This paper investigates the application of low-density parity-check (LDPC) codes to Flash memories. Multiple cell reads with distinct word-line voltages provide limited-precision soft information for the LDPC decoder. The values of the word-line volt
ages (also called reference voltages) are optimized by maximizing the mutual information (MI) between the input and output of the multiple-read channel. Constraining the maximum mutual-information (MMI) quantization to enforce a constant-ratio constraint provides a significant simplification with no noticeable loss in performance. Our simulation results suggest that for a well-designed LDPC code, the quantization that maximizes the mutual information will also minimize the frame error rate. However, care must be taken to design the code to perform well in the quantized channel. An LDPC code designed for a full-precision Gaussian channel may perform poorly in the quantized setting. Our LDPC code designs provide an example where quantization increases the importance of absorbing sets thus changing how the LDPC code should be optimized. Simulation results show that small increases in precision enable the LDPC code to significantly outperform a BCH code with comparable rate and block length (but without the benefit of the soft information) over a range of frame error rates.
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.
