Multi-Permutation Codes Correcting a Single Burst Unstable Erasure

Abstract

Error-correcting codes on permutations and multi-permutations have recently attracted much attention for their applications in flash memories through rank modulation. We propose a new rank demodulation method to transform the problem of a single burst unstable erasure (BUE) in a $t$ -balanced multi-permutation into the sub-problems of a single permutation-invariant erasure (PIE) in $t$ permutations. Based on the rank demodulation method, we propose two classes of $t$ -balanced multi-permutation codes to correct a single BUE of length up to $t$ by interleaving $t$ single-PIE-correcting permutation codes. The decoding methods for the proposed codes are included in the proofs and demonstrated by examples.