Learning to Maximize Mutual Information for Read Threshold Design in Flash Memories

NAND flash memory suffers from a variety of noises that are difficult to model accurately, hence machine learningbased channel quantization approaches have been studied. However, to enable soft-decision decoding of error correction codes, the existing methods either rely on approximated log-likelihood ratio (LLR) or can only generate a limited number of read thresholds. In this letter, we propose a systematic design for deep neural network (DNN)-aided quantization to approach the optimal performance without any knowledge of the channel. To achieve this, incorporating with a bidirectional gated recurrent unit (BiGRU)-based DNN architecture (two BiGRU layers, one layer normalization, one dropout layer and one fully-connected output layer), the loss function is designed to force the DNN outputs to accurately approximate the channel LLR by maximizing the observed mutual information between the DNN outputs and their labels. Then, a dynamic programming algorithm is proposed to design an arbitrary number of read thresholds by maximizing the mutual information (MMI) between the quantized DNN outputs and their labels, which reduces the computational complexity from exponential (exhaustive search) to quadratic. Simulation results show that the bit error rate (BER) performance of our proposed method is close to that of the MMI quantizer with full channel knowledge, and it outperforms the MMI quantizer in the presence of channel mismatch.