Field size of random network coding in untrustworthy networks

We examine the effect of the field size on the probability of symbol error and the throughput in untrustworthy networks that employ random network coding, where the network nodes provide false data purposely or unknowingly and the information transmission is subject to channel error. We show that the probability of correct decoding decays exponentially with the number of combined packets and that the throughput scales as (log₂ q)/q bits per symbol transmission where q is the field size. We present the optimum field size that maximizes the throughput or minimizes the probability of symbol error in terms of the trustworthiness of node and the number of combined packets.