Scalar MSCR Codes via the Product Matrix Construction
Zhang, Yaqian1,2; Zhang, Zhifang1,2
AbstractAn (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 alpha symbols which indicates the sub-packetization level of the code. A scalar MSCR code attains the minimum sub-packetization, i.e., alpha = 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 alpha approximate to 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 < d < 2k - 2 - t we prove the nonexistence of linear scalar MSCR codes that have invariant repair spaces. Our construction and most of the previous scalar MSCR codes all have invariant repair spaces and this property is appealing in practice because of convenient repair. In this sense, this work presents an almost full description of usual scalar MSCR codes.
KeywordMaintenance engineering Bandwidth Symmetric matrices Encoding Indexes Measurement Regenerating code cooperative repair product matrix
Indexed BySCI
Funding ProjectNational Natural Science Foundation of China[61872353]
WOS Research AreaComputer Science ; Engineering
WOS SubjectComputer Science, Information Systems ; Engineering, Electrical & Electronic
WOS IDWOS:000510646900019
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Document Type期刊论文
Corresponding AuthorZhang, Yaqian
Affiliation1.Chinese Acad Sci, Acad Math & Syst Sci, Key Lab Math Mechanizat, Beijing 100190, Peoples R China
2.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China
Recommended Citation
GB/T 7714
Zhang, Yaqian,Zhang, Zhifang. Scalar MSCR Codes via the Product Matrix Construction[J]. IEEE TRANSACTIONS ON INFORMATION THEORY,2020,66(2):995-1006.
APA Zhang, Yaqian,&Zhang, Zhifang.(2020).Scalar MSCR Codes via the Product Matrix Construction.IEEE TRANSACTIONS ON INFORMATION THEORY,66(2),995-1006.
MLA Zhang, Yaqian,et al."Scalar MSCR Codes via the Product Matrix Construction".IEEE TRANSACTIONS ON INFORMATION THEORY 66.2(2020):995-1006.
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