HashTag Erasure Codes: From Theory to Practice
  Minimum-Storage Regenerating (MSR) codes have emerged as a viable alternative to Reed-Solomon (RS) codes as they minimize the repair bandwidth while they are still optimal in terms of reliability and storage overhead. Although several MSR constructions exist, so far they have not been practically implemented mainly due to the big number of I/O operations. In this paper, we analyze high-rate MDS codes that are simultaneously optimized in terms of storage, reliability, I/O operations, and repair-bandwidth for single and multiple failures of the systematic nodes. The codes were recently introduced in \cite{7463553} without any specific name. Due to the resemblance between the hashtag sign \# and the procedure of the code construction, we call them in this paper \emph{HashTag Erasure Codes (HTECs)}. HTECs provide the lowest data-read and data-transfer, and thus the lowest repair time for an arbitrary sub-packetization level $\alpha$, where $\alpha \leq r^{\lceil \sfrac{k}{r} \rceil}$, among all existing MDS codes for distributed storage including MSR codes. The repair process is linear and highly parallel. Additionally, we show that HTECs are the first high-rate MDS codes that reduce the repair bandwidth for more than one failure. Practical implementations of HTECs in Hadoop release 3.0.0-alpha2 demonstrate their great potentials. 
Katina Kralevska, Danilo Gligoroski, Rune E. Jensen, and Harald   {\O}verby
cs.IT cs.DC math.IT