Abstract
With the number of nodes increasing in scale, the requirements of storage space enlarge sharply in distributed storage systems. Failure-tolerance schemes such as Reed–Solomon codes (RS codes in short) and Cauchy Reed–Solomon codes (CRS codes in short) are used to save storage space. However, these failure-tolerance schemes severely degrade the system performance. In this paper, we propose optimal RS codes (OptRS codes in short) based on RS codes and CRS codes that can offer better performance for encoding and decoding as well as maximizing the utilization of storage space. OptRS codes can speed up the matrix computation which is regarded as the most important factor to impact the efficiency of coding by transferring the matrix computation from the Galois field mapping to the XOR operation. OptRS codes employ an algorithm called row elimination scheme (RE scheme in short), which can eliminate the same XOR operation to minimize the number of XOR operations. We analyze optimal matrices (OM in short) in theory, which prove the optimal performance of OptRS codes over the Galois field. Our method is implemented on the top of the distributed storage system, and code parameters were carefully chosen. The test result shows that OptRS codes can improve the performance in different data block numbers, parity block numbers, block size, normal reading, and degraded reading, compared with RS codes and CRS codes.
Highlights
Background and MotivationErasure codes can save storage space as an alternative to replication in storage systems
Data are encoded in an erasure-coded storage system with three schemes, RS codes, CRS codes, and OptRS codes. e experiments are implemented on a fournode cluster of machines
We have proposed OptRS codes that extend the theoretical construction with practical considerations that lead directly to implementation
Summary
Chao Yin ,1 Haitao Lv ,1 Tongfang Li ,1 Xiaoping Qu, Jianzong Wang ,2 and Guangyong Gao 3. All the user data and redundancy data within a coding group should be read from surviving nodes, and the lost data are reconstructed through the complex decoding process It requires a large amount of read data and high computation cost during the decoding, which result in a higher repair cost compared with the replication. We have developed the RE scheme constructed by eliminating redundant rows from the analysis of the related rows It can improve the system performance by decreasing the computation cost in the encoding and decoding process. E RE scheme has been used in the computation to get the coded values in OptRS codes It can decrease the numbers of XOR and improve the encoding and decoding speed.
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