Biblio

Fractional repetition (FR) codes are a special family of regenerating codes with the repair-by-transfer property. The constructions of FR codes are naturally related to combinatorial designs, graphs, and hypergraphs. Given the file size of an FR code, it is desirable to determine the minimum number of storage nodes needed. The problem is related to an extremal graph theory problem, which asks for the minimum number of vertices of an α-regular graph such that any subgraph with k vertices has at most δ edges. In this paper, we present a class of regular graphs for this problem to give the bounds for the minimum number of storage nodes for the FR codes.

{1 We present a construction for exact-repair regenerating codes with an information-theoretic secrecy guarantee against an eavesdropper with access to the content of (up to) ℓ nodes. The proposed construction works for the entire range of per-node storage and repair bandwidth for any distributed storage system with parameters (n

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.