The multi-level-cell (MLC) NAND flash channel exhibits non-stationary behavior over increasing program and erase (PE) cycles and data retention time. In this paper, an optimization scheme for adjusting the read (quantized) and write (verify) voltage levels to adapt to the non-stationary flash channel is presented. Using a model-based approach to represent the flash channel, incorporating the programming noise, random telegraph noise (RTN), data retention noise and cell-to-cell interference as major signal degradation components, the writevoltage levels are optimized by minimizing the channel error probability. Moreover, for selecting the quantization levels for the read-voltage to facilitate soft LDPC decoding, an entropybased function is introduced by which the voltage erasure regions (error dominating regions) are controlled to produce the lowest bit/frame error probability. The proposed write and read voltage optimization schemes not only minimize the error probability throughout the operational lifetime of flash memory, but also improve the decoding convergence speed. Finally, to minimize the number of read-voltage quantization levels while ensuring LDPC decoder convergence, the extrinsic information transfer (EXIT) analysis is performed over the MLC flash channel.

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In this letter, a novel scheduling scheme for decoding irregular low-density parity-check (LDPC) code, based on the column weight of variable nodes in the code graph, is introduced. In this scheme, the irregular LDPC code is decoded using the shuffled belief-propagation (BP) algorithm by selecting the variable nodes in descending order of their column weight. Via numerical simulation, it is shown that the proposed high-to-low column-weight based decoding schedule can noticeably increase the convergence speed at medium to high signal-to-noise ratio (SNR) over AWGN and Rayleigh fading channels without introducing additional complexity or error rate degradation. Furthermore, it is found that the improvement in decoding convergence is proportional to the maximum column-weight in the code graph.

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