Coded Modulation Using Lattices and Reed-Solomon Codes, with Applications to Flash Memories

This paper describes a coded modulation scheme where low-dimension lattices are used as the constellation, and Reed-Solomon codes are used for error correction. Low-dimension lattices, such as the eight-dimensional E₈ lattice, have better distance properties than one- and two-dimensional constellations, and they have efficient soft-input decoding algorithms as well. On the other hand, Reed-Solomon codes have optimal distance properties, and their decoding algorithms are well understood. This construction is targeted at high-rate flash memories, where BCH codes using Gray-coded pulse-amplitude modulation are often used. Performance gains of 1.0 dB to 1.8 dB over BCH codes is demonstrated through analysis and simulation, under the assumption of additive white Gaussian noise. For flash memory systems where the ECC chip is separate from the flash chip, this code construction allows using soft information entirely inside a flash memory chip which has a low-complexity lattice decoder implementation.