Tensor product based subspace interference alignment for network coding applications

In this paper, we develop an interference alignment framework for multi-source (non-multicast) network coding applications. The framework developed here is based on using a tensor product structure for the network coding matrices at nodes in a network. The framework is presented in this paper in the specific context of exact repair for distributed storage, which is a multi-source network coding application. Using this framework, we generalize previously known MDS codes with optimal exact repair in distributed storage.