Minimum-overhead network coding in the short packet regime

This paper addresses the linear dependency problem that arises in random linear network coding (RLNC) when a small field size is used. We show that, by appropriate precoding with maximum-rank-distance (MRD) codes, the linear dependency problem can be virtually eliminated, even over a binary field. Besides simplifying operations at the intermediate nodes, decreasing the field size has the benefit of reducing the header overhead from coding coefficients, which comprises a large fraction of the total overhead for practical (short to moderate) packet lengths. Thus, for a moderate increase in decoding complexity, the total overhead of RLNC can be significantly reduced. The proposed scheme can be applied to any form of generation-based RLNC, including schemes that use overlapping generations.