General Sub-Packetized Access-Optimal Regenerating Codes

• Published in: IEEE communications letters Vol. 20; no. 7; pp. 1281 - 1284
• Main Authors: Kralevska, Katina, Gligoroski, Danilo, Overby, Harald
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.07.2016; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: access-optimal; Algorithms; Arrays; Bandwidth; Codes; Computation; Construction; Indexes; Maintenance engineering; Minimum storage regenerating codes; Parallel processing; Phased arrays; Reliability; Repair; sub-packetization; Symbols; Systematics; Upper bounds
• ISSN: 1089-7798; 1558-2558
• DOI: 10.1109/LCOMM.2016.2561287

This letter presents a novel construction of (n, k, d = n - 1) access-optimal regenerating codes for an arbitrary sub-packetization level α for exact repair of any systematic node. We refer to these codes as general sub-packetized, because we provide an algorithm for constructing codes for any α less than or equal to r [(k/r)] , where (k/r) is not necessarily an integer. This leads to a flexible construction of codes for different code rates compared with existing approaches. We derive the lower and upper bounds of the repair bandwidth. The repair bandwidth depends on the code parameters and α. The repair process of a failed systematic node is linear and highly parallelized, which means that a set of [(α/r)] symbols is independently repaired first and used along with the accessed data from other nodes to recover the remaining symbols.