arXiv subjects

Anyu Wang

Publications and source records attributed to Anyu Wang.

22 records · Page 2Linked to original sources

arXiv2014

An Integer Programming Based Bound for Locally Repairable Codes

The locally repairable code (LRC) studied in this paper is an $[n,k]$ linear code of which the value at each coordinate can be recovered by a linear combination of at most $r$ other coordinates. The central problem in this work is to determine the largest possible minimum distance for LRCs. First, an integer programming based upper bound is derived for any LRC. Then by solving the programming problem under certain conditions, an explicit upper bound is obtained for LRCs with parameters $n_1>n_2$, where $n_1 = \left\lceil \frac{n}{r+1} \right\rceil$ and $n_2 = n_1 (r+1) - n$. Finally, an explicit construction for LRCs attaining this upper bound is presented over the finite field $\mathbb{F}_{2^m}$, where $m\geq n_1r$. Based on these results, the largest possible minimum distance for all LRCs with $r \le \sqrt{n}-1$ has been definitely determined, which is of great significance in practical use.

cs.IT↗

arXiv2014

Repair Locality From a Combinatorial Perspective

Repair locality is a desirable property for erasure codes in distributed storage systems. Recently, different structures of local repair groups have been proposed in the definitions of repair locality. In this paper, the concept of regenerating set is introduced to characterize the local repair groups. A definition of locality $r^{(δ-1)}$ (i.e., locality $r$ with repair tolerance $δ-1$) under the most general structure of regenerating sets is given. All previously studied locality turns out to be special cases of this definition. Furthermore, three representative concepts of locality proposed before are reinvestigated under the framework of regenerating sets, and their respective upper bounds on the minimum distance are reproved in a uniform and brief form. Additionally, a more precise distance bound is derived for the square code which is a class of linear codes with locality $r^{(2)}$ and high information rate, and an explicit code construction attaining the optimal distance bound is obtained.

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arXiv2013

Repair Locality with Multiple Erasure Tolerance

In distributed storage systems, erasure codes with locality $r$ is preferred because a coordinate can be recovered by accessing at most $r$ other coordinates which in turn greatly reduces the disk I/O complexity for small $r$. However, the local repair may be ineffective when some of the $r$ coordinates accessed for recovery are also erased. To overcome this problem, we propose the $(r,δ)_c$-locality providing $δ-1$ local repair options for a coordinate. Consequently, the repair locality $r$ can tolerate $δ-1$ erasures in total. We derive an upper bound on the minimum distance $d$ for any linear $[n,k]$ code with information $(r,δ)_c$-locality. For general parameters, we prove existence of the codes that attain this bound when $n\geq k(r(δ-1)+1)$, implying tightness of this bound. Although the locality $(r,δ)$ defined by Prakash et al provides the same level of locality and local repair tolerance as our definition, codes with $(r,δ)_c$-locality are proved to have more advantage in the minimum distance. In particular, we construct a class of codes with all symbol $(r,δ)_c$-locality where the gain in minimum distance is $Ω(\sqrt{r})$ and the information rate is close to 1.

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arXiv2012

Exact Cooperative Regenerating Codes with Minimum-Repair-Bandwidth for Distributed Storage

We give an explicit construction of exact cooperative regenerating codes at the MBCR (minimum bandwidth cooperative regeneration) point. Before the paper, the only known explicit MBCR code is given with parameters $n=d+r$ and $d=k$, while our construction applies to all possible values of $n,k,d,r$. The code has a brief expression in the polynomial form and the data reconstruction is accomplished by bivariate polynomial interpolation. It is a scalar code and operates over a finite field of size $q\geq n$. Besides, we establish several subspace properties for linear exact MBCR codes. Based on these properties we prove that linear exact MBCR codes cannot achieve repair-by-transfer.

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