LDPC codes for rank modulation in flash memories

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.