Reliability guarantees for lossy network coding subgraph construction

Random linear network coding can provide robustness to link losses, and in this work we present an approach to achieve a chosen level of reliability. We formulate the subgraph construction problem, in which participating links are identified along with the number of coded packets contributed by each, as a min-cost network flow problem with probabilistic constraints to represent per-link reliability requirements. We show how to transform this problem into an integer linear program and provide an approximate algorithm to solve it. We then analyze the end-to-end reliability provided by the scheme, and present an algorithm to compute the probability of successful decoding at the destination node, in the case that the network coding subgraph is a Two Terminal Series Parallel (TTSP) graph. Results from numerical examples and Monte Carlo simulation indicate that the end-to-end reliability is accurately computed by our scheme, and that our subgraph construction approach provides a means to select the operating point in the tradeoff between reliability and subgraph cost.