An Improved Cooperative Repair Scheme for Reed-Solomon Codes

Zhang, Yaqian; Zhang, Zhifang

doi:10.1109/iscit.2019.8905159

Cited by 12 publications

(16 citation statements)

References 15 publications

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“…Both perform the same steps during the Download Phase but follow different procedures in the Collaboration Phase: the one-round procedure allows the two RNs to exchange all − m missing traces at once while the multi-round allows the missing traces to be recovered batch-by-batch. Note that in [6], [17], [20], only one missing trace needs to be recovered in the Collaboration Phase, which is easier to handle.…”

Section: Repairing Two Erasures In Reed-solomon Codesmentioning

confidence: 99%

“…There has been a considerable effort by the research community to improve and optimize the repair bandwidth of Reed-Solomon codes [9]- [16]. Several extensions to the case of multiple erasures were also studied [6], [16]- [20]. The optimal repair bandwidth of Reed-Solomon codes is generally unknown, except for some full-length codes [1], [10], [11] and for codes with exponentially large subpacketizations [15], [16].…”

mentioning

confidence: 99%

“…We also develop distributed schemes that repair two erasures for Reed-Solomon codes. When r ≥ q −1 , it has been shown by Dau et al [6], [17] and by Zhang and Zhang [20] that two erasures can be repaired using a bandwidth of (n − 1) log 2 q bits per erasure via trace polynomial approaches. Our goal is to consider the more general case when r ≥ q m , 1 ≤ m ≤ .…”

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confidence: 99%

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Repairing Reed-Solomon Codes via Subspace Polynomials

Dau¹,

Xinh²,

Kiah³

et al. 2020

Preprint

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We propose new repair schemes for Reed-Solomon codes that use subspace polynomials and hence generalize previous works in the literature that employ trace polynomials. The Reed-Solomon codes are over F q and have redundancy r = n − k ≥ q m , 1 ≤ m ≤ , where n and k are the code length and dimension, respectively. In particular, for one erasure, we show that our schemes can achieve optimal repair bandwidths whenever n = q and r = q m , for all 1 ≤ m ≤ . For two erasures, our schemes use the same bandwidth per erasure as the single erasure schemes, for /m is a power of q, and for = q a , m = q b − 1 > 1 (a ≥ b ≥ 1), and for m ≥ /2 when is even and q is a power of two. I. INTRODUCTIONThe repair bandwidth is a crucial performance metric of erasure codes when deployed in distributed storage systems [2], [3]. In such systems, for an underlying finite field F, e.g. F = GF(256), a data vector in F k is transformed into a codeword vector in F n , whose components are subsequently stored at different storage nodes. When a node fails, the codedword symbol stored at that node is erased (lost). A replacement node (RN) has to recover the content stored at the failed node by downloading relevant information from the remaining operational nodes. The repair bandwidth refers to the total amount of information (in bits) that the RN has to download in order to complete the repair process. If multiple erasures occur, different RNs may also exchange information in a distributed manner, and we are interested in the bandwidth used per erasure. Alternatively, multiple erasures can be recovered by a centralized entity, which, however, is not the focus of this work.Reed-Solomon codes [4], the most practically used maximum distance separable codes [5], have been deployed in major distributed storage systems such as the Google File System II, Quantcast File System, Yahoo Object Store, Facebook f4 Storage System, Baidu Atlas Cloud Storage, Backblaze Vaults, and HDFS (see [6, Table I]). However, they perform poorly as erasure codes under the repair bandwidth metric. For instance, to repair a data chunk of size 256 MB, the default repair scheme for the Reed-Solomon code (14, 10) employed by Facebook's f4 [7]

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Section: Repairing Two Erasures In Reed-solomon Codesmentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

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Repairing Reed-Solomon Codes via Subspace Polynomials

Dau¹,

Xinh²,

Kiah³

et al. 2020

Preprint

View full text Add to dashboard Cite

show abstract

“…However, the repair schemes for two failed symbols in [26] are either confined to the case of char(F ) | t, or demand a sequential repair of the two erasures, where char(F ) represents the character of the finite field F . An improved distributed repair scheme with two erasures of RS codes was proposed in [27], which eliminates all limitations of [26]. When n − k ≥ |B| m , 1 ≤ m < t, [28] displayed some distributed repair schemes with one or more rounds, which can repair two failed symbols of RS codes by applying subspace polynomials.…”

Section: Introductionmentioning

confidence: 99%

Distributed Repairing Multiple Erasures in Reed-Solomon Codes

Lin

2023

Preprint

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The application of Reed-Solomon (RS) codes in distributed storage systems is widespread. A lot of literature have proposed repair schemes for RS codes with one or multiple failed symbols, which can reduce communication cost during repair (i.e. repair bandwidth). However, for repair schemes of RS codes with multiple failed symbols, the existing distributed repair schemes can only repair $e=2,3$ erasures. In this paper, by intelligently dividing the set of evaluation points corresponding to failed symbols, a distributed repair scheme for RS codes with $e\geq 4$ erasures are proposed.

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“…More surprisingly, in recent years a new interest in these codes has risen in the research community. It is caused by the fact that they are extensively used in cloud technology, namely in distributed storage systems [5,6,7,8,9]. In [1] it was shown that RS codes could be extended not only three times, but even five times when they are constructed over certain finite fields.…”

Section: Introductionmentioning

confidence: 99%

Decoding Five Times Extended Reed Solomon Codes Using Syndromes

Farkas

Rakús

2020

cai

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Recently a new family of five times extended Reed Solomon codes constructed over certain finite fields GF (2 ζ ), where ζ ≥ 3 is an odd integer, was discovered. Until now only an erasure decoding algorithm for these codes was published. In this paper a new decoding algorithm is presented, which allows correcting up to two errors in a codeword from the five times extended Reed Solomon codes. The proposed decoding algorithm is based on syndrome usage.

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An Improved Cooperative Repair Scheme for Reed-Solomon Codes

Cited by 12 publications

References 15 publications

Repairing Reed-Solomon Codes via Subspace Polynomials

Repairing Reed-Solomon Codes via Subspace Polynomials

Distributed Repairing Multiple Erasures in Reed-Solomon Codes

Decoding Five Times Extended Reed Solomon Codes Using Syndromes

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