Erasure coding is widely used for massive storage in data centers to achieve high fault tolerance and low storage redundancy. Since the cross-rack communication cost is often high, it is critical to design erasure codes that minimize the cross-rack repair bandwidth during failure repair. In this paper, we analyze the optimal trade-off between storage redundancy and cross-rack repair bandwidth specifically for data centers, subject to the condition that the original data can be reconstructed from a sufficient number of any non-failed nodes. We characterize the optimal trade-off curve under functional repair, and propose a general family of erasure codes called rack-aware regenerating codes (RRC), which achieve the optimal trade-off. We further propose exact repair constructions of RRC that have minimum storage redundancy and minimum cross-rack repair bandwidth, respectively. We show that (i) the minimum storage redundancy constructions support a wide range of parameters and have cross-rack repair bandwidth that is strictly less than that of the classical minimum storage regenerating codes in most cases, and (ii) the minimum cross-rack repair bandwidth constructions support all the parameters and have less cross-rack repair bandwidth than that of the minimum bandwidth regenerating codes for almost all of the parameters.
In distributed storage systems, cooperative regenerating codes tradeoff storage for repair bandwidth in the case of multiple node failures. In rack-aware distributed storage systems, there is no cost associated with transferring symbols within a rack. Hence, the repair bandwidth will only take into account cross-rack transfer. Rack-aware regenerating codes for the case of single node failures have been studied and their repair bandwidth tradeoff characterized. In this paper, we consider the framework of rack-aware cooperative regenerating codes for the case of multiple node failures where the …
In large data centers, storage nodes are organized in racks, and the cross-rack transmission dominates the bandwidth cost. For the repair of single node failures, codes achieving the tradeoff between the storage redundancy and cross-rack repair bandwidth are called rack-aware regenerating codes (RRCs). In this work, we give the first explicit construction of RRCs with the minimum repair bandwidth (i.e., the cross-rack bandwidth equals the storage size per node). Our construction applies to all admissible parameters and has the lowest sub-packetization level. Moreover, the underlying finite fie…
We consider the rack-aware storage system where $n=\bar{n}u$ nodes are organized in $\bar{n}$ racks each containing $u$ nodes, and any $k=\bar{k}u+u_0~(0\leq u_0<u)$ nodes can retrieve the original data file. More importantly, the cross-rack communication cost is much more expensive than the intra-rack communication cost, so that the latter is usually neglected in the system bandwidth. The MSRR (minimum storage rack-aware regenerating) code is an important variation of regenerating codes that achieves the optimal repair bandwidth for single node failures in the rack-aware model. However, expli…
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. In…
In a modern distributed storage system, storage nodes are organized in racks, and the cross-rack communication dominates the system bandwidth. In We study the rack-aware storage system where all storage nodes are organized in racks and within each rack the nodes can communicate freely without taxing the system bandwidth. Rack-aware regenerating codes (RRCs) were proposed for minimizing the repair bandwidth for single erasures. In the initial setting of RRCs, the repair of a single node requires the participation of all the remaining nodes in the rack containing the failed node as well as a lar…
In modern practical data centers, storage nodes are usually organized into equally sized groups, which is called racks. The cost of cross-rack communication is much more expensive compared with the intra-rack communication cost. The codes for this system are called rack-aware regenerating codes. Similar to standard minimum storage regenerating (MSR) codes, it is a challenging task to construct minimum storage rack-aware regenerating (MSRR) codes achieving the cut-set bound. The known constructions of MSRR codes achieving the cut-set bound give codes with alphabet size $q$ exponential in the co…
In the traditional two-rack distributed storage system (DSS) model, due to the assumption that the storage capacity of each node is the same, the minimum bandwidth regenerating (MBR) point becomes infeasible. In this paper, we design a new non-homogeneous two-rack model by proposing a generalization of the threshold function used to compute the tradeoff curve. We prove that by having the nodes in the rack with higher regenerating bandwidth stores more information, all the points on the tradeoff curve, including the MBR point, become feasible. Finally, we show how the non-homogeneous two-rack m…
