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Journal ArticleDOI

Polynomial Codes Over Certain Finite Fields

01 Jun 1960-Journal of The Society for Industrial and Applied Mathematics (Society for Industrial and Applied Mathematics)-Vol. 8, Iss: 2, pp 300-304
TL;DR: A mapping of m symbols into 2 symbols will be shown to be (2 m)/2 or ( 2 m 1)/2 symbol correcting, depending on whether m is even or odd.
Abstract: a._) into the 2-tuple (P(0), P(a), P(a:), P(1 ); this m-tuple might be some encoded message and the corresponding 2n-tuple is to be transmitted. This mapping of m symbols into 2 symbols will be shown to be (2 m)/2 or (2 m 1)/2 symbol correcting, depending on whether m is even or odd. A natural correspondence is established between the field elements of K and certain binary sequences of length n. Under this correspondence, code E may be regarded as a mapping of binary sequences of mn bits into binary sequences of n2 bits. Thus code E can be interpreted to be a systematic multiple-error-correcting code of binary sequences.
Citations
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Proceedings Article
13 Jun 2012
TL;DR: This paper describes how LRC is used in WAS to provide low overhead durable storage with consistently low read latencies, and introduces a new set of codes for erasure coding called Local Reconstruction Codes (LRC).
Abstract: Windows Azure Storage (WAS) is a cloud storage system that provides customers the ability to store seemingly limitless amounts of data for any duration of time WAS customers have access to their data from anywhere, at any time, and only pay for what they use and store To provide durability for that data and to keep the cost of storage low, WAS uses erasure coding In this paper we introduce a new set of codes for erasure coding called Local Reconstruction Codes (LRC) LRC reduces the number of erasure coding fragments that need to be read when reconstructing data fragments that are offline, while still keeping the storage overhead low The important benefits of LRC are that it reduces the bandwidth and I/Os required for repair reads over prior codes, while still allowing a significant reduction in storage overhead We describe how LRC is used in WAS to provide low overhead durable storage with consistently low read latencies

1,002 citations

Journal ArticleDOI
TL;DR: In this article, the authors survey the current state of phase change memory (PCM), a nonvolatile solid-state memory technology built around the large electrical contrast between the highly resistive amorphous and highly conductive crystalline states in so-called phase change materials.
Abstract: The authors survey the current state of phase change memory (PCM), a nonvolatile solid-state memory technology built around the large electrical contrast between the highly resistive amorphous and highly conductive crystalline states in so-called phase change materials. PCM technology has made rapid progress in a short time, having passed older technologies in terms of both sophisticated demonstrations of scaling to small device dimensions, as well as integrated large-array demonstrators with impressive retention, endurance, performance, and yield characteristics. They introduce the physics behind PCM technology, assess how its characteristics match up with various potential applications across the memory-storage hierarchy, and discuss its strengths including scalability and rapid switching speed. Challenges for the technology are addressed, including the design of PCM cells for low reset current, the need to control device-to-device variability, and undesirable changes in the phase change material that c...

921 citations

Journal ArticleDOI
TL;DR: This work contributes to understanding which design components of reputation systems are most vulnerable, what are the most appropriate defense mechanisms and how these defense mechanisms can be integrated into existing or future reputation systems to make them resilient to attacks.
Abstract: Reputation systems provide mechanisms to produce a metric encapsulating reputation for a given domain for each identity within the system. These systems seek to generate an accurate assessment in the face of various factors including but not limited to unprecedented community size and potentially adversarial environments.We focus on attacks and defense mechanisms in reputation systems. We present an analysis framework that allows for the general decomposition of existing reputation systems. We classify attacks against reputation systems by identifying which system components and design choices are the targets of attacks. We survey defense mechanisms employed by existing reputation systems. Finally, we analyze several landmark systems in the peer-to-peer domain, characterizing their individual strengths and weaknesses. Our work contributes to understanding (1) which design components of reputation systems are most vulnerable, (2) what are the most appropriate defense mechanisms and (3) how these defense mechanisms can be integrated into existing or future reputation systems to make them resilient to attacks.

907 citations

Proceedings ArticleDOI
23 Oct 2011
TL;DR: The WAS architecture, global namespace, and data model is described, as well as its resource provisioning, load balancing, and replication systems.
Abstract: Windows Azure Storage (WAS) is a cloud storage system that provides customers the ability to store seemingly limitless amounts of data for any duration of time. WAS customers have access to their data from anywhere at any time and only pay for what they use and store. In WAS, data is stored durably using both local and geographic replication to facilitate disaster recovery. Currently, WAS storage comes in the form of Blobs (files), Tables (structured storage), and Queues (message delivery). In this paper, we describe the WAS architecture, global namespace, and data model, as well as its resource provisioning, load balancing, and replication systems.

871 citations

Journal ArticleDOI
TL;DR: An overview of the research effort on volume holographic digital data storage is presented, highlighting new insights gained in the design and operation of working storage platforms, novel optical components and techniques, data coding and signal processing algorithms, systems tradeoffs, materials testing and tradeoff, and photon-gated storage materials.
Abstract: We present an overview of our research effort on volume holographic digital data storage. Innovations, developments, and new insights gained in the design and operation of working storage platforms, novel optical components and techniques, data coding and signal processing algorithms, systems tradeoffs, materials testing and tradeoffs, and photon-gated storage materials are summarized.

773 citations

References
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Journal ArticleDOI
TL;DR: The author was led to the study given in this paper from a consideration of large scale computing machines in which a large number of operations must be performed without a single error in the end result.
Abstract: The author was led to the study given in this paper from a consideration of large scale computing machines in which a large number of operations must be performed without a single error in the end result. This problem of “doing things right” on a large scale is not essentially new; in a telephone central office, for example, a very large number of operations are performed while the errors leading to wrong numbers are kept well under control, though they have not been completely eliminated. This has been achieved, in part, through the use of self-checking circuits. The occasional failure that escapes routine checking is still detected by the customer and will, if it persists, result in customer complaint, while if it is transient it will produce only occasional wrong numbers. At the same time the rest of the central office functions satisfactorily. In a digital computer, on the other hand, a single failure usually means the complete failure, in the sense that if it is detected no more computing can be done until the failure is located and corrected, while if it escapes detection then it invalidates all subsequent operations of the machine. Put in other words, in a telephone central office there are a number of parallel paths which are more or less independent of each other; in a digital machine there is usually a single long path which passes through the same piece of equipment many, many times before the answer is obtained.

5,408 citations

Journal ArticleDOI
01 Sep 1954
TL;DR: A class of multiple-error-correcting codes and their decoding scheme to device a coding scheme which is able to detect and correct such errors.
Abstract: linear error-correcting codes used in communications. (14) I. S. Reed, “A class of multiple-errorcorrecting codes and the decoding scheme,” IRE. Trans. A class of multiple-error-correcting codes and the decoding scheme. more. less. I. Reed · Details · Authors · Fields of science · Bibliography · Quotations · Similar. linear error correcting codes used in communications (2).For bit study is to device a coding scheme which is able to detect and correct such errors (6). (8) Reed, I. S., 'Class of multiple error correcting codes and their decoding scheme'.

868 citations