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As technology continues to scale down, NAND Flash memory has been increasingly relying on error-correction codes (ECCs) to ensure the overall data storage integrity. Although advanced ECCs such as low-density parity-check (LDPC) codes can provide significantly stronger error-correction capability over BCH codes being used in current practice, their decoding requires soft-decision log-likelihood ratio (LLR) information. This results in two critical issues. First, accurate calculation of LLR demands fine-grained memory-cell sensing, which nevertheless tends to incur implementation overhead and access latency penalty. Hence, it is critical to minimize the fine-grained memory sensing precision. Second, accurate calculation of LLR also demands the availability of a memory-cell threshold-voltage distribution model. As the major source for memory-cell threshold-voltage distribution distortion, cell-to-cell interference must be carefully incorporated into the model. However, these two critical issues have not been ever addressed in the open literature. This paper attempts to address these open issues. We derive mathematical formulations to approximately model the threshold-voltage distribution of memory cells in the presence of cell-to-cell interference, based on which the calculation of LLRs is mathematically formulated. This paper also proposes a nonuniform memory sensing strategy to reduce the memory sensing precision and, thus, sensing latency while still maintaining good error-correction performance. In addition, we investigate these design issues under the scenario when we can also sense interfering cells and hence explicitly estimate cell-to-cell interference strength. We carry out extensive computer simulations to demonstrate the effectiveness and involved tradeoffs, assuming the use of LDPC codes in 2-bits/cell NAND Flash memory.