Multi-source erasure networks with source precoding and random linear network coding

In this paper, we show that the capacity of multi-source single-sink erasure networks can be asymptotically achieved by employing random linear network coding at the intermediate nodes over a sufficiently large number of time extensions. The main idea is to model the resulting network as a finite-field linear deterministic multiple-access channel (MAC), and show that linear precoding at the source nodes is capacity-achieving. Since linear processing is performed at all the source and intermediate nodes, desired symbols can be decoded at the sink node by simply solving a set of linear equations. The result has also been extended to multi-source wireless erasure networks which incorporate the broadcast nature of wireless transmissions.