On noncoherent correction of network errors and erasures with random locations

We consider the problem of correcting errors and erasures with network coding. Unlike existing works which consider performance limits for worst-case locations of given numbers of errors and erasures, we consider the performance of given (not necessarily optimal) coding and forwarding strategies for given (not necessarily worst-case) models of error and erasure locations. Our approach characterizes decoding success in terms of the rank of certain matrices corresponding to useful and erroneous information received at the sink nodes. We use this approach to analyze random coding and forwarding strategies on a family of simple networks with random error and erasure locations, and show that the relative performance of the strategies depends on the erasure and error probabilities.