Research On Error Correct Permutation Code In Rank Modulated Flash Memory

As the mainstream memory of non-volatile storage,flash memory has the advantages of low power consumption,high reliability,and high density.However,with the increasing density of flash memory and the shrinking size of chip packages,flash memory faces serious challenges from the reliability of data storage.Permutation codes and multi-permutation codes developed based on rank modulation can correct asymmetric errors in flash memory,thus effectively improving the reliability of flash memory equipment.The underlying permutation codes open up a new research direction in the field of error-control codes of the flash data storage systems.For typical error types in flash memory,this thesis analyzes and proposes the corresponding constructions and decoding methods of permutation codes and multi-permutation codes.The main works and innovations of the thesis are summarized as follows:(1)This thesis introduces the basic knowledge of flash memory,rank modulation and permutation codes,analyzes several typical error types of flash memory,and imports several distance metrics commonly used for permutation codes.(2)The stability of burst erasure errors in rank modulated flash memory cells and the corresponding construction of permutation codes are studied.A class of permutation codes is constructed by using interleaving technique for permutations,which can correct a single stable burst erasure and a single unstable burst erasure respectively.The proposed construction can transform the problem of a single burst erasure into a single erasure,thus effectively reducing the complexity of error correction for burst erasure.Meanwhile,the corresponding decoding methods of two burst erasure errors are given.The code construction and the decoding methods are validated with examples.(3)The construction of multi-permutation codes for translocation errors in rank modulated flash memory cells is studied.Two types of errors are considered: translocation errors and multi-transposition errors.A class of multi-permutation codes is constructed under the Chebyshev distance by using the interleaving and mapping techniques for multi-permutations,which can correct a single translocation error and single multi-transposition errors respectively.Meanwhile,the asymptotic code rates are analyzed,and the corresponding decoding methods of two translocation errors are given.The code construction and the decoding methods are validated with examples.