Construction of Partial MDS (PMDS) and Sector-Disk (SD) Codes with Two
Global Parity Symbols
Abstract
Partial MDS (PMDS) codes are erasure codes combining local (row) correction
with global additional correction of entries, while Sector-Disk (SD) codes are
erasure codes that address the mixed failure mode of current RAID systems. It
has been an open problem to construct general codes that have the PMDS and the
SD properties, and previous work has relied on Monte-Carlo searches. In this
paper, we present a general construction that addresses the case of any number
of failed disks and in addition, two erased sectors. The construction requires
a modest field size. This result generalizes previous constructions extending
RAID~5 and RAID~6.