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=2n+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.
Highlights
The NAND (NOT AND) logic type 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 disk, etc
The hierarchical structure of NAND flash is as follows: A series of NAND cells is connected in strings which are organized in pages, pages are organized in blocks and so on
In this paper we propose a constructions of codes over Z2n +1 correcting single asymmetric errors of type (1, 2), (±1, ±2) or (1, 2, 3)
Summary
The NAND (NOT AND) logic type 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 disk, etc. Asymmetric limited-magnitude error-correcting codes were proposed by Varshamov and Tenengolz [1,2] and in a more general form by Ahlswede et al [3]. Bose [5] proposed systematic codes that correct single limited-magnitude systematic asymmetric errors and achieve a higher rate than the ones given in [4]. They showed how their code construction can be slightly modified to give codes correcting symmetric errors of limited magnitude. In this paper we propose a constructions of codes over Z2n +1 correcting single asymmetric errors of type (1, 2), (±1, ±2) or (1, 2, 3). In the Appendix, more detailed information about constructed codes is presented
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