Reliability of Relay Networks Under Random Linear Network Coding

We consider a single-source, multiple-relay, and single-destination lossy network employing random linear network coding at all transmitting nodes. We address the problem of calculating the probability of successful decoding at the destination node. In contrast to some previous studies, we assume the classical random linear network coding scheme, in which the relaying nodes simply recode packets, without resorting to decoding. In addition, we consider an arbitrary field size and take into account the correlation between the relay nodes. We propose a novel upper bound for an arbitrary number of relays, which becomes exact for a single relay. Using Monte Carlo simulations, we show that the proposed bound is very accurate, exhibiting the mean square error as low as 10
^-6
. We also demonstrate the throughput gain of the proposed scheme over alternative coding and relaying strategies.