Multiple reads of the same Flash memory cell with distinct word-line voltages provide enhanced precision for LDPC decoding. In this paper, the word-line voltages are optimized by maximizing the mutual information (MI) of the quantized channel. The enhanced precision from a few additional reads allows frame error rate (FER) performance to approach that of full-precision soft information and enables an LDPC code to significantly outperform a BCH code. A constant-ratio constraint provides a significant simplification in the optimization with no noticeable loss in performance. For a well-designed LDPC code, the quantization that maximizes the mutual information also minimizes the FER in our simulations. However, for an example LDPC code with a high error floor caused by small absorbing sets, the MMI quantization does not provide the lowest frame error rate. The best quantization in this case introduces more erasures than would be optimal for the channel MI in order to mitigate the absorbing sets of the poorly designed code. The paper also identifies a trade-off in LDPC code design when decoding is performed with multiple precision levels; the best code at one level of precision will typically not be the best code at a different level of precision.

High-capacity NAND flash memory can achieve high density storage by using multi-level cells (MLC) to store more than one bit per cell. Although this larger storage capacity is certainly beneficial, the increased density also increases the raw bit error rate (BER), making powerful error correction coding necessary. Traditional flash memories employ simple algebraic codes, such as BCH codes, that can correct a fixed, specified number of errors. This paper investigates the application of low-density parity-check (LDPC) codes which are well known for their ability to approach capacity in the AWGN channel. We obtain soft information for the LDPC decoder by performing multiple cell reads with distinct word-line voltages. The values of the word-line voltages (also called reference voltages) are optimized by maximizing the mutual information between the input and output of the multiple-read channel. Our results show that using this soft information in the LDPC decoder provides a significant benefit and enables us to outperform BCH codes over a range of block error rates.