Scalar MSCR Codes via the Product Matrix Construction

doi:10.1109/TIT.2019.2934114

CSpace

	Scalar MSCR Codes via the Product Matrix Construction
	Zhang, Yaqian 1,2; Zhang, Zhifang 1,2
	2020-02-01
发表期刊	IEEE TRANSACTIONS ON INFORMATION THEORY
ISSN	0018-9448
卷号	66 期号:2 页码:995-1006
摘要	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 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.
关键词	Maintenance engineering Bandwidth Symmetric matrices Encoding Indexes Measurement Regenerating code cooperative repair product matrix
DOI	10.1109/TIT.2019.2934114
收录类别	SCI
语种	英语
资助项目	National Natural Science Foundation of China[61872353]
WOS研究方向	Computer Science ; Engineering
WOS类目	Computer Science, Information Systems ; Engineering, Electrical & Electronic
WOS记录号	WOS:000510646900019
出版者	IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/50802
专题	中国科学院数学与系统科学研究院
通讯作者	Zhang, Yaqian
作者单位	1.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
推荐引用方式 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.