Minimum cost content distribution using network coding: Replication vs. coding at the source nodes

Consider a large file that needs to be multicast over a network to a given set of terminals. Storing the file at a single server may result in server overload. Accordingly, there are distributed storage solutions that operate by dividing the file into pieces and placing copies of the pieces (replication) or coded versions of the pieces (coding) at multiple source nodes. Suppose that the cost of a given network coding based solution to this problem is defined as the sum of the storage cost and the cost of the flows required to support the multicast. In this work, we consider a network with a set of source nodes that can either contain subsets or coded versions of the pieces of the file and are interested in finding the storage capacities and flows at minimum cost. We provide succinct formulations of the corresponding optimization problems by using information measures. In particular, we show that when there are two source nodes, there is no loss in considering subset sources. For three source nodes, we derive a tight upper bound on the cost gap between the two cases. Algorithms for determining the content of the source nodes are also provided.