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

Abstract

In this paper, we show that the capacity of multisource 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 capacityachieving. 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.