  High-capacity NAND flash memories use multi-level cells (MLCs) to store
multiple bits per cell and achieve high storage densities. Higher densities
cause increased raw bit error rates (BERs), which demand powerful error
correcting codes. Low-density parity-check (LDPC) codes are a well-known class
of capacity-approaching codes in AWGN channels. However, LDPC codes
traditionally use soft information while the flash read channel provides only
hard information. Low resolution soft information may be obtained by performing
multiple reads per cell with distinct word-line voltages.
  We select the values of these word-line voltages to maximize the mutual
information between the input and output of the equivalent multiple-read
channel under any specified noise model. Our results show that maximum
mutual-information (MMI) quantization provides better soft information for LDPC
decoding given the quantization level than the constant-pdf-ratio quantization
approach. We also show that adjusting the LDPC code degree distribution for the
quantized setting provides a significant performance improvement.
