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This paper focuses on the design of regeneration codes. An (n, k, d) exact-regenerating code encodes and stores the data into n nodes such that the entire data can be recovered from any k nodes, and the missing coded information of any failed node can be identically recovered by the help of d nodes. In an earlier work of the authors, determinant codes are introduced for any (n, k, d = k) system, and...
The exact-repair regenerating codes for distributed storage system are studied in this work. A novel coding scheme is proposed for code construction for any $(n,k,d=k)$ system. It is shown that the proposed codes are optimum, in the sense that any operating point satisfying the lower bound for the storage-bandwidth trade-off can be achieved with the proposed construction. As a consequence, the optimum...
The exact-repair regeneration codes for distributed storage system are studied in this work. A novel coding scheme is proposed for code construction for any (n, k, d = k) system, and it is shown to be optimal. In particular, the optimum tradeoff of exact-repair regeneration system is fully characterized for any system with d = k. The new construction is based on fundamental properties of matrix determinant,...
Regeneration codes with exact-repair property for distributed storage systems is studied in this paper. For exact-repair problem, the achievable points of (α,β) tradeoff match with the outer bound only for minimum storage regenerating (MSR), minimum bandwidth regenerating (MBR), and some specific values of n, k, and d. Such tradeoff is characterized in this work for general (n, k, k), (i.e., k = d)...
Characterizing the exact repair storage-vs-repair bandwidth tradeoff for distributed storage systems remains an open problem for more than four storage nodes. Motivated by the prevalence and practical applicability of linear codes, the exact repair problem when restricted to linear codes is considered. The main result of this paper is a new approach to develop bounds for exact repair distributed storage...
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