2018/10/10 by Zhang, Yaqian, Zhang, Zhifang
#FOS: Computer and information sciences #Information Theory (cs.IT)
paper · doi:10.48550/arxiv.1810.04611
An (n,k,d) cooperative regenerating code provides the optimal-bandwidth repair for any t~(t > 1) node failures in a cooperative way. In particular, an MSCR (minimum storage cooperative regenerating) code retains the same storage overhead as an (n,k) MDS code. Suppose each node stores α symbols which indicates the sub-packetization level of the code. A scalar MSCR code attains the minimum sub-packetization, i.e., α=d-k+t. By now, all existing constructions of scalar MSCR codes restrict to very special parameters, eg. d=k or k=2, etc. In a recent work, Ye and Barg construct MSCR codes for all n,k,d,t, however, their construction needs α≈\rm exp(nt) which is almost infeasible in practice. In this paper, we give an explicit construction of scalar MSCR codes for all d≥ max\2k-1-t,k\, which covers all possible parameters except the case of k≤ d≤ 2k-2-t when k<2k-1-t. Moreover, as a complementary result, for k