Exact Optimized-cost Repair in Multi-hop Distributed Storage Networks

The problem of exact repair of a failed node in multi-hop networked distributed storage systems is considered. Contrary to the most of the current studies which model the repair process by the direct links from surviving nodes to the new node, the repair is modeled by considering the multi-hop network structure, and taking into account that there might not exist direct links from all the surviving nodes to the new node. In the repair problem of these systems, surviving nodes may cooperate to transmit the repair traffic to the new node. In this setting, we define the total number of packets transmitted between nodes as repair-cost. A lower bound of the repaircost can thus be found by cut-set bound analysis. In this paper, we show that the lower bound of the repair-cost is achievable for the exact repair of MDS codes in tandem and grid networks, thus resulting in the minimum-cost exact MDS codes. Further, two suboptimal (achievable) bounds for the large scale grid networks are proposed.Comment: (To appear in ICC 2014

A Repair Framework for Scalar MDS Codes

Several works have developed vector-linear maximum-distance separable (MDS) storage codes that min- imize the total communication cost required to repair a single coded symbol after an erasure, referred to as repair bandwidth (BW). Vector codes allow communicating fewer sub-symbols per node, instead of the entire content. This allows non trivial savings in repair BW. In sharp contrast, classic codes, like Reed- Solomon (RS), used in current storage systems, are deemed to suffer from naive repair, i.e. downloading the entire stored message to repair one failed node. This mainly happens because they are scalar-linear. In this work, we present a simple framework that treats scalar codes as vector-linear. In some cases, this allows significant savings in repair BW. We show that vectorized scalar codes exhibit properties that simplify the design of repair schemes. Our framework can be seen as a finite field analogue of real interference alignment. Using our simplified framework, we design a scheme that we call clique-repair which provably identifies the best linear repair strategy for any scalar 2-parity MDS code, under some conditions on the sub-field chosen for vectorization. We specify optimal repair schemes for specific (5,3)- and (6,4)-Reed- Solomon (RS) codes. Further, we present a repair strategy for the RS code currently deployed in the Facebook Analytics Hadoop cluster that leads to 20% of repair BW savings over naive repair which is the repair scheme currently used for this code.Comment: 10 Pages; accepted to IEEE JSAC -Distributed Storage 201

Warranty Cost Analysis with an Alternating Geometric Process

In this study we model the warranty claims process and evaluate the warranty servicing costs under non-renewing and renewing free repair warranties. We assume that the repair time for rectifying the claims is non-zero and the repair cost is a function of the length of the repair time. To accommodate the ageing of the product and repair equipment, we use a decreasing geometric process to model the consecutive operational times and an increasing geometric process to model the consecutive repair times. We identify and study the alternating geometric process (AGP), which is an alternating process with cycles consisting of the item's operational time followed by the corresponding repair time. We derive new results for the AGP in finite horizon and use them to evaluate the warranty costs over the warranty period and over the life cycle of the product under a non-renewing free repair warranty (NRFRW), a renewing free repair warranty (RFRW) and a restricted renewing free repair warranty (RRFRW(n)). Properties of the model are demonstrated using a simulation study

Local Codes with Addition Based Repair

We consider the complexities of repair algorithms for locally repairable codes and propose a class of codes that repair single node failures using addition operations only, or codes with addition based repair. We construct two families of codes with addition based repair. The first family attains distance one less than the Singleton-like upper bound, while the second family attains the Singleton-like upper bound

Three DNA polymerases, recruited by different mechanisms, carry out NER repair synthesis in human cells

Nucleotide excision repair (NER) is the most versatile DNA repair system that deals with the major UV photoproducts in DNA, as well as many other DNA adducts. The early steps of NER are well understood, whereas the later steps of repair synthesis and ligation are not. In particular, which polymerases are definitely involved in repair synthesis and how they are recruited to the damaged sites has not yet been established. We report that, in human fibroblasts, approximately half of the repair synthesis requires both polκ and polδ, and both polymerases can be recovered in the same repair complexes. Polκ is recruited to repair sites by ubiquitinated PCNA and XRCC1 and polδ by the classical replication factor complex RFC1-RFC, together with a polymerase accessory factor, p66, and unmodified PCNA. The remaining repair synthesis is dependent on polɛ, recruitment of which is dependent on the alternative clamp loader CTF18-RFC

Increasing Availability in Distributed Storage Systems via Clustering

We introduce the Fixed Cluster Repair System (FCRS) as a novel architecture for Distributed Storage Systems (DSS), achieving a small repair bandwidth while guaranteeing a high availability. Specifically we partition the set of servers in a DSS into $s$ clusters and allow a failed server to choose any cluster other than its own as its repair group. Thereby, we guarantee an availability of $s-1$. We characterize the repair bandwidth vs. storage trade-off for the FCRS under functional repair and show that the minimum repair bandwidth can be improved by an asymptotic multiplicative factor of $2/3$ compared to the state of the art coding techniques that guarantee the same availability. We further introduce Cubic Codes designed to minimize the repair bandwidth of the FCRS under the exact repair model. We prove an asymptotic multiplicative improvement of $0.79$ in the minimum repair bandwidth compared to the existing exact repair coding techniques that achieve the same availability. We show that Cubic Codes are information-theoretically optimal for the FCRS with $2$ and $3$ complete clusters. Furthermore, under the repair-by-transfer model, Cubic Codes are optimal irrespective of the number of clusters