Heuristics for optimizing matrix-based erasure codes for fault-tolerant storage systems

Large scale, archival and wide-area storage systems use erasure codes to protect users from losing data due to the inevitable failures that occur. All but the most basic erasure codes employ bit-matrices so that encoding and decoding may be effected solely with the bitwise exclusive-OR (XOR) operation. There are CPU savings that can result from strategically scheduling these XOR operations so that fewer XOR's are performed. It is an open problem to derive a schedule from a bit-matrix that minimizes the number of XOR operations. We attack this open problem, deriving two new heuristics called Uber-CHRS and X-Sets to schedule encoding and decoding bit-matrices with reduced XOR operations. We evaluate these heuristics in a variety of realistic erasure coding settings and demonstrate that they are a significant improvement over previously published heuristics. We provide an open-source implementation of these heuristics so that practitioners may leverage our work.