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

TL;DR

This paper introduces a novel error correction scheme for multi-level flash memory using the E8 lattice combined with Reed-Solomon codes, achieving significant performance improvements over traditional BCH codes.

Contribution

It presents a new coded modulation approach utilizing the E8 lattice and Reed-Solomon codes for enhanced error correction in flash memory systems.

Findings

Achieves 1.6 to 1.8 dB performance gain at a word error rate of 10^-6

Operates effectively at high data rates of 2.9 bits per cell

Outperforms conventional BCH code techniques in error correction

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.