Bounds for Binary Linear Locally Repairable Codes via a Sphere-Packing Approach

doi:10.1109/TIT.2019.2895315

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	Bounds for Binary Linear Locally Repairable Codes via a Sphere-Packing Approach
	Wang, Anyu 1; Zhang, Zhifang2,3 ; Lin, Dongdai 1,4
	2019-07-01
发表期刊	IEEE TRANSACTIONS ON INFORMATION THEORY
ISSN	0018-9448
卷号	65 期号:7 页码:4167-4179
摘要	For locally repairable codes (LRCs), Cadambe and Nlazumdar derived the first field-dependent parameter hound, known as the C-M hound. However, the C-M hound depends on ( an undetermined parameter k(opt)((q)) (n, d). In this paper, a sphere packing approach is developed fir upper hounding the parameter k for [n, k, 61 linear LRCs with locality r. When restricted to the binary field, three upper bounds (i.e., Bound A, Bound B, and Bound C) are derived in an explicit form. More specifically, Bound A holds under the hypothesis that the local repair groups are disjoint and of equal size. Comparing with previous bounds obtained under the same hypothesis, Bound A either covers them as special cases or has an advantage due to its explicit form. Then, the hypothesis is removed in Bound B and Bound C. As the price for explicit thrm, Bound B specially holds for d >= 5 and Bound C for r = 2. Through specific comparisons, we show that Bound B and Bound C both tend to outperform the C-M hound, as n goes large. Moreover, a family of hinary linear LRCs with d >= 6 attaining Bound B are constructed and later extended to a wider range of parameters by a shortening technique. Lastly, most of the bounds and constructions are extended to q-ary LRCs.
关键词	Distributed storage locally repairable codes binary codes sphere packing bound
DOI	10.1109/TIT.2019.2895315
语种	英语
资助项目	National Natural Science Foundation of China[61872359] ; National Natural Science Foundation of China[61601457] ; National Natural Science Foundation of China[61872353] ; Young Elite Scientist Sponsorship Program by China Association for Science and Technology (CAST)[2016QNRC001]
WOS研究方向	Computer Science ; Engineering
WOS类目	Computer Science, Information Systems ; Engineering, Electrical & Electronic
WOS记录号	WOS:000472186800014
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/35018
专题	系统科学研究所
通讯作者	Wang, Anyu
作者单位	1.Chinese Acad Sci, Inst Informat Engn, State Key Lab Informat Secur, Beijing 100093, Peoples R China 2.Chinese Acad Sci, Acad Math & Syst Sci, Key Lab Math Mechanizat, Beijing 100190, Peoples R China 3.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China 4.Univ Chinese Acad Sci, Sch Cyber Secur, Beijing 100093, Peoples R China
推荐引用方式 GB/T 7714	Wang, Anyu,Zhang, Zhifang,Lin, Dongdai. Bounds for Binary Linear Locally Repairable Codes via a Sphere-Packing Approach[J]. IEEE TRANSACTIONS ON INFORMATION THEORY,2019,65(7):4167-4179.
APA	Wang, Anyu,Zhang, Zhifang,&Lin, Dongdai.(2019).Bounds for Binary Linear Locally Repairable Codes via a Sphere-Packing Approach.IEEE TRANSACTIONS ON INFORMATION THEORY,65(7),4167-4179.
MLA	Wang, Anyu,et al."Bounds for Binary Linear Locally Repairable Codes via a Sphere-Packing Approach".IEEE TRANSACTIONS ON INFORMATION THEORY 65.7(2019):4167-4179.