Asymptotic analysis of failed recovery probability in a distributed wireless storage system with limited sum storage capacity

In distributed wireless storage systems, failed recovery probability depends on not only wireless channel conditions but also storage size of each distributed storage node. For efficient utilization of limited storage capacity, we asymptotically analyze the failed recovery probability of a distributed wireless storage system with a sum storage capacity constraint when signal-to-noise ratio goes to infinity, and find the optimal storage allocation strategy across distributed storage nodes in terms of the asymptotic failed recovery probability. It is also shown that when the number of storage nodes is sufficiently large the storage size required at each node is not so large for high exponential order of the failed recovery probability.