This paper studies the capacity of single-source single-sink noiseless networks under adversarial or arbitrary errors on no more thanzedges. Unlike prior papers, which assume equal capacities on all links, arbitrary link capacities are considered. Results include new upper bounds, network error-correction coding strategies, and examples of network families where our bounds are tight. An example is provided of a network where the capacity is 50% greater than the best rate that can be achieved with linear coding. While coding at the source and sink suffices in networks with equal link capacities, in networks with unequal link capacities, it is shown that intermediate nodes may have to do coding, nonlinear error detection, or error correction in order to achieve the network error-correction capacity.

We describe a new tiling approach for network code design. The proposed method applies dynamic programming to find the best strategy among a restricted collection of network codes. We demonstrate the proposed strategy as a method for efficiently accommodating multiple unicasts in a wireless coding environment on a triangular lattice and discuss its generalization.