On lowest density MDS codes

Abstract-The complexity of software implementations of MDS erasure codes mainly depends on the efficiency of the finite field operations implementation. In this paper, we propose a method to reduce the complexity of the finite field multiplication by using simple transforms between a field and a ring to perform the multiplication in a ring. We show that moving to a ring reduces the complexity of the operations. Then, we show that this construction allows the use of simple scheduling to reduce the number of operations.

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“…Its factor over optimal is equal to 1.2 which is lower than the values given in Figure 1 and which is close to the lowest bound given in [3].…”

Section: (Min(k M)+k+m−1)w+(k−1)(m−1)w = Kw+kmwmentioning

confidence: 70%

“…the number of xor operations, depends on the size of the finite field and also on the element itself. This kind of complexity is studied for Maximum-Distance Separable (MDS) codes in [3]. Other work has been done to reduce redundant xor operations by applying scheduling [4].…”

Section: Introductionmentioning

confidence: 99%

Polynomial ring transforms for efficient XOR-based erasure coding

Detchart

Lacan

2017

2017 IEEE International Symposium on Information Theory (ISIT)

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“…As mentioned in [6,Introduction], each [n, k] MDS linear code over the finite field GF (2 b ) could be considered as an MDS b × n array code (not necessarily array BP-XOR code). However, the converse is not true (see Theorem 5.1 in Section V-C. Table X lists some known maximum value of n (see, e.g., [12], [28]) for the existence of [n, k] MDS linear codes over…”

Section: B Comparison With Bounds For Linear Mds Codesmentioning

confidence: 99%

“…Array codes have been studied extensively for burst error correction in communication systems and storage systems (see, e.g., [3], [4], [5], [6], [8], [14], [36], [37]). Array codes are linear codes where information and parity data are placed in a two dimensional matrix array.…”

Section: Introductionmentioning

confidence: 99%

On encoding symbol degrees of array BP-XOR codes

2015

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Abstract-Low density parity check (LDPC) codes, LT codes and digital fountain techniques have received significant attention from both academics and industry in the past few years. By employing the underlying ideas of efficient Belief Propagation (BP) decoding process (also called iterative message passing decoding process) on binary erasure channels (BEC) in LDPC codes, Wang has recently introduced the concept of array BP-XOR codes and showed the necessary and sufficient conditions for MDS [k + 2, k] and [n, 2] array BP-XOR codes. In this paper, we analyze the encoding symbol degree requirements for array BP-XOR codes and present new necessary conditions for array BP-XOR codes. These new necessary conditions are used as a guideline for constructing several array BP-XOR codes and for presenting a complete characterization (necessary and sufficient conditions) of degree two array BP-XOR codes and for designing new edge-colored graphs. Meanwhile, these new necessary conditions are used to show that the codes by Feng, Deng, Bao, and Shen in IEEE Transactions on Computers are incorrect.

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“…The update problem in such a cloud storage system has been investigated in several research works [10], [11], [12], [13]. Reed-Solomon codes originally are non-binary cyclic error correcting codes that have been used in many data storage and communication applications [14].…”

Section: Related Workmentioning

confidence: 99%

An update model for network coding in cloud storage systems

Zakerinasab¹,

Wang²

2012

2012 50th Annual Allerton Conference on Communication, Control, and Computing (Allerton)

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Abstract-The fast emerging cloud services have received a tremendous amount of attention in both industry and academia. Storage services such as Dropbox and iCloud enabled us to share files among multiple users or devices. Providing the benefits of network coding in distributed systems such as Peerto-Peer file sharing and multimedia streaming, researchers have also been trying to apply network coding in storage systems. Existing works have been focusing on mechanisms for preserving the level of redundancy when one or more nodes fail or leave the system. However, file updates, the most frequent operations performed on files, pose challenges in maintaining coded information in the system up to date. In other words, any change in the file will impact all coded blocks in the system, so all traces of the file must be completely replaced. This becomes costly since recomputing coded blocks is very CPU intensive and replacing all the coded blocks consumes an excessive amount of bandwidth. To the best of our knowledge, there has been no work addressing this update problem. To this end, we propose a Differential Update Model (DUM) that will update coded blocks by delivering only the changes in the file. We also present our objective view of the model through a complete analysis on computational complexity and bandwidth saving and simulated experiments.

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On lowest density MDS codes

Cited by 198 publications

References 6 publications

Polynomial ring transforms for efficient XOR-based erasure coding

Polynomial ring transforms for efficient XOR-based erasure coding

On encoding symbol degrees of array BP-XOR codes

An update model for network coding in cloud storage systems

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