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Investigation of the Characteristics of the Internal Stage of the Concatenated Coding Scheme for Multilevel Flash Memory

The article considers a concatenated coding scheme for multi-level flash memory, with codes based on relatively simple lattices used in inner stage, and the Reed-Solomon code used in outer stage. The analysis is performed for a model of a flash memory cell with non-uniformly spaced target voltage levels in the cell and noise variance depending on the recorded value (input-dependent additive Gaussian noise, ID-AGN). The problem of constructing a discrete mapping of the recording channel is considered. The specified mapping is performed as a multilevel quantization of the signal at the output of the recording cell. The goal of a such quantization is to simplify the scheme implementing the maximum likelihood decoding in inner stage. The error decoding probability of the internal code is calculated by numerical integration of an expression containing the characteristic functions of the logarithms of the likelihood ratio and taking into account the lattice structure of the internal code. The influence of the number of quantization levels on the probability of an internal code decoding error is analyzed. Numerical results are they shows that the performance degradation caused by quantization is small compared to a decoding scheme using a non-quantized channel output.