Exact Regenerating Codes for Byzantine Fault Tolerance in Distributed   Storage
  Due to the use of commodity software and hardware, crash-stop and Byzantine failures are likely to be more prevalent in today's large-scale distributed storage systems. Regenerating codes have been shown to be a more efficient way to disperse information across multiple nodes and recover crash-stop failures in the literature. In this paper, we present the design of regeneration codes in conjunction with integrity check that allows exact regeneration of failed nodes and data reconstruction in presence of Byzantine failures. A progressive decoding mechanism is incorporated in both procedures to leverage computation performed thus far. The fault-tolerance and security properties of the schemes are also analyzed. 
Yunghsiang S. Han, Rong Zheng and Wai Ho Mow
cs.IT math.IT