On the number of transmissions vs. redundancy tradeoff for flooded fountain codes

We consider a multihop ad hoc network where a source node must reliably deliver a set of data packets to a given destination node. To do so, the source applies a fountain code and floods the encoded packets through the network, until they reach their destination or are lost in the process. We model the probability that the destination can recover the original transmissions from the received coded packets as a function of the network topology and of the number of redundant packets generated by the source, and show that our analytical results predict the outcome of simulations very well. These results are finally employed to discuss how the number of cooperating relays and the redundancy of the code should be set in order to achieve a good working point on the tradeoff between the reliability of end-to-end communications and the number of packet transmissions that take place in the network.