Outer Bounds on the Storage-Repair Bandwidth Tradeoff of Exact-Repair Regenerating Codes
Abstract
In this paper, three outer bounds on the normalized storage-repair bandwidth (S-RB) tradeoff of regenerating codes having parameter set \(n,k,d),(α,β)\ under the exact-repair (ER) setting are presented. The first outer bound is applicable for every parameter set (n,k,d) and in conjunction with a code construction known as improved layered codes, it characterizes the normalized ER tradeoff for the case (n,k=3,d=n-1). It establishes a non-vanishing gap between the ER and functional-repair (FR) tradeoffs for every (n,k,d). The second bound is an improvement upon an existing bound due to Mohajer et al. and is tighter than the first bound, in a regime away from the Minimum Storage Regeneraing (MSR) point. The third bound is for the case of k=d, under the linear setting. This outer bound matches with the achievable region of layered codes thereby characterizing the normalized ER tradeoff of linear ER codes when k=d=n-1.