8 research outputs found
A Local Perspective on the Edge Removal Problem
The edge removal problem studies the loss in network coding rates that results when a network communication edge is removed from a given network. It is known, for example, that in networks restricted to linear coding schemes and networks restricted to Abelian group codes, removing an edge e^β with capacity R_(e^β) reduces the achievable rate on each source by no more than R_(e^β). In this work, we seek to uncover larger families of encoding functions for which the edge removal statement holds. We take a local perspective: instead of requiring that all network encoding functions satisfy certain restrictions (e.g., linearity), we limit only the function carried on the removed edge e^β. Our central results give sufficient conditions on the function carried by edge e^β in the code used to achieve a particular rate vector under which we can demonstrate the achievability of a related rate vector once e^β is removed