Coding for networks of compound channels

Abstract

In this paper, we consider networks where every edge is a compound Binary Symmetric Channel whose transition probability is determined by a global network state. We first examine the setting where the sum of the transition probabilities for all edges satisfies an overall global upper bound. For networks with exactly one source and one sink we show that capacity is given by the smallest min-cut among all permitted networks states. We show that routing along with end-to-end error correction is optimal for such networks. Next, we consider networks with one source and multiple sinks with multicast demands. We give upper and lower bounds on the capacity of such networks. The coding strategy that leads to our lower bound is intriguing — it involves both end-to-end error correction across the network as well as link-by-link error correction. Finally, we give a lower bound on the capacity of networks where the transition probabilities can take any arbitrary value from a known state-space.