Robust Redundancy Scheme for the Repair Process: Hierarchical Codes in the Bandwidth-Limited Systems

Abstract

High performance computing can be well supported by the Grid or cloud computing systems. However, these systems have to overcome the failure risks, where data is stored in the "unreliable" storage nodes that can leave the system at any moment and the nodes' network bandwidth is limited. In this case, the basic way to assure data reliability is to add redundancy using either replication or erasure codes. As compared to replication, erasure codes are more space efficient. Erasure codes break data into blocks, encode these blocks and distribute them into different storage nodes. When storage nodes permanently or temporarily abandon the system, new redundant blocks must be created to guarantee the data reliability, which is referred to as repair. Later when the churn nodes rejoin the system, the blocks stored in these nodes can reintegrate the data group to enhance the data reliability. For "classical" erasure codes, generating a new block requires to transmit a number of k blocks over the network, which brings lots of repair traffic, high computation complexity and high failure probability for the repair process. Then a near-optimal erasure code named Hierarchical Codes, has been proposed that can significantly reduce the repair traffic by reducing the number of nodes participating in the repair process, which is referred to as the repair degree d. To overcome the complexity of reintegration and provide an adaptive reliability for Hierarchical Codes, we refine two concepts called location and relocation, and then propose an integrated maintenance scheme for the repair process. Our experiments show that Hierarchical Code is the most robust redundancy scheme for the repair process as compared to other famous coding schemes.