Upper bound for unequal zig-zag network with small downstream

We consider the problem of characterizing network capacity in the presence of adversarial errors on network links, focusing in particular on the effect of small downstream links, where the downstream link is the directed link of feedback links across the cut of network. In this paper, we present a family of zig-zag networks where the inner bound and the outer bound coincide. We also establish tight condition for this family of zig-zag network, and develop encoding scheme and detection and decoding strategy.