The E8 Lattice and Error Correction in Multi-Level Flash Memory

Abstract

A construction using the E8 lattice and Reed-Solomon codes for error-correction in flash memory is given. Since E8 lattice decoding errors are bursty, a Reed-Solomon code over GF($2^8$) is well suited. This is a type of coded modulation, where the Euclidean distance of the lattice, which is an eight-dimensional signal constellation, is combined with the Hamming distance of the code. This system is compared with the conventional technique for flash memories, BCH codes using Gray-coded PAM. The described construction has a performance advantage of 1.6 to 1.8 dB at a probability of word error of $10^{-6}$. Evaluation is at high data rates of 2.9 bits/cell for flash memory cells that have an uncoded data density of 3 bits/cell.