An outer bound on the storage-bandwidth tradeoff of exact-repair cooperative regenerating codes
Hyuk Lee, Jungwoo Lee · 2016
(n, k, d, r)-cooperative regenerating codes are a kind of erasure codes, where r failed nodes can be repaired cooperatively with the help of arbitrary d surviving nodes. In this paper, we consider exact-repair cooperative regenerating codes whose parameters satisfy k = d = n - r. There exists a tradeoff between the storage capacity of each node α and the repair bandwidth γ in regenerating codes, but the optimal storage-bandwidth tradeoff of the exact-repair cooperative regenerating codes has not been fully specified. We propose an outer bound on the storage-bandwidth tradeoff for the case of k = d = n - r. This result can be regarded as a generalization of the outer bound proposed by Prakash et al. that specifies the optimal tradeoff of exact-repair regenerating codes for the case of k = d = n - 1. Although the proposed outer bound is not always tighter than the cutset bound of the functional repair model, in the cases where n is large and r is small, the proposed outer bound suggests the region on the α-γ plane that no exact-repair codes can achieve, but functional-repair codes can.