Distributed storage plays a crucial role in the current cloud computing framework. After the theoretical bound for distributed storage was derived by the pioneer work of the regenerating code, Reed-Solomon code based regenerating codes were developed. The RS code based minimum storage regeneration code (RS-MSR) and the minimum bandwidth regeneration code (RS-MBR) can achieve theoretical bounds on the MSR point and the MBR point respectively in code regeneration. They can also maintain the MDS property in code reconstruction. However, in the hostile network where the storage nodes can be compromised and the packets can be tampered with, the storage capacity of the network can be significantly affected. In this paper, we propose a Hermitian code based minimum storage regenerating (H-MSR) code and a minimum bandwidth regenerating (H-MBR) code. We first prove that our proposed Hermitian code based regenerating codes can achieve the theoretical bounds for MSR point and MBR point respectively. We then propose data regeneration and reconstruction algorithms for the H-MSR code and the H-MBR code in both error-free network and hostile network. Theoretical evaluation shows that our proposed schemes can detect the erroneous decodings and correct more errors in hostile network than the RS-MSR code and the RS-MBR code with the same code rate. Our analysis also demonstrates that the proposed H-MSR and H-MBR codes have lower computational complexity than the RS-MSR RS-MBR codes in both code regeneration and code reconstruction.
In this paper, we propose a Hermitian code based minimum storage regeneration (H-MSR) code and a Hermitian code based minimum bandwidth regeneration (H-MBR) code. The proposed H-MSR H-MBR codes can correct more errors than the RS-MSR RS-MBR codes and can always determine whether the error correction is successful. Our design is based on the structural analysis of the Hermitian code and the efficient decoding algorithm proposed in @cite_7 .
@cite_7
2128268793 2063987864 2963362241 2115394571
Erasure codes, such as Reed-Solomon (RS) codes, are increasingly being deployed as an alternative to data-replication for fault tolerance in distributed storage systems. While RS codes provide significant savings in storage space, they can impose a huge burden on the I O and network resources when reconstructing failed or otherwise unavailable data. A recent class of erasure codes, called minimum-storage-regeneration (MSR) codes, has emerged as a superior alternative to the popular RS codes, in that it minimizes network transfers during reconstruction while also being optimal with respect to storage and reliability. However, existing practical MSR codes do not address the increasingly important problem of I O overhead incurred during reconstructions, and are, in general, inferior to RS codes in this regard. In this paper, we design erasure codes that are simultaneously optimal in terms of I O, storage, and network bandwidth. Our design builds on top of a class of powerful practical codes, called the product-matrix-MSR codes. Evaluations show that our proposed design results in a significant reduction the number of I Os consumed during reconstructions (a 5× reduction for typical parameters), while retaining optimality with respect to storage, reliability, and network bandwidth. 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 codes are 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 ≥ 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. This paper presents a construction for high-rate MDS codes that enable bandwidth-efficient repair of a single node. Such MDS codes are also referred to as the minimum storage regenerating (MSR) codes in the distributed storage literature. The construction presented in this paper generates MSR codes for all possible number of helper nodes d as d is a design parameter in the construction. Furthermore, the obtained MSR codes have polynomial sub-packetization (a.k.a. node size) α. The construction is built on the recent code proposed by [1], which works only for d = n — 1, i.e., where all the remaining nodes serve as the helper nodes for the bandwidth-efficient repair of a single node. The results of this paper broaden the set of parameters where the constructions of MSR codes were known earlier. In this paper, distributed storage systems with exact repair are studied. Constructions for exact-regenerating codes between the minimum storage regenerating (MSR) and the minimum bandwidth regenerating (MBR) points are given. To the best of our knowledge, no previous construction of exact-regenerating codes between MBR and MSR points is done except in the works by and In contrast to their works, the methods used here are elementary. In this paper, it is shown that in the case that the parameters (n ) , (k ) , and (d ) are close to each other, the given construction is close to optimal when comparing with the known functional repair capacity. This is done by showing that when the distances of the parameters (n ) , (k ) , and (d ) are fixed but the actual values approach to infinity, the fraction of the performance of constructed codes with exact repair and the known capacity of codes with functional repair, approaches to one. Also, a simple variation of the constructed codes with almost the same performance is given. Also some bounds for the capacity of exact-repairing codes are given. These bounds illustrate the relationships between storage codes with different parameters.