KMS Of Academy of mathematics and systems sciences, CAS
| Bounds for Binary Linear Locally Repairable Codes via a Sphere-Packing Approach | |
Wang, Anyu1; Zhang, Zhifang2,3 ; Lin, Dongdai1,4
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| 2019-07-01 | |
| Source Publication | IEEE TRANSACTIONS ON INFORMATION THEORY
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| ISSN | 0018-9448 |
| Volume | 65Issue:7Pages:4167-4179 |
| Abstract | 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. |
| Keyword | Distributed storage locally repairable codes binary codes sphere packing bound |
| DOI | 10.1109/TIT.2019.2895315 |
| Language | 英语 |
| Funding Project | 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 Research Area | Computer Science ; Engineering |
| WOS Subject | Computer Science, Information Systems ; Engineering, Electrical & Electronic |
| WOS ID | WOS:000472186800014 |
| Publisher | IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC |
| Citation statistics | |
| Document Type | 期刊论文 |
| Identifier | http://ir.amss.ac.cn/handle/2S8OKBNM/35018 |
| Collection | 系统科学研究所 |
| Corresponding Author | Wang, Anyu |
| Affiliation | 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 |
| Recommended Citation 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. |
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