is considered. An upper bound on capacity is obtained for any channel parameters, and asymptotic expressions are provided in the limit of long packet length and/or large field size. A simple and efficient coding scheme is provided that achieves capacity in both limiting cases. The scheme has zero error probability and a probability of failure that decreases exponentially both in the packet length and in the field size in bits.