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Bit-error correction is crucial for realizing cost-effective and reliable NAND Flash-memory-based storage systems. In this paper, low-power and high-throughput error-correction circuits have been developed for multilevel cell (MLC) nand Flash memories. The developed circuits employ the Bose-Chaudhuri-Hocquenghem code to correct multiple random bit errors. The error-correcting codes for them are designed based on the bit-error characteristics of MLC NAND Flash memories for solid-state drives. To trade the code rate, circuit complexity, and power consumption, three error-correcting architectures, named as whole-page, sector-pipelined, and multistrip ones, are proposed. The VLSI design applies both algorithmic and architectural-level optimizations that include parallel algorithm transformation, resource sharing, and time multiplexing. The chip area, power consumption, and throughput results for these three architectures are presented.