Easy repair via codes with simplex locality
Margreta Kuijper, Julia Lieb, Diego Napp
TL;DR
This work studies locally repairable codes optimized for easy repair in distributed storage systems. It develops multiple simplex-code–based constructions, including binary simplex block codes, punctured LDGM variants, and unit-memory convolutional simplex codes, all designed to allow low-complexity repairs using XOR operations and to enable parallel repairs when possible. Key contributions are the formalization of the Easy Repair Property, proofs of availability and repair capabilities for the simplex and LDGM codes, and the introduction of UM simplex convolutional codes that support sliding-window easy repairs for streaming data. The results demonstrate that high-rate, low-complexity, easy-repair codes can be realized across block and convolutional settings, with comparable erasure-correcting capability and practical parallel-repair benefits for NDSS workloads.
Abstract
In the context of distributed storage systems, locally repairable codes have become important. In this paper we focus on codes that allow for multi-erasure pattern decoding with low computational effort. Different optimality requirements, measured by the code's rate, minimum distance, locality, availability as well as field size, influence each other and can not all be maximized at the same time. We focus on the notion of easy repair, more specifically on the construction of codes that can repair correctable erasure patterns with minimal computational effort. In particular, we introduce the easy repair property and then present codes of different rates that possess this property. The presented codes are all in some way related to simplex codes and comprise block codes as well as unit-memory convolutional codes. We also formulate conditions under which the easy repairs can be performed in parallel, thus improving access speed of the distributed storage system.