Fast Random Network Coding in Small Finite Field Size

Network coding and requires multiplications and inversions over finite fields whose implementation complexity quickly increases with the field size. In this paper, the bound of finite field size is considered to reduce complexity by implement the random network coding in small field size. And some improved coding schemes are proposed to increase the decoding success rate in small field size. The simulation results proved that small field size is sufficient in some practice case. Then the fast random network coding with enough decoding success rate is achieved by the improved coding schemes with small field size in this paper.