## 6 Conclusions  
This paper proposed a fast, read-performance-improving, and low-cost RBER estimation method suitable for HSD NAND flash, including interleaving, RBER estimating and enhancement strategies for decoding. Interleaving alleviates the effect of unbalanced error distribution on pages caused by data modulation and thus improves accuracy for RBER estimation. RBER estimation is achieved with true-value data comparison, which can make estimation fast. The estimated BER is close to the actual one and they are highly linearly correlated, so the estimated BER can be sensitive to RBER change and reflect it in time. However, the redundancy brought by the true-value data reduces reading efficiency of the flash, so to solve the problem, two enhancement strategies are proposed to improve error performance of ECC in both hard-decision and soft-decision decoding. For hard-decision decoding, the improvement can raise the \(BER_{th}\) in decoding status selection so that some frames with relatively higher FER, which should have been decoded with soft-decision, can be decoded by the hard-decision decoding. Considering that hard-decision decoding has much lower computational complexity than soft-decision decoding, the enhancement will improve read performance at low RBER. For soft-decision decoding, the enhancement strategy speeds up the decoding convergence so that errors can be corrected with fewer iterations. Moreover, with the enhancement strategy, the frames with high FER close to the upper bound of ECC can be corrected within the maximum iteration times without falling in re-read status, which will take much longer than soft-decision decoding. Hence, the read performance at high RBER is also increased. The hardware complexity of the proposed RBER estimation method is very low. Therefore, the method has a high potential for long-term and frequent monitoring on RBER in HSD NAND flash.  
Incidentally, more applications of the proposed method can be developed. The future work will focus on designing a reading mechanism with a neural network aided by the RBER estimation to soft sense the \(V_{th}\) shift for the SPA decoder to achieve better error correction performance.  
Conceptualization, K.M.; formal analysis, K.M.; funding acquisition, M.L. and H.C.; investigation, K.M. and Y.Y.; methodology, K.M.; project administration, M.L.; resources, K.M. and Y.Y.; software, K.M. and T.L.; supervision, M.L.; writing--original draft, K.M.; writing--review and editing, K.M. and M.L. All authors have read and agreed to the published version of the manuscript. This work has been supported by the National Key Technologies R&D Program (Grant No. 2017 YFB0405604); Key Research Program of Frontier Science, Chinese Academy of Sciences (Grant No. QYZDJ-SSW-JSC004); The Basic Research Project of Shanghai Science and Technology Commission (Grant No. 16 JC1400101); Beijing S&T Planning Task (Grant No. Z161100002616019).  
The authors declare no conflict interest.  
Figure 14: Datapath of the RBER estimation method embedded into the error control framework of the high storage density (HSD) NAND flash, where the grey modules are related to the proposed RBER estimation method and the white modules are related to the low-density parity-check (LDPC) error control process.