Multi-Permutation Codes Correcting a Single Burst Unstable Deletions in Flash Memory

Abstract

Multi-permutation codes for rank modulation scheme have been recently proposed for efficiently storing data in flash memories. In this letter, we investigate the problem of a single burst unstable deletion (BUD) of length $t$ in a $t$ -balanced multi-permutation and this problem can be decomposed into the sub-problems of a single permutation-invariant deletion (PID) in $t$ permutations by a rank demodulation method. Based on the rank demodulation method and the interleaving of $t$ single-PID-correcting permutation codes, we construct two classes of $t$ -balanced multi-permutation codes that are capable of correcting a single BUD of length $t$ . Moreover, the constructed codes can achieve higher rates compared with the existing code. The decoding methods are provided in the proofs and verified by some examples.