Linear binary code for write-once memories (Corresp.)

Cohen, Gérard; Godlewski, Philippe; Merkx, F.

doi:10.1109/tit.1986.1057221

Cited by 83 publications

(69 citation statements)

References 7 publications

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“…RELATED WORK WOM codes were first studied by Rivest, Shamir [10] [11], and multiple classes of codes have been invented. The majority of those codes are binary, and they include tabular codes [10], linear codes [2] [10], codes constructed using Golay codes [2] or projective geometries [9], etc. Besides WOM, constrained memories also include write efficient memory (WEM), write unidirectional memory (WUM) and write isolated memory (WIM) [8].…”

Section: Introductionmentioning

confidence: 99%

Floating Codes for Joint Information Storage in Write Asymmetric Memories

Jiang

Bohossian

Bruck

2007

2007 IEEE International Symposium on Information Theory

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Abstract-Memories whose storage cells transit irreversibly between states have been common since the start of the data storage technology. In recent years, flash memories and other non-volatile memories based on floating-gate cells have become a very important family of such memories. We model them by the Write Asymmetric Memory (WAM), a memory where each cell is in one of q states -state 0, 1, ***, q -1 -and can only transit from a lower state to a higher state. Data stored in a WAM can be rewritten by shifting the cells to higher states. Since the state transition is irreversible, the number of times of rewriting is limited. When multiple variables are stored in a WAM, we study codes, which we call floating codes, that maximize the total number of times the variables can be written and rewritten.In this paper, we present several families of floating codes that either are optimal, or approach optimality as the codes get longer. We also present bounds to the performance of general floating codes. The results show that floating codes can integrate the rewriting capabilities of different variables to a surprisingly high degree.

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Section: Introductionmentioning

confidence: 99%

Floating Codes for Joint Information Storage in Write Asymmetric Memories

Jiang

Bohossian

Bruck

2007

2007 IEEE International Symposium on Information Theory

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“…Many attempts have been made to determine the theoretical limit of maximum number of bits stored per cell. Several code constructions for the binary WOM were proposed by Rivest, Shamir [12] and Cohen, Godlewski, and Merkx [3]. Wolf, Wyner, Ziv, and Körner [13] established the (zero-error) capacity region of the binary WOM.…”

Section: Introduction and Main Resultsmentioning

confidence: 99%

Sum-capacity of multiple-write noisy memory

Wang

Kim

2011

2011 IEEE International Symposium on Information Theory Proceedings

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Abstract-Motivated by the emerging interests in non-volatile solid-state computer memories such as flash memories, this paper studies the problem of repeatedly storing information on memory cells with noise and state. The goal is to reliably convey t messages by writing X n j on an n-cell noisy memory p(yj|xj, yj−1), which stores Y n j at the j-th write. We model this problem as a channel with state and introduce the multiple-write noisy memory model, which includes the write-once memory and flash memory models as special cases. The t-write sum-capacity for the multiple-write noisy memory is established aswhere the maximum is over all pmfs p(x1) t j=2 p(uj|yj−1) and functions xj(uj , yj−1), j = 2, . . . , t. We derive three outer bounds on the capacity region and discuss their extension to other classes of memory models. These results extend Wolf, Wyner, Ziv, and Körner's work on the binary write-once memory and Fu and Vinck's work on the generalized writeonce memory to noisy memories.

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“…A number of very interesting WOM code constructions have been presented over the years, including the tabular codes, linear codes, etc. in [29], the linear codes in [6], the codes constructed using projective geometries [27], and the coset coding in [5]. Fine results on the capacity of WOM have been presented in [8,13,29,33].…”

Section: Extended Information Theoretic Resultsmentioning

confidence: 99%

Data Representation for Flash Memories

Jiang¹,

Bruck²

2010

Data Storage

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In this chapter, we introduce theories on data representation for flash memories. Flash memories are a milestone in the development of the data storage technology. The applications of flash memories have expanded widely in recent years, and flash memories have become the dominating member in the family of non-volatile memories. Compared to magnetic recording and optical recording, flash memories are more suitable for many mobile-, embeddedand mass-storage applications. The reasons include their high speed, physical robustness, and easy integration with circuits. The representation of data plays a key role in storage systems. Like magnetic recording and optical recording, flash memories have their own distinct properties, including block erasure, iterative cell programming, etc. These distinct properties introduce very interesting coding problems that address many aspects of a successful storage system, which include efficient data modification, error correction, and more. In this chapter, we first introduce the flash memory model, then study some newly developed codes, including codes for rewriting data and the rank modulation scheme. A main theme is understanding how to store information in a medium that has asymmetric properties when it transits between different states.

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Linear binary code for write-once memories (Corresp.)

Cited by 83 publications

References 7 publications

Floating Codes for Joint Information Storage in Write Asymmetric Memories

Floating Codes for Joint Information Storage in Write Asymmetric Memories

Sum-capacity of multiple-write noisy memory

Data Representation for Flash Memories

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