On a capacity equivalence between network and index coding and the edge removal problem

In recent work by Effros, El Rouayheb, and Langberg, an equivalence of code feasibility between network and index coding is derived. The authors ask whether the capacity region of a network coding problem can be obtained by solving the capacity region of an index coding problem. We answer in the affirmative for the linear coding case. While the question is still open for the general case, we show that it is related to the edge removal problem, which has been studied recently.