Generalization of Minimum Storage Regenerating Codes for Heterogeneous Distributed Storage Systems

Real-world distributed storage systems (DSSs) are heterogeneous because storage nodes may have unequal per-symbol storage costs, and network links may have unequal per-symbol transmission costs. For some general classes of heterogeneous DSSs, the optimal tradeoff between storage and repair costs achievable by functional repair codes is known (at least numerically). However, it is unclear whether exact-repair codes can achieve any point of such an optimal storage-repair tradeoff curve, especially at the point of the minimum storage cost. In this paper, we provide an affirmative answer to the question by constructing the so-called heterogeneous minimum storage repair (HMSR) codes for both the average and worst-case repair costs. To optimize storage and repair costs, a heterogeneous DSS may need to adopt irregular array codes and repair a node by downloading unequal numbers of symbols from helper nodes. However, our results show that for almost all heterogeneous DSSs, exact-repair HMSR codes are regular array codes covering an adequately chosen set of nodes. Specifically, exact-repair HMSR codes are designed by stacking conventional MSR codes and applying different repair schemes to different layers. Still, this does not work for every heterogeneous DSS. It is proven that using regular or linear irregular array codes for constructing exact-repair HMSR codes is insufficient in some cases.