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Multiple reads of the same Flash memory cell with distinct word-line voltagesprovide enhanced precision for LDPC decoding. In this paper, the word-linevoltages are optimized by maximizing the mutual information (MI) of thequantized channel. The enhanced precision from a few additional reads allowsFER performance to approach that of full-precision soft information and enablesan LDPC code to significantly outperform a BCH code. A constant-ratioconstraint provides a significant simplification in the optimization with nonoticeable loss in performance. For a well-designed LDPC code, the quantizationthat maximizes the mutual information also minimizes the frame error rate inour simulations. However, for an example LDPC code with a high error floorcaused by small absorbing sets, the MMI quantization does not provide thelowest frame error rate. The best quantization in this case introduces moreerasures than would be optimal for the channel MI in order to mitigate theabsorbing sets of the poorly designed code. The paper also identifies atrade-off in LDPC code design when decoding is performed with multipleprecision levels; the best code at one level of precision will typically not bethe best code at a different level of precision.

Enhanced Precision Through Multiple Reads for LDPC Decoding in Flash Memories