Optimizing redundancy using MDS codes and dynamic symbol allocation in mobile ad hoc networks

We consider the design of a network in which packet transmissions between two nodes are to be guaranteed a certain probability of success. There are N independent paths between the two nodes, each path having a fixed probability of success (perhaps representing an a priori estimate of the security of the path). The original message is encoded using a maximum-distance separable code. We find the minimum redundancy and optimal path symbol allocation for the 3-path case based on a desired success probability and the path success probabilities. Two algorithms are presented for determining the minimum required redundancy - an exponential time algorithm (MRAET) and a polynomial time algorithm (MRAPT). We show that MRAET is optimal in several cases, and that both algorithms perform very well.