Network Coding for Joint Storage and Transmission with Minimum Cost

Network coding provides elegant solutions to many data transmission problems. The usage of coding for distributed data storage has also been explored. In this work, we study a joint storage and transmission problem, where a source transmits a file to storage nodes whenever the file is updated, and clients read the file by retrieving data from the storage nodes. The cost includes the transmission cost for file update and file read, as well as the storage cost. We show that such a problem can be transformed into a pure flow problem and is solvable in polynomial time using linear programming. Coding is often necessary for obtaining the optimal solution with the minimum cost. However, we prove that for networks of generalized tree structures, where adjacent nodes can have asymmetric links between them, file splitting instead of coding - is sufficient for achieving optimality. In particular, if there is no constraint on the numbers of bits that can be stored in storage nodes, there exists an optimal solution that always transmits and stores the file as a whole. The proof is accompanied by an algorithm that optimally assigns file segments to storage nodes