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As the process technology scales down and the number of bits per cell increases, NAND Flash memory is more prone to bit errors. In this paper, we employ a rate-0.96 (68254, 65536) Euclidean geometry (EG) low-density parity-check (LDPC) code for NAND Flash memory error correction, and evaluate the performance under binary input (BI) additive white Gaussian noise (AWGN) and NAND Flash memory channels. The performance effect of output signal quantization is also studied. We show the strategies for determining the optimum quantization boundaries and computing the quantized log-likelihood ratio (LLR) for the NAND Flash channel model that is approximated as a mixture of Gaussian distributions. Simulation results show that the error performance with the NAND Flash memory channel is much different from that with the BI-AWGN channel. Since the distribution of NAND Flash memory output signal is not stationary, it is important to accurately assess the stochastic distribution of the signal for optimum sensing.