Codes Correcting Asymmetric/Unidirectional Errors along with Bidirectional Errors of Small Magnitude

Abstract

Dominant error sources in multi-level cell NAND Flash memories shift threshold voltage levels to either positive or negative values, thus errors are modeled by nonbinary unidirectional channels. However, bidirectional errors can also be caused when positive and negative errors have equivalent significance. Compared to unidirectional cases, error magnitude of bidirectional errors are considered to be small. In this correspondence, novel error correcting codes which correct limited magnitude asymmetric/unidirectional errors along with bidirectional errors of relatively small magnitude are presented. They can be used to reduce encoding and decoding complexity compared to conventional symmetric error correcting codes.