On a capacity equivalence between multiple multicast and multiple unicast

摘要

An equivalence between multiple multicast and multiple unicast network coding is proven in a 2007 paper by Dougherty and Zeger. The result is extended to index coding under the assumption of linear coding in recent work by Maleki et al. In this work, we extend the result to arbitrary (e.g. possibly noisy) memoryless networks under an asymptotic definition of reliability. We show the equivalence for non-linear index codes as a special case. Our result implies that solving the multiple unicast communication problem is sufficient to solve all communication problems in memoryless networks.