Compressed network coding vectors

In networks that employ network coding, two main approaches have been proposed in the literature to allow the receivers to recover the source information: (i) use of coding vectors, that keep track of the linear combinations the received packets contain, and (ii) subspace coding, that dispenses of the need to know the linear combinations, since information is conveyed from the choice of subspaces alone. Both these approaches impose the strong requirement that all source packets get potentially combined. We here present a third approach that relaxes this assumption, and is thus not a special case from either of the previous two. This relaxation allows to employ compressed coding vectors to efficiently convey the coding coefficients, without altering the operation of intermediate network nodes. We develop optimal designs for such vectors.