With random linear network coding, mixed packets contain in their headers information about the coding operations performed on the original packets to allow their recovery by the receiver. This introduces an overhead that could be significant if the packet size is relatively small w.r.t. the size of the generation. In this paper, we propose to remove the part of the added header related to the network coding coefficients and to consider network decoding as a source separation problem. This problem is addressed using a maximum a posteriori estimation technique. It exploits some a priori information related to the content of the headers added to the original packets by the upper layers of the protocol stack, before network coding. Experiments show that, despite the fact that traditional source separation techniques are completely inadequate to handle this scenario, the proposed approach is able to recover all packets within streams of thousands of generations without a single decoding error