Concatenated Reed–Solomon/lattice coding for multilevel flash memory

The article considers concatenated coding scheme for multilevel flash memory. In this scheme the inner stage is a finite subset of a multidimensional lattice (lattice code) and the outer stage uses Reed–Solomon code.
Performance analysis is done for a model characterizing the basic physical features of a flash memory cell with non-uniform target voltage levels and noise variance dependent on the recorded value (input-dependent additive Gaussian noise, ID-AGN). For this model we develop a new approach to evaluating the error probability for the inner code. This approach is based on one-dimensional numerical integration of product of the characteristic functions of random variables used in the decoding process. It is shown how the parameters of the concatenated coding scheme can be adapted to keep the required error probability when the retention period and/or number of program-erasure cycles increase.