Network error correction from matrix network coding

TL;DR: It is proved that matrix network coding outperforms linear network coding, since it corrects more errors than linear network coded, while the amount of header overhead per packet can be kept the same by reducing the finite field size.

Abstract: We present matrix network coding methods that are naturally amenable to a distributed implementation method, i.e., do not require the knowledge of network topology, and that are suitable for network error correction. First, the Singleton bound can be K-fold increased by employing a K×K matrix coefficient. Moreover, we prove that matrix network coding outperforms linear network coding, since it corrects more errors than linear network coding, while the amount of header overhead per packet can be kept the same by reducing the finite field size. This comes from the fact that the finite field size of matrix network coding required to guarantee the sufficient decoding probability is much smaller than linear network coding. Secondly, matrix network coding is refinable in the sense that, by receiving a larger number of network coded packets, larger error correction capabilities are achieved. Simulation results show that matrix network coding can provide 0.7–2[dB] more coding gain than the linear network coding schemes.