Explicit Construction of Minimum Storage Rack-Aware Regenerating Codes for All Parameters
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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_0 (0≤ u_0<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 rack-aware 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)^n̅ to (d̅-k̅+1)^⌈n̅/u-u_0⌉ 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.
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