Construction of multi-permutation codes for correcting translocation errors in rank modulated flash memory

Error-correcting codes based on multi-permutation groups allow multiple cells to be rank modulated with the same charge levels, which helps to reduce the range of charge levels for flash memory. Compared with permutation codes, multi-permutation codes can more effectively resist the storage errors caused by small differences between cell charges, so as to improve the information storage rates of flash memory. To correct a single translocation error caused by charge leakage or cell over-injection in flash memory devices, a class of multipermutation codes is constructed under the Chebyshev distance by using interleaving and mapping techniques for multi-permutations. The decoding method is presented in the proof of the proposed construction, and the asymptotic code rates are analyzed. The code construction and the decoding method are validated with examples.