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 en
hanced precision from a few additional reads allows 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 frame error rate 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.
Certain binary asymmetric channels, such as Z-channels in which one of the two crossover probabilities is zero, demand optimal ones densities different from 50%. Some broadcast channels, such as broadcast binary symmetric channels (BBSC) where each c
omponent channel is a binary symmetric channel, also require a non-uniform input distribution due to the superposition coding scheme, which is known to achieve the boundary of capacity region. This paper presents a systematic technique for designing nonlinear turbo codes that are able to support ones densities different from 50%. To demonstrate the effectiveness of our design technique, we design and simulate nonlinear turbo codes for the Z-channel and the BBSC. The best nonlinear turbo code is less than 0.02 bits from capacity.
