Explicit Construction of Minimum Storage Rack-Aware Regenerating Codes for All Parameters
Liyang Zhou, Zhifang Zhang
Abstract
We consider the rack-aware storage system where n= n̅u nodes are organized in n̅ racks each containing u nodes, and any k = k̅u+u <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> (0 ≤ u <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> <; u) nodes can retrieve the original data file. More importantly, the cross-rack communication cost is much more expensive than the intra-rack communication cost, so that the latter is usually neglected in the system bandwidth. The MSRR (minimum storage rack-aware regenerating) code is an important variation of regenerating codes that achieves the optimal repair bandwidth for single node failures in the rackaware model. However, explicit construction of MSRR codes for all parameters were not developed until Chen&Barg's work. In this paper we present another explicit construction of MSRR codes for all parameters that improve Chen&Barg's construction in two aspects: (1) The sub-packetization is reduced from (d̅-k̅+ 1) <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n̅</sup> to (d̅ - k̅+ 1) <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">⌈n̅/u-u^-0⌉</sup> ⌉ where d̅ is the number of helper racks that participate in the repair process; (2) The field size is reduced to |F|>n which is almost half of the field used in Chen&Barg's construction. Besides, our code keeps the same access level as Chen&Barg's low-access construction.