STAR+ Codes: Triple-Fault-Tolerant Codes with Asymptotically Optimal Updates and Efficient Encoding/Decoding

STAR codes are well-known binary Maximum Distance Separable (MDS) array codes with triple fault tolerance and low encoding/decoding complexity, yet the update complexity of STAR codes is sub-optimal. We propose STAR+ codes, which extend STAR codes to achieve asymptotically optimal update complexity. We show that STAR+ codes are the generalized version of STAR codes with triple fault tolerance, and additionally have strictly less complexity in encoding, decoding, and updates than STAR codes for most parameters.

[1]  Cheng Huang,et al.  STAR : An Efficient Coding Scheme for Correcting Triple Storage Node Failures , 2005, IEEE Transactions on Computers.

[2]  Jehoshua Bruck,et al.  EVENODD: An Efficient Scheme for Tolerating Double Disk Failures in RAID Architectures , 1995, IEEE Trans. Computers.

[3]  Jehoshua Bruck,et al.  X-Code: MDS Array Codes with Optimal Encoding , 1999, IEEE Trans. Inf. Theory.

[4]  Wu Yu,et al.  Improved decoding algorithm for the generalized EVENODD array code , 2012, Proceedings of 2012 2nd International Conference on Computer Science and Network Technology.

[5]  Randy H. Katz,et al.  Introduction to redundant arrays of inexpensive disks (RAID) , 1989, Digest of Papers. COMPCON Spring 89. Thirty-Fourth IEEE Computer Society International Conference: Intellectual Leverage.

[6]  Mario Blaum,et al.  On Lowest Density MDS Codes , 1999, IEEE Trans. Inf. Theory.

[7]  Hanxu Hou,et al.  Binary MDS Array Codes With Optimal Repair , 2018, IEEE Transactions on Information Theory.

[8]  Hanxu Hou,et al.  A New Construction of EVENODD Codes With Lower Computational Complexity , 2018, IEEE Communications Letters.

[9]  Peter F. Corbett,et al.  RAID triple parity , 2012, OPSR.

[10]  Hai Jin,et al.  The EVENODD Code and its Generalization: An Efficient Scheme for Tolerating Multiple Disk Failures in RAID Architectures , 2002 .

[11]  Yunghsiang Sam Han,et al.  Triple-fault-tolerant binary MDS array codes with asymptotically optimal repair , 2017, 2017 IEEE International Symposium on Information Theory (ISIT).

[12]  Minyi Guo,et al.  TIP-Code: A Three Independent Parity Code to Tolerate Triple Disk Failures with Optimal Update Complextiy , 2015, 2015 45th Annual IEEE/IFIP International Conference on Dependable Systems and Networks.

[13]  Hui Li,et al.  A New Design of Binary MDS Array Codes With Asymptotically Weak-Optimal Repair , 2019, IEEE Transactions on Information Theory.

[14]  Kenneth W. Shum,et al.  A Unified Form of EVENODD and RDP Codes and Their Efficient Decoding , 2018, IEEE Transactions on Communications.

[15]  Peter F. Corbett,et al.  Row-Diagonal Parity for Double Disk Failure Correction (Awarded Best Paper!) , 2004, USENIX Conference on File and Storage Technologies.