Reliability of Relay Networks under Random Linear Network Coding
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We consider a single-source, multiple-relay, 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 with some previous studies, we assume the classical RLNC scheme, in which the relaying nodes simply re-encode packets, without resorting to decoding. In addition, we consider an arbitrary field size and take into account correlation between the relay nodes. We derive exact expressions for networks with up to two relays, and propose a novel upper bound for the general case of multiple relays. Using Monte Carlo simulations, we show that the exact results match the simulated ones for the case of two relays. For networks with more than two relays, we show that the proposed bound is very accurate, exhibiting the mean square error as low as 10^-6.
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