Locally Repairable Codes from Sum-Rank Codes
Umberto Martínez-Peñas, Frank R. Kschischang · Repository for Publications and Research Data (ETH Zurich) · 2020
Locally repairable codes (LRCs) are considered with equal or unequal localities, local distances, and local field sizes.An explicit two-layer architecture with a sum-rank outer code is obtained, having disjoint local groups and achieving maximal recoverability (MR) for all families of local linear codes (MDS or not) simultaneously, up to a specified maximum locality r.Furthermore, the local linear codes (thus the localities, local distances, and local fields) can be efficiently and dynamically modified without global recoding or changes in architecture or outer code, while preserving the MR property, easily adapting to new configurations in storage or new hot and cold data.In addition, local groups and file components can be added, removed or updated without global recoding.The construction requires global fields of size roughly g r , for g local groups and maximum or specified locality r.For equal localities, these global fields are smaller than those of previous MR-LRCs when r ≤ h (global parities).For unequal localities, they provide an exponential field size reduction on all previous best known MR-LRCs.For bounded