Multicluster Interleaving on Paths and Cycles

Jiang, Anxiao; Bruck, Jehoshua

doi:10.1109/tit.2004.840893

Cited by 12 publications

(7 citation statements)

References 17 publications

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“…Most 2-D burst error correcting codes that have been studied in the literature correct only error bursts of given rectangular [1,5,6,10,12,15,16,21] or other prescribed shapes [2,7,11,20]. See also [17,18] for related interleaving schemes on tori, paths, and cycles, and [4,9,19] for 2-D interleaving schemes for multiple random error correction codes. In [3], the authors have considered arbitrarily shaped error bursts and studied the problem of interleaving a minimum number of codewords in a 2-D (or 3-D) array such that any error burst of given size t can be corrected.…”

Section: Introduction and Statement Of Main Resultsmentioning

confidence: 99%

Optimal interleaving schemes for correcting two-dimensional cluster errors

Golomb

2007

Discrete Applied Mathematics

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We present an elementary theory of optimal interleaving schemes for correcting cluster errors in two-dimensional digital data. It is assumed that each data page contains a fixed number of, say n, codewords with each codeword consisting of m code symbols and capable of correcting a single random error (or erasure). The goal is to interleave the codewords in the m × n array such that different symbols from each codeword are separated as much as possible, and consequently, an arbitrary error burst with size up to t can be corrected for the largest possible value of t. We show that, for any given m, n, the maximum possible interleaving distance, or equivalently, the largest size of correctable error bursts in an m × n array, is given by t = √ 2n if n m 2 /2 , and t = m + (n − m 2 /2 )/m if n m 2 /2 . Furthermore, we develop a simple cyclic shifting algorithm that can provide a systematic construction of an m × n optimal interleaving array for arbitrary m and n. This extends important earlier work on the complementary problem of constructing interleaving arrays that, given the burst size t, minimize the interleaving degree, that is, the number of different codewords in a 2-D (or 3-D) array such that any error burst with given size t can be corrected. Our interleaving scheme thus provides the maximum burst error correcting power without requiring prior knowledge of the size or shape of an error burst.

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Section: Introduction and Statement Of Main Resultsmentioning

confidence: 99%

Optimal interleaving schemes for correcting two-dimensional cluster errors

Golomb

2007

Discrete Applied Mathematics

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“…Etzion and Vardy have investigated 2D interleaving schemes with repetitions [113]. Jiang and Bruck introduced the concept of multicluster interleaving (MCI), a generalization of traditional interleaving problems [114]. Compared to traditional interleaving schemes, MCI has the distinct feature that the diversity of integers is required in multiple, instead of single, clusters.…”

Section: Error Correction Codesmentioning

confidence: 99%

Recent advances in holographic data storage

Ruan

2014

Front. Optoelectron.

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Nowadays, big-data centers still rely on hard drives. However, there is strong evidence that these surface-storage technologies are approaching fundamental limits that may be difficult to overcome, as ever-smaller bits become less thermally stable and harder to access. An intriguing approach for next generation data-storage is to use light to store information throughout the threedimensional (3D) volume of a material. Holographic data storage (HDS) is poised to change the way we write and retrieve data forever. After many years of developing appropriate recording media and optical read-write architectures, this promising technology is now moving industriously to the market. In this paper, a review of the major achievements of HDS in the past ten years is presented and the key technique details are discussed. The author concludes that HDS technology is an attractive candidate for big data centers in the future. On the other hand, there are many challenges ahead for HDS technology to overcome in the years to come.

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“…[33]. Various heuristic algorithms have been proposed to optimize color diversify in graphs of different topology [33,34]. For instance, in tree networks one can adopt the method suggested in Ref.…”

Section: Frequency Allocationmentioning

confidence: 99%

Networking—a statistical physics perspective

Yeung¹,

Saad²

2013

J. Phys. A: Math. Theor.

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Efficient networking has a substantial economic and societal impact in a broad range of areas including transportation systems, wired and wireless communications and a range of Internet applications. As transportation and communication networks become increasingly more complex, the ever increasing demand for congestion control, higher traffic capacity, quality of service, robustness and reduced energy consumption require new tools and methods to meet these conflicting requirements. The new methodology should serve for gaining better understanding of the properties of networking systems at the macroscopic level, as well as for the development of new principled optimization and management algorithms at the microscopic level. Methods of statistical physics seem best placed to provide new approaches as they have been developed specifically to deal with non-linear large scale systems. This paper aims at presenting an overview of tools and methods that have been developed within the statistical physics community and that can be readily applied to address the emerging problems in networking. These include diffusion processes, methods from disordered systems and polymer physics, probabilistic inference, which have direct relevance to network routing, file and frequency distribution, the exploration of network structures and vulnerability, and various other practical networking applications.

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Multicluster Interleaving on Paths and Cycles

Cited by 12 publications

References 17 publications

Optimal interleaving schemes for correcting two-dimensional cluster errors

Optimal interleaving schemes for correcting two-dimensional cluster errors

Recent advances in holographic data storage

Networking—a statistical physics perspective

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