A nested code approach for erroneous wiretap networks

A wiretap network with errors occurred on some edges is called a erroneous wiretap networks, for which we propose a nested code approach. Given a linear network code for an erroneous wiretap network, we derive the necessary and sufficient condition for a nested code to combat errors on d edges and prevent eavesdropping from μ edges. Furthermore, we prove that using nested codes the maximum rate at which the source can multicast information reliably and securely to all sink nodes is ω-2d-μ, where w is the minimum of the maximum flows of all the sinks. Finally, we propose two algorithms to construct nested codes that can achieve the maximum rate.