On (.+-.1) Error Correctable Integer Codes

Kostadinov, Hristo; Morita, Hiroyuki; Manev, Nikolai L.

doi:10.1587/transfun.e93.a.2758

Cited by 7 publications

(4 citation statements)

References 8 publications

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“…All examples below choose minimum element of A as x when we make the set L. This code is equivalent to (±1) error correcting code in [9]. Actually, any codes in [9] can be constructed by proposed method when the minimum element of A is chosen as x in the algorithm to determine L. Therefore, proposed codes are said to be generalization of the code.…”

Section: Qed) the Number Of Column Vectors In Respective Submatricmentioning

confidence: 99%

“…Sato and Kitakami realized the function by taking advantage of Gray code for MLC Flash memories [8]. Also, Kostadinov et al did it by constructing codes over integer ring, called integer codes [9]. These codes are originally proposed for communication systems, but applicable for MLC Flash memories.…”

Section: Introductionmentioning

confidence: 99%

“…The codes is constructed over integer ring because integer codes can correct errors of a given type [9]. In other words, we can select neighborhood values as correctable error patterns.…”

Section: Introductionmentioning

confidence: 99%

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Neighborhood Level Error Control Codes for Multi-Level Cell Flash Memories

Kotaki

Kitakami

2013

IEICE Trans. Inf. & Syst.

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SUMMARYNAND Flash memories are widely used as data storages today. The memories are not intrinsically error free because they are affected by several physical disturbances. Technology scaling and introduction of multi-level cell (MLC) has improved data density, but it has made error effect more significant. Error control codes (ECC) are essential to improve reliability of NAND Flash memories. Efficiency of codes depends on error characteristic of systems, and codes are required to be designed to reflect this characteristic. In MLC Flash memories, errors tend to direct values to neighborhood. These errors are a class of M-ary asymmetric symbol error. Some codes which reflect the asymmetric property were proposed. They are designed to correct only 1 level shift errors because almost all of the errors in the memories are in such errors. But technology scaling, increase of program/erase (P/E) cycles, and MLC storing the large number of bits can cause multiple-level shift. This paper proposes single error control codes which can correct an error of more than 1 levels shift. Because the number of levels to be corrected is selectable, we can fit it into noise magnitude. Furthermore, it is possible to add error detecting function for error of the larger shift. Proposed codes are equivalent to a conventional integer codes, which can correct 1 level shift, on a certain parameter. Therefore, the codes are said to be generalization of conventional integer codes. Evaluation results show information lengths to respective check symbol lengths are larger than nonbinary Hamming codes and other M-ary asymmetric symbol error correcting codes.

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Section: Qed) the Number Of Column Vectors In Respective Submatricmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Neighborhood Level Error Control Codes for Multi-Level Cell Flash Memories

Kotaki

Kitakami

2013

IEICE Trans. Inf. & Syst.

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“…Errors occuring in the channel usually have a limited magnitude, and this effect is particularly applicable to flash memories. There have been a couple of papers regarding the optimal ±1 single error correcting codes over alphabet [1,2]. In this paper we will consider on errors with the magnitude ±1 or ±2.…”

Section: Introductionmentioning

confidence: 99%