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This paper proposes a semi-analytical framework for estimating the erasure probability in single-hop multi-relay networks. Specifically, we consider a system, in which relays do not decode the information but simply forward coded packets that have been previously received from the source. This allows for uncoordinated, low-complexity processing at the relays. We present a detailed analysis of the proposed network model, which represents an instance of a new coding scheme that we refer to as distributed fountain coding.