Rack-Aware Regenerating Codes with Fewer Helper Racks
Zhifang Zhang, Liyang Zhou · 2021
We consider the rack-aware storage system where$n$nodes are organized in$\bar{n}$racks each containing$u$nodes, and any$k$nodes can retrieve the stored file. Moreover, any single node erasure can be recovered by downloading data from$\bar{d}$helper racks as well as the remaining$u-1$nodes in the same rack. Previous work mostly focuses on minimizing the cross-rack repair bandwidth under the condition$\bar{d}\geq\bar{k}$, where$\bar{k}=\lfloor\frac{k}{u}\rfloor$. However,$\bar{d}\geq\bar{k}$is not an intrinsic condition for the rack-aware storage model. Reducing$\bar{d}$can improve the repair efficiency in practice and bring more flexibility into the repair process. We establish a tradeoff between the storage overhead and cross-rack repair bandwidth for the more interesting case$\bar{d} < \bar{k}$, and explicitly construct codes with parameters lying on the tradeoff curve respectively at the minimum storage point and minimum bandwidth point. The codes are scalar or have sub-packetization$\bar{d}$, and operate over finite fields of size comparable to$n$. Moreover, they remove the restriction of MBR codes having rate less than$\frac{1}{2}$and that of high-rate MSR codes having exponential sub-packetization level.