A Novel Decoding Method for the Erasure Codes

Dan Tang,Hongliang Cai,Zhili Zhou

doi:10.1155/2021/8755697

Dan Tang, Hongliang Cai + Show 1 more

Open Access

https://doi.org/10.1155/2021/8755697

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Abstract

The erasure codes are widely used in the distributed storage with low redundancy compared to the replication method. However, the current research studies about the erasure codes mainly focus on the encoding methods, while there are few studies on the decoding methods. In this paper, a novel erasure decoding method is proposed; it is a general decoding method and can be used both over the multivariate finite field and the binary finite field. The decoding of the failures can be realized based on the transforming process of the decoding transformation matrix, and it is convenient to avoid the overburdened visiting problem by tiny modification of the method. The correctness of the method is proved by the theoretical analysis; the experiments about the comparison with the traditional methods show that the proposed method has better decoding efficiency and lower reconstruction bandwidth.

Highlights

Erasure coding is a widely used method in the distributed storage system to protect against the failures of the storage nodes; it can provide better failure tolerance and much lower storage redundancy. e original information is first divided into k blocks; the k blocks are encoded into n blocks using the encoding method; when there are less than n−k blocks missed, the lost blocks can be recovered by the decoding method. ere are a lot of research studies about the encoding methods, while only a few studies focus on the decoding methods
A storage system based on the RS erasure code can achieve the optimal tradeoff between the storage redundancy and the ability of the failure tolerance
We propose a novel method for the erasure codes for the storage system which is different from the replication method, so the erasure codes do not include the repetition code which is the replication method; there are three cases for the elementary row transformation over GF(q) [21]:

Summary

Introduction

Erasure coding is a widely used method in the distributed storage system to protect against the failures of the storage nodes; it can provide better failure tolerance and much lower storage redundancy. e original information is first divided into k blocks; the k blocks are encoded into n blocks using the encoding method; when there are less than n−k blocks missed, the lost blocks can be recovered by the decoding method. ere are a lot of research studies about the encoding methods, while only a few studies focus on the decoding methods. Ere are two properties about the transformation of the linear relation matrix, which are important for the proposed decoding method. For Case 1, from the definition of the linear relation matrix, the ith row in the linear relation matrix represents the linear combination about ci, i is an integer and 0 ≤ i ≤ n − 1: ci ai,0c0 + ai,1c1 + · · · + ai,n−1cn−1. The vector v by t and add the result to ith row of the linear relation matrix W, and it is still a linear relation matrix. From the definition of the linear relation matrix, the ith row vector After multiplying the vector v by t and adding the result to ith row of W, the ith row of the renewed linear matrix becomes The renewed matrix after the row transformation is still a linear relation matrix

The Proposed Decoding Method for the Erasure Codes

Experiments and Analysis

Conclusion