Trustworthiness of random network coded information in untrustworthy networks

We examine the trustworthiness of random network coded information in untrustworthy networks, where the network nodes provide false data purposely or unknowingly and data transmissions are subject to channel errors. The trustworthiness of information x is defined as the probability of x being true. We show that the trustworthiness of random network coded packet decreases exponentially with the number of packets that are combined and that of random network coded symbol decreases monotonically with the field size. The latter indicates that the binary field is optimal in the sense of maximizing the trustworthiness of network coded symbol in untrustworthy networks. We analyze the fundamental tradeoff between the trustworthiness of coded packet and the information transmission rate in Rayleigh fading channel with additive white Gaussian noise.