Patent ID: 11693983

Abstract:
Commutative coding in a geographically diverse data storage system is disclosed. Commutative coding can achieve a same result as more conventional hierarchical erasure coding of data, but can be more efficient. Commutative coding can employ Galois Field (GF) based bit-matrix operations. The bit-matrix operations can employ a reduced GF order in associated with expanding elements of input matrixes. A reduced GF order can perform matrix operations at a lower complexity, e.g., employing AND operations for a GF(2) in contrast to XOR operations for a GF(2w), where w=4, 8, 16, etc. In an aspect, commutative coding can comprise generating a second-tier coding fragment based on applying a second erasure coding scheme, via bit-matrix operations, to a first-tier encoded fragment, wherein the first-tier encoded fragment is based on an input data fragment and a first erasure coding scheme.