An Outer Bound on the Storage-Bandwidth Tradeoff of Exact-Repair Cooperative Regenerating Codes

Cooperative regenerating codes are a kind of erasure codes, which are optimal in terms of minimizing the repair bandwidth. An (n, k, d, r)-cooperative regenerating code has n storage nodes, where k arbitrary nodes are enough to reconstruct original data, and r failed nodes can be repaired cooperatively with the help of d arbitrary surviving nodes. In the regenerating-code framework, there exists a tradeoff between the storage capacity of each node α and the repair bandwidth y, but the problem of specifying the optimal storage-bandwidth tradeoff of the exact-repair cooperative regenerating codes remains open. A key contribution of this paper is that an outer bound on the storage-bandwidth tradeoff of exact-repair linear cooperative regenerating codes is proposed. This result can be regarded as a generalization of the outer bound proposed by Prakash et al., which specifies the optimal tradeoff of exact-repair regenerating codes for the case of d = k = n - 1. The proposed outer bound suggests the (α, γ) pairs that no exact-repair codes can achieve but only functional-repair codes can. By observing the size of the set of such (α, γ) pairs, the performance of the proposed outer bound is evaluated under various parameter settings.