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Abstract
Edge computing, as an emerging computing paradigm, aims to reduce network bandwidth transmission overhead while storing and processing data on edge nodes. However, the storage strategies required for edge nodes are different from those for existing data centers. Erasure code (EC) strategies have been applied in some decentralized storage systems to ensure the privacy and security of data storage. Product-matrix (PM) regenerating codes (RGCs) as a state-of-the-art EC family are designed to minimize the repair bandwidth overhead or minimize the storage overhead. Nevertheless, the high complexity of the PM framework contains more finite-domain multiplication operations than classical ECs, which heavily consumes computational resources at the edge nodes. In this paper, a theoretical derivation of each step of the PM minimum storage regeneration (PM-MSR) and PM minimum bandwidth regeneration (PM-MBR) codes is performed and the XOR complexity over finite fields is analyzed. On this basis, a new construct called product bitmatrix (PB) is designed to reduce the complexity of XOR operations in the PM framework, and two heuristics are used to further reduce the XOR numbers of the PB-MSR and PB-MBR codes, respectively. The evaluation results show that the PB construction significantly reduces the XOR number compared to the PM-MSR, PM-MBR, Reed–Solomon (RS), and Cauchy RS codes while retaining optimal performance and reliability.
Highlights
Edge computing has emerged as a new paradigm for addressing local computing needs and moving data computation or storage to an edge node near the end user [1,2,3]
regenerating codes (RGCs) maintains the same reliability as erasure code (EC), but both of them are calculated over a finite field. ere are two principal RGC classes, Security and Communication Networks namely, minimum storage regenerating (MSR) and minimum bandwidth regenerating (MBR) codes, which imply two extreme points in a trade-off known as the storage-repair bandwidth trade-off. ere have been many frameworks designed for MSR and MBR codes, respectively [7, 18,19,20], but as far as we know, the product-matrix (PM) framework proposed by Rashmi et al is the only framework that constructs two codes in a unified way [21], and the PM framework provides exact repair of PM minimum storage regeneration (PM-MSR) (2k − 2 ≤ d) and PM minimum bandwidth regeneration (PM-MBR) (k ≤ d ≤ n − 1) codes
Since the PM framework has a large number of XORs at each step, especially in the decoding process of the PM-MSR code, the computational complexity of the inversion of the Vandermonde matrix is O(n3). erefore, we propose a new construction called product bitmatrix (PB)
Summary
Edge computing has emerged as a new paradigm for addressing local computing needs and moving data computation or storage to an edge node near the end user [1,2,3]. In contrast to cloud storage built on a network, edge computing-based storage is distributed among the edges of the network structure [4, 5] These edge nodes are in need of fault-tolerant techniques to ensure system reliability and availability and even more importantly to ensure data privacy and security [6]. We focus on the PM framework, analyzing the computational complexity of the encoding, decoding, and repair processes over GF(2w). Since the PM framework has a large number of XORs at each step, especially in the decoding process of the PM-MSR code, the computational complexity of the inversion of the Vandermonde matrix is O(n3). (ii) A new construction called product bitmatrix for MSR and MBR codes is designed, and we elaborate on the encoding, decoding, and repair processes in detail.
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