SlowGuess/NeurIPS_2023_OCR huggingface dataset:
for  $\Delta$  in  $\{15, 30, 45, 60, 75, 90\}$ . The evaluation itself uses two criteria:
1. BER: We compare the real and generated BER of each WL in the block.
2. Histograms: We compare between the histograms generated by our model and those measured on a real chip (i.e. when programming an actual batch of cells to the same target).
The quality of both train and perturbed predicted  $v_{th}$  histograms can be seen in Fig. 7. Specifically, we measure a Wasserstein distance of  $6 \pm 2 \mathrm{mV}$  between the real and generated histograms. For comparison, the average Wasserstein distance between two real blocks in the same chip is  $6 \mathrm{mV}$  as well. A detailed description of the distance calculation is given in the supplementary materials. In Fig. 6 we compare the real and predicted BER of a QLC block for different target voltages, i.e., values of  $\Delta$ . Again, we see that the BER prediction is very good and has an error margin of up to  $5\%$ . This reassures us we can indeed use the trained model to generate targets from the entire  $v_{th}$  range (including targets it did not train over).
4.2 Neural-modulation experiments
We train the neural-modulation system as described in Section 3.4. Table 1 summarizes the performance of the model in terms of average block BER at the EOL work-point. We note that not only did the model significantly improve the BER compared to the baseline targets, but it also accurately predicted the BER results via the channel model GAN (see the 'GAN prediction' column of Table 1). Specifically, we pass the modulator targets through the GAN, and use the generated  $v_{th}$  distribution to calculate the predicted BER.
Fig. 8 illustrates the pulse amplitude modulation (PAM) constellation the modulator learned for a single QLC WL, compared to the original 16 PAM constellation. The modulator found lower targets for cells with higher symbol neighbors. Such scheme is consistent with the observation discussed in Section 2.1.4, that the charge lose depends on symbols of the cell and its neighbors.
Next, we analyze the model effect as function of the data retention time. We measure the average BER as a result of programming with the default and modulated targets, at different time points during the data retention process. Fig. 9 (a) presents the BER reduction of the modulated targets compared to the default targets. We found that the pre-distortion of the targets helps keeping the BER low over
Figure 8: The original and learned PAM constellations. The first row presents the original targets of the WL which we used for the channel model training. The second row shows the learned by the neural modulator; a zoom in of symbols 12 and 13 is displayed in the bottom row. In agreement with the observation from Section 2.1.4, the modulator found lower targets for cells with higher symbol neighbors, as we saw that such cells tend to lose less charge over time.
Table 1: The BER reduction achieved by the neural modulator. We extract the redaction by calculating the BER after programming the cells once with the targets found by the neural modulator and once with the default targets.
Average	Worst case WL
BPC	GAN prediction	Empirical result	GAN prediction	Empirical result
QLC	16%	17%	8%	9%
TLC	54%	56%	35%	36%
longer retention periods. Interestingly, the pre-distortion slightly deteriorate the BER at short times. Since the BER at these time is overall small, there is no real price for using our modulator.
The ultimate purpose of our modulator is to extend the EOL work-point of the NAND block. We would, therefore, like to estimate the change in the number of PE cycles before the memory device reaches its EOL. The EOL point is determined by a threshold BER value above which the data cannot be reconstructed. This information can be extracted from Fig. 9 (b), where we show the BER after a constant retention time as a function of PE cycles. We found that the modulator extends the number of PE cycles by  $25\%$  (notice that the BER is normalized to its EOL value)
5 Conclusions and limitations
In this work, we demonstrated the potential of pre-distorted programming of the flash memory device to mitigate errors caused by ICI. We applied state-of-the-art optimization methods for the programming  $v_{th}$  targets by performing end-to-end training of the channel's modulator and demodulator through a pre-trained channel model. To the best of our knowledge, our work is the first to introduce an unsupervised learning based modulation for the flash memory. The importance of our modulator is in reducing the BER for the stored information by  $56\%$  compared to conventional writing schemes, and extending the NAND EOL work point by  $25\%$  in terms of PE cycles. Currently, our modulator was optimized for a single work-point with a constant read disturb and PE cycles. Future work may generalize the channel model and modulator to overcome this limitation using a dedicated input features. Another drawback is that implementing the modulator in a flash controller requires allocating extra write buffers for the neighbors data. $^3$
Figure 9: Comparison between the default and modulated targets BERs. Panel (a) shows the model's BER reduction at different time points during the data retention process, measured on QLC flash. The modulated targets BER is higher right after programming the block, and lower along the rest of the retention process due to the effect of the ICI on the programmed cells. Panel (b) presents the block's BER at different PE cycle workpoints and effective data retention time of one month at room temperature. Programming the block with the modulator generated targets extends the EOL point of the block by  $25\%$  in terms of PE cycles, while maintaining the same BER. The shaded area marks the standard deviation of the tested WLs.
Modern programming schemes already compromise about the buffer size for increased programming accuracy [22].
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