The minimum storage rack-aware regenerating (MSRR) code is a variation of regenerating codes that achieves the optimal repair bandwidth for a single node failure in the rack-aware model. The authors in~\cite{Chen-Barg2019} and~\cite{Zhou-Zhang2021} provided explicit constructions of MSRR codes for all parameters to repair a single failed node. This paper generalizes the results in~\cite{Chen-Barg2019} to the case of multiple node failures. We propose a class of MDS array codes and scalar Reed-Solomon (RS) codes, and show that these codes have optimal repair bandwidth and error resilient capabi…
This paper proposes an algorithm to minimize weighted service latency for different classes of tenants (or service classes) in a data center network where erasure-coded files are stored on distributed disks/racks and access requests are scattered across the network. Due to limited bandwidth available at both top-of-the-rack and aggregation switches and tenants in different service classes need differentiated services, network bandwidth must be apportioned among different intra- and inter-rack data flows for different service classes in line with their traffic statistics. We formulate this prob…
Tri-Band Channel Measurement-Enabled Multi-Layer Digital Twin for Terahertz Wireless Data Centers
Terahertz Wireless Communications (TWC) Interdisciplinary Research Center, Shanghai Jiao Tong University（上海交通大学太赫兹无线通信（TWC）跨学科研究中心）；Huawei Technologies Company Ltd.（华为技术有限公司）；School of Information Science and Electronic Engineering, Shanghai Jiao Tong University（上海交通大学信息科学与工程学院）
In distributed storage systems (DSSs), the optimal tradeoff between node storage and repair bandwidth is an important issue for designing distributed coding strategies to ensure large scale data reliability. The capacity of DSSs is obtained as a function of node storage and repair bandwidth parameters, characterizing the tradeoff. There are lots of works on DSSs with clusters (racks) where the repair bandwidths from intra-cluster and cross-cluster are differentiated. However, separate nodes are also prevalent in the realistic DSSs, but the works on DSSs with clusters and separate nodes (CSN-DS…
In a distributed storage system, code symbols are dispersed across space in nodes or storage units as opposed to time. In settings such as that of a large data center, an important consideration is the efficient repair of a failed node. Efficient repair calls for erasure codes that in the face of node failure, are efficient in terms of minimizing the amount of repair data transferred over the network, the amount of data accessed at a helper node as well as the number of helper nodes contacted. Coding theory has evolved to handle these challenges by introducing two new classes of erasure codes,…
Clustered distributed storage models real data centers where intra- and cross-cluster repair bandwidths are different. In this paper, exact-repair minimum-storage-regenerating (MSR) codes achieving capacity of clustered distributed storage are designed. Focus is given on two cases: $ε=0$ and $ε=1/(n-k)$, where $ε$ is the ratio of the available cross- and intra-cluster repair bandwidths, $n$ is the total number of distributed nodes and $k$ is the number of contact nodes in data retrieval. The former represents the scenario where cross-cluster communication is not allowed, while the latter corre…
A new system model reflecting the clustered structure of distributed storage is suggested to investigate bandwidth requirements for repairing failed storage nodes. Large data centers with multiple racks/disks or local networks of storage devices (e.g. sensor network) are good applications of the suggested clustered model. In realistic scenarios involving clustered storage structures, repairing storage nodes using intact nodes residing in other clusters is more bandwidth-consuming than restoring nodes based on information from intra-cluster nodes. Therefore, it is important to differentiate bet…
A new system model reflecting the clustered structure of distributed storage is suggested to investigate interplay between storage overhead and repair bandwidth as storage node failures occur. Large data centers with multiple racks/disks or local networks of storage devices (e.g. sensor network) are good applications of the suggested clustered model. In realistic scenarios involving clustered storage structures, repairing storage nodes using intact nodes residing in other clusters is more bandwidth-consuming than restoring nodes based on information from intra-cluster nodes. Therefore, it is i…
Erasure codes, such as Reed-Solomon (RS) codes, are being increasingly employed in data centers to combat the cost of reliably storing large amounts of data. Although these codes provide optimal storage efficiency, they require significantly high network and disk usage during recovery of missing data. In this paper, we first present a study on the impact of recovery operations of erasure-coded data on the data-center network, based on measurements from Facebook's warehouse cluster in production. To the best of our knowledge, this is the first study of its kind available in the literature. Our …
