Explicit Constructions of Optimal-Access MSCR Codes for All Parameters
Yaqian Zhang, Zhifang Zhang, Lu Wang · IEEE Communications Letters · 2020
The MSCR (minimum storage cooperative regenerating) code is an important variation of regenerating codes for repairing multiple node failures in a cooperative way and retaining the minimum storage. However, explicit constructions of MSCR codes for all parameters were not developed untill Ye&Barg's recent work. Here we present another explicit construction of MSCR codes for all parameters. Specifically, we design an (n, k) MDS code that can cooperatively repair any h (2 ≤ h ≤ n - k) erasures from any d (k ≤ d ≤ n - h) helper nodes. The superiority of our code to Ye&Barg's is three fold: (1) Our code additionally has the optimal access property, i.e., the amount of data accessed at each helper node meets a lower bound on this quantity; (2) The subpacketization level is reduced by a factor of (d - k)(h-1)(hn); (3) Our code is built over a smaller field F with |F| ≥ n + d - k, compared to Ye&Barg's requirement |F| ≥ (d - k + 1)n.