Convertible Codes: New Class of Codes for Efficient Conversion of Coded Data in Distributed Storage Erasure codes are typically used in largescale distributed storage systems to provide durability of data in the face of failures. In this setting, a set of k blocks to be stored is encoded using an n, k code to generate n blocks that are then stored on different storage nodes. A recent work by Kadekodi et al. Kadekodi et al., 2019 shows that the failure rate of storage devices vary significantly over time, and that changing the rate of the code (via a change in the parameters n and k) in response to such variations provides significant reduction in storage space requirement. However, the resource overhead of realizing such a change in the code rate on already encoded data in traditional codes is prohibitively  by this :124,application, in this work we first present a new framework to formalize the notion of code conversion  the process of converting data encoded with an nI, kI code into data encoded with an nF, kF code while maintaining desired decodability properties, such as the maximumdistanceseparable (MDS) property. We then introduce convertible codes, a new class of code pairs that allow for code conversions in a resourceefficient manner. For an important parameter regime (which we call the merge regime) along with the widely used linearity and MDS decodability constraint, we prove tight bounds on the number of nodes accessed during code conversion. In particular, our achievability result is an explicit construction of MDS convertible codes that are optimal for all parameter values in the merge regime albeit with a high field size. We then present explicit lowfieldsize constructions of optimal MDS convertible codes for a broad range of parameters in the merge regime. Our results thus show that it is indeed possible to achieve code conversions with significantly lesser resources as compared to the default approach of reencoding.

StorageReliabilityRepair TradeOffs in Distributed Storage System For reliability purpose, data redundancy is anessential in distributed storage system. In the evolving of data redundancy schemes, storagereliabilityrepair tradeoffs always exist. From replication to erasure codes, higher reliability achieves with lower storage cost, but the higher repair penalty can not be ignored. Optimized data redundancy schemes like regenerating codes or basic pyramid codes are proposed to relieve the high repair penalty. In order to study the storagereliabilityrepair tradeoffs, we propose a new model based on the standard Markov Chain, it takes the irregular fault tolerance, latent sector error and correlated failures into account, and measures the storage and repair cost from system perspective. Through interscheme and intrascheme discussions, we find some principles about choosing data redundancy schemes and corresponding parameters to achieve better storagereliabilityrepair tradeoffs. Our goal is to provide system designers and administrators with concrete information to help them achieve proper storagereliabilityrepair tradeoffs.