Network reduction for coded multiple-hop networks

Data transmission over multiple-hop networks is impaired by random deleterious events, and characterizing the probability of error for the end-to-end transmission is challenging as the size of networks grows. Adams et al. showed that, when re-encoding at intermediate nodes is enabled, coded transmission over tandem/parallel links can be reduced to a single equivalent link with a specified probability function. Although iterative application of the tandem/parallel reduction techniques in alternation can simplify the task, they are generally not sufficient to reduce an arbitrary network to a single link. In this paper, we propose upper- and lower- bounding processes to bound the end-to-end probability distribution of a network by combining the parallel/tandem link reduction with the structure of flows over the network. We evaluate the performance of the proposed bounding methods at the 99% success rate of end-to-end data transmission over randomly generated acyclic networks. The numerical results demonstrate that our bounding approaches enable us to characterize a network by a single probability function to a very good precision.