Steiner triple systems as multiple erasure correcting codes in large disk arrays

Abstract

Desirable RAID architectures provide fast performance with minimal overhead costs and short reconstruction times. Increasing the size of a disk array decreases its reliability. Developing new architectures that guarantee no information is lost in the presence of multiple disk failures, therefore, becomes important as disk arrays grow large. One class of 3-erasure correcting codes which have minimal check disk overhead and update penalty arise from a class of well studied combinatorial designs, the Steiner triple systems. They provide data recovery for a large number of 4-erasures as well. A preliminary performance analysis using Steiner triple systems of order 15 as mappings for RAID is performed. The ordering of triples within a system appears to have the greatest impact on system performance.