QC-LDPC Codes with Fast Encoding for Error Control in NAND Flash Memories

In this paper we show the construction procedure for QC-LDPC codes with low encoding complexity and structure optimized for hard decision decoding and low precision soft decoding, which both are involved in a modern error correction control for NAND flash memories. The procedure is based on a computer search for codes with linear encodability, while error correction performance is optimized by reducing the number of weight-2 columns in the parity check matrix and optimizing structure of the code graph, particularly eliminating short cycles. We also show a simple method for code rate adjustment by extending the parity check matrix altogether with codeword shortening to enable more robust error correction when raw error rate of memory cells increases with the memory lifetime. The approach is validated via error rate Monte Carlo simulations with hard decisions and low precision soft decisions LDPC decoding, with a flash memory cell error model.