Outer Bounds on the Storage-Repair Bandwidth Tradeoff of Exact-Repair Regenerating Codes

摘要

In this paper, three outer bounds on the normalized storage-repair bandwidth(S-RB) tradeoff of regenerating codes having parameter set$\{(n,k,d),(\alpha,\beta)\}$ under the exact-repair (ER) setting are presented.The first outer bound is applicable for every parameter set $(n,k,d)$ and inconjunction with a code construction known as {\em improved layered codes}, itcharacterizes the normalized ER tradeoff for the case $(n,k=3,d=n-1)$. Itestablishes a non-vanishing gap between the ER and functional-repair (FR)tradeoffs for every $(n,k,d)$. The second bound is an improvement upon anexisting bound due to Mohajer et al. and is tighter than the first bound, in aregime away from the Minimum Storage Regeneraing (MSR) point. The third boundis for the case of $k=d$, under the linear setting. This outer bound matcheswith the achievable region of {\em layered codes} thereby characterizing thenormalized ER tradeoff of linear ER codes when $k=d=n-1$.