Memory Allocation in Distributed Storage Networks

We consider the problem of distributing a file in a network of storage nodes whose storage budget is limited but at least equals to the size file. We first generate $T$ encoded symbols (from the file) which are then distributed among the nodes. We investigate the optimal allocation of $T$ encoded packets to the storage nodes such that the probability of reconstructing the file by using any $r$ out of $n$ nodes is maximized. Since the optimal allocation of encoded packets is difficult to find in general, we find another objective function which well approximates the original problem and yet is easier to optimize. We find the optimal symmetric allocation for all coding redundancy constraints using the equivalent approximate problem. We also investigate the optimal allocation in random graphs. Finally, we provide simulations to verify the theoretical results.