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An LDPC code is proposed for flash memories based on rank modulation. In contrast to previous approaches, this enables the use of long ECCs with fixed-length modulation codes. For ECC design, the rank modulation scheme is treated as part of an equivalent channel. A probabilistic model of the equivalent channel is derived and a simple high-SNR approximation is given. LDPC codes over integer rings and finite fields are designed for the approximate channel and a low-complexity Symbol-Flipping Verification-Based (SFVB) message-passing decoding algorithm is proposed to take advantage of the channel structure. Density Evolution (DE) is used to calculate decoding thresholds and simulations are used to compare the low-complexity decoder with sum-product decoding.
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