Coding for linear operator channels over finite fields

Linear operator channels (LOCs) are motivated by the communications through networks employing random linear network coding (RLNC). Following the recent information theoretic results about LOCs, we propose two coding schemes for LOCs and evaluate their performance. These schemes can be used in networks employing RLNC without constraints on the network size and the field size. Our first scheme makes use of rank-metric codes and generalizes the rank-metric approach of subspace coding proposed by Silva et al. Our second scheme applies linear coding. The second scheme can achieve higher rate than the first scheme, while the first scheme has simpler decoding algorithm than the second scheme. Our coding schemes only require the knowledge of the expectation of the rank of the transformation matrix. The second scheme can also be realized ratelessly without any priori knowledge of the channel statistics.