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Integer Codes Correcting Asymmetric Errors in Nand Flash Memory

Author

Listed:
  • Hristo Kostadinov

    (Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Acad. G. Bonchev Str., Bl.8, 1113 Sofia, Bulgaria)

  • Nikolai Manev

    (Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Acad. G. Bonchev Str., Bl.8, 1113 Sofia, Bulgaria)

Abstract

Memory devices based on floating-gate transistor have recently become dominant technology for non-volatile storage devices like USB flash drives, memory cards, solid-state disks, etc. In contrast to many communication channels, the errors observed in flash memory device use are not random but of special, mainly asymmetric, type. Integer codes which have proved their efficiency in many cases with asymmetric errors can be applied successfully to flash memory devices, too. This paper presents a new construction and integer codes over a ring of integers modulo A = 2 n + 1 capable of correcting single errors of type ( 1 , 2 ) , ( ± 1 , ± 2 ) , or ( 1 , 2 , 3 ) that are typical for flash memory devices. The construction is based on the use of cyclotomic cosets of 2 modulo A . The parity-check matrices of the codes are listed for n ≤ 10 .

Suggested Citation

  • Hristo Kostadinov & Nikolai Manev, 2021. "Integer Codes Correcting Asymmetric Errors in Nand Flash Memory," Mathematics, MDPI, vol. 9(11), pages 1-9, June.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:11:p:1269-:d:566789
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    Cited by:

    1. Hristo Kostadinov & Nikolai Manev, 2023. "A General Construction of Integer Codes Correcting Specific Errors in Binary Communication Channels," Mathematics, MDPI, vol. 11(11), pages 1-8, May.

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