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

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 trellis-coded modulation, where the Euclidean distance of the lattice (which is an eight-dimensional 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. This construction has a performance advantage of 1.7 to 2.0 dB for an uncoded data density of 3 bits/cell